Prosecution Insights
Last updated: May 29, 2026
Application No. 18/242,193

TRAJECTORY TRACKING USING PATH SIGNATURES

Non-Final OA §101§103
Filed
Sep 05, 2023
Examiner
EVANS, KARSTON G
Art Unit
3657
Tech Center
3600 — Transportation & Electronic Commerce
Assignee
Nvidia Corporation
OA Round
3 (Non-Final)
71%
Grant Probability
Favorable
3-4
OA Rounds
0m
Est. Remaining
88%
With Interview

Examiner Intelligence

Grants 71% — above average
71%
Career Allowance Rate
106 granted / 150 resolved
+18.7% vs TC avg
Strong +17% interview lift
Without
With
+17.2%
Interview Lift
resolved cases with interview
Typical timeline
2y 8m
Avg Prosecution
18 currently pending
Career history
176
Total Applications
across all art units

Statute-Specific Performance

§101
0.5%
-39.5% vs TC avg
§103
69.7%
+29.7% vs TC avg
§102
21.5%
-18.5% vs TC avg
§112
1.3%
-38.7% vs TC avg
Black line = Tech Center average estimate • Based on career data from 150 resolved cases

Office Action

§101 §103
DETAILED ACTION Notice of Pre-AIA or AIA Status The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA . Response to Arguments The amendment filed 2/5/2026 has been entered. Claims 1-10, 12, 14-19, and 21 are amended. Claims 22-25 are newly added. Claims 1-19 and 21-25 are pending in the application. Applicant's arguments, see pages 9-11, with respect to the 101 rejections have been fully considered but they are not persuasive. The applicant argues that the claims (A) are not directed to a mental process, (B) integrate any alleged abstract idea into a practical application, and (C) recite additional elements amounting to significantly more. Applicant argues (A) that the claims are not directed to a mental process because the claims are directed to a computer-implemented method and recites operations involving accessing information from memory and updating stored information between successive observations with a plurality of coefficients of a subpath signature. However, the argument is unpersuasive because a human can practically perform accessing a stored path signature in memory associated with a past path traveled by an object, where the path signature "comprises a plurality of coefficients determined based at least in part on an aggregation of data over a plurality of subpaths." For example, a human can mentally “access from memory a stored past path signature” by recalling from a mentally remembered past path signature. Alternatively, accessing the memory is an additional element of mere data gathering and is insignificant extra-solution activity (MPEP 2106.05(g)). Further updating the stored past path signature can be performed mentally by adjusting the remembered past path signature. The other claim limitations of claim 1 can also be practically performed in the human mind with the help of pen and paper. None of the claim limitations are impossible to be performed mentally. The examiner suggests adding a claim limitation to actually control the object based on the updated path signature and the reference path because a human can’t mentally control an object. Another suggestion is to add a claim limitation such that the claimed process is performed in real-time such that it would require processing at a rate that a human does not have the mental capacity to perform. Applicant argues (B) that the claims integrate any alleged abstract idea into a practical application because the combination of maintaining an updated stored representation of a past path and using that updated representation together with a reference path to identify actions is tied to the technical context of path tracking described in the specification. However, the argument is unpersuasive because the claim does not actually describe a practical application that improves path tracking. Even though actions are identified as a result of the process, there is no practical application since the actions aren’t actually performed by the claimed process. Additionally, the process described in the claim does not necessarily track a path. Applicant argues (C) that the claims recite additional elements amounting to significantly more because how the information is accessed and updated are not recited as mere data gathering or post-solution activity. However, the argument is unpersuasive “accessing from memory” and “updating the stored past path signature” are part of the mental process. Alternatively, “accessing from memory” is considered an additional element of mere data gathering and is insignificant extra-solution activity (MPEP 2106.05(g)) because it is does not present any unique technique of obtaining the path signature data. Applicant’s arguments, see pages 12-14, with respect to the 103 rejection(s) of claim(s) in view of the amendments have been fully considered and are persuasive. Therefore, the rejection has been withdrawn. However, upon further consideration, a new ground(s) of rejection is made in view of Tong (US 20210208596 A1) and Barcelos (NPL: “Path Signatures for Diversity in Probabilistic Trajectory Optimisation”). Claim Rejections - 35 USC § 101 35 U.S.C. 101 reads as follows: Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title. The claimed invention is not directed to patent eligible subject matter. Claims 1-3, 5, 7-10, 12-17, 19, and 21-24 are rejected under 35 U.S.C. 101 because the claimed invention is directed to the judicial exception, abstract idea, without significantly more. Claims 1-3, 5, 7, and 21-24 are directed to a process, which is one of the statutory categories of invention. (Step 1: YES) Under Step 2A Prong 1, Claim 1 recites a judicial exception: an abstract idea. The limitations of “a fall under the abstract idea of a mental process. A human can practically perform these steps mentally, for example, by remembering path signature data of a past path and observing a current position/movement of the object, adjusting the path signature data between observations, and determining, based on the observations and a reference path, a path for the object and movements for the object to perform the determined path. The claim does not include any control that actually causes the object to move. Under Step 2A Prong 2, the additional element is the “computer” that implements the method. The additional element does not integrate the abstract idea into a practical application because it is merely a tool to apply the abstract idea in a generic or general purpose computer. Similarly, under Step 2B, the claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception because the computer is merely a tool to apply the abstract idea in a generic or general purpose computer. Additionally, accessing the memory can be an additional element of mere data gathering and is insignificant extra-solution activity (MPEP 2106.05(g)). Re Claim 2, the limitation “wherein the updated stored past path signature indicates one or more geometric characteristics of a path comprising one or more of a shift invariance property, a tree-like equivalency property, a universality property, a concatenation property, and time parameterization property invariance property” is also part of the abstract idea of Step 2A Prong 1. The claim limitation describes the path signature, however, a human could still practically perform the steps mentally using the described path signature. Under Step 2A Prong 2 and Step 2, the use of “computer” as an additional element does not add more as already described in the analysis of independent Claim 1. Re Claim 3, the limitation “wherein identifying the one or more actions to be performed is based on a calculated cost defined over an overall path that includes the updated stored past path signature and a path-to-go that represents a candidate future trajectory based, at least in part, on a most recent observed state of the object relative to the reference path, wherein the calculated cost is defined over a signature of the overall path” is also part of the abstract idea of Step 2A Prong 1. The claim limitation describes what is used to identify the action(s), however, a human could still practically perform the steps mentally using a calculated cost of the past path, a path-to-go, and the reference path. Under Step 2A Prong 2 and Step 2, the use of “computer” as an additional element does not add more as already described in the analysis of independent Claim 1. Re Claim 5, the limitation “wherein the updated stored past path signature includes a signature transform of subpath of the past path between successive observations of the object, the subpath being traversed since a last time interval” is also part of the abstract idea of Step 2A Prong 1. The claim limitation describes what is used to determine the updated path signature, however, a human could still practically perform the steps mentally using the described sub-path. Under Step 2A Prong 2 and Step 2, the use of “computer” as an additional element does not add more as already described in the analysis of independent Claim 1. Re Claim 7, the limitation “further comprising generating a path-to-go path signature based on identifying the one or more actions, wherein: the path-to-go path signature is concatenated with the updated stored past path signature to represent an overall path; the overall path includes a portion of the past path traversed by the object and a future path is used to determine the one or more actions; and the path-to-go path signature indicates, at least, a trajectory between a current location of the object and a final location of the reference path” is also part of the abstract idea of Step 2A Prong 1. A human could practically perform generating a path-to-go signature based on identifying the one or more actions, for example, by mentally determining the rest of a path the object should travel based on determining movements. Under Step 2A Prong 2 and Step 2, the use of “computer” as an additional element does not add more as already described in the analysis of independent Claim 1. Re Claim 21, the limitation “further comprising, determining a path-to-go using one or more cost functions defined over the reference path and based at least in part on the updated stored past path signature, wherein the plurality of coefficients of the stored past path signature encode geometric features, and wherein the path-to-go represents a candidate future trajectory to be followed by the object” is also part of the abstract idea of Step 2A Prong 1. A human could practically perform determining a path-to-go signature using a cost function with the help of pen and paper. Under Step 2A Prong 2 and Step 2, the use of “computer” as an additional element does not add more as already described in the analysis of independent Claim 1. Re Claim 22, the limitation “wherein updating the stored past path signature includes concatenating the subpath signature with the stored past path signature using a tensor product operation” is also part of the abstract idea of Step 2A Prong 1. A human could practically perform this mathematic process with the help of pen and paper. Under Step 2A Prong 2 and Step 2, the use of “computer” as an additional element does not add more as already described in the analysis of independent Claim 1. Re Claim 23, the limitation “wherein identifying the one or more actions comprises evaluating a cost function defined over a signature of an overall path that includes the past path and a path-to-go, wherein the overall path corresponds to a concatenation of the past path and the path-to-go” is also part of the abstract idea of Step 2A Prong 1. A human could practically perform identifying an action using a cost function with the help of pen and paper. Under Step 2A Prong 2 and Step 2, the use of “computer” as an additional element does not add more as already described in the analysis of independent Claim 1. Re Claim 24, the limitation “wherein the one or more actions are identified in a receding-horizon manner based on successive updates to the stored past path signature” is also part of the abstract idea of Step 2A Prong 1. A human could practically perform identifying an action using a receding-horizon technique with the help of pen and paper. Under Step 2A Prong 2 and Step 2, the use of “computer” as an additional element does not add more as already described in the analysis of independent Claim 1. Claims 8-10, 12-17, and 19 are directed to a machine, which is one of the statutory categories of invention. (Step 1: YES) Under Step 2A Prong 1, Claim 8 recites a judicial exception: an abstract idea. The limitations of “access from storage a stored past path signature associated with a past path traveled by an object in accordance with a reference path; determine a current state associated with the object; between successive observations, update the stored past path signature with a plurality of coefficients of a subpath signature based, at least in part, on successive observed current states; and identify one or more actions to be performed by the object based on the updated stored past path signature and the reference path” fall under the abstract idea of a mental process. A human can practically perform these steps mentally, for example, by remembering path signature data of a past path and observing a current position/movement of the object, adjusting the path signature data between observations, and determining, based on the observations and a reference path, a path for the object and movements for the object to perform the determined path. The claim does not include any control that actually causes the object to move. Under Step 2A Prong 2, the additional element is “a non-transitory computer readable storage medium storing thereon executable instructions that, as a result of being executed by one or more processors of a computer system, cause the computer system to:” perform the claimed steps. The additional element does not integrate the abstract idea into a practical application because the it is merely a tool to apply the abstract idea in a generic or general purpose computer. Similarly, under Step 2B, the claim does not include additional elements are sufficient to amount to significantly more than the judicial exception because the non-transitory computer readable storage medium is merely a tool to apply the abstract idea in a generic or general purpose computer. Additionally, accessing the memory can be an additional element of mere data gathering and is insignificant extra-solution activity (MPEP 2106.05(g)). Re Claim 9, the limitation “wherein the updated stored past path signature indicates a trajectory previously traveled by the object including one or more geometric characteristics of the past path that comprise one or more of a shift invariance property, a tree-like equivalency property, a universality property, and a concatenation property” is also part of the abstract idea of Step 2A Prong 1. The claim limitation describes the path signature, however, a human could still practically perform the steps mentally using the described path signature. Under Step 2A Prong 2 and Step 2, the use of “the non-transitory computer readable storage medium” as an additional element does not add more as already described in the analysis of independent Claim 8. Re Claim 10, the limitation “wherein the one or more actions to be performed are identified at least in part, by calculating a cost based, at least in part, on the updated stored past path signature and a path-to-go that indicates a candidate trajectory based on the current state of the object relative to the reference path” is also part of the abstract idea of Step 2A Prong 1. The claim limitation describes what is used to identify the action(s), however, a human could still practically perform the steps mentally using a calculated cost of the past path, a path-to-go, and the reference path. Under Step 2A Prong 2 and Step 2, the use of “the non-transitory computer readable storage medium” as an additional element does not add more as already described in the analysis of independent Claim 8. Re Claim 12, the limitation “wherein the updated stored pastpath signature is determined based on a subpath of the past path corresponding to an interval of time between the successive observations, wherein the interval has elapsed since a previous update to the stored past path signature” is also part of the abstract idea of Step 2A Prong 1. The claim limitation describes what is used to determine the updated path signature, however, a human could still practically perform the steps mentally using the described sub-path. Under Step 2A Prong 2 and Step 2, the use of “the non-transitory computer readable storage medium” as an additional element does not add more as already described in the analysis of independent Claim 8. Re Claim 13, the limitation “wherein the object is an autonomous machine, where at least a portion of the autonomous machine is to move in accordance with the reference path” is merely an additional element that indicates an autonomous machine as a field of use or technological environment in which to apply the steps of claim 8. The claim does not positively state that they are actually controlling the machine. Under Step 2A Prong 2 and Step 2, the claim limitation does not add more because limitations that amount to merely indicating a field of use or technological environment in which to apply a judicial exception do not amount to significantly more than the exception itself, and cannot integrate a judicial exception into a practical application (MPEP 2106.05(h)). Also, under Step 2A Prong 2 and Step 2, the use of “the non-transitory computer readable storage medium” as an additional element does not add more as already described in the analysis of independent Claim 8. Re Claim 14, the limitation “wherein the computer system is to further generate a path-to-go path signature based on identifying the one or more actions, wherein: the path-to-go path signature is concatenated with the updated stored past path signature to represent an overall path used to identify the one or more actions; the overall path includes a portion of the past path already traversed by the object and a future path implied by the one or more actions; and the path-to-go path signature represents a trajectory between a current location of the object and a final location of the reference path” is also part of the abstract idea of Step 2A Prong 1. A human could practically perform generating a path-to-go signature based on identifying the one or more actions, for example, by mentally determining the rest of a path the object should travel based on determining movements. Under Step 2A Prong 2 and Step 2B, the use of “the non-transitory computer readable storage medium” as an additional element does not add more as already described in the analysis of independent Claim 8. Under Step 2A Prong 1, Claim 15 recites a judicial exception: an abstract idea. The limitations of “access a stored past path signature associated with a past path traveled by an autonomous vehicle in accordance with a reference path; observe a current state associated with the autonomous vehicle; between successive observations, update the stored past path signature with a plurality of coefficients of a subpath signature based, at least in part, on successive observed current states; and identify one or more actions to be performed by the autonomous vehicle based on the updated stored past path signature and the reference path” fall under the abstract idea of a mental process. A human can practically perform these steps mentally, for example, by remembering path signature data of a past path and observing a current position/movement of the object, adjusting the path signature data between observations, and determining, based on the observations and a reference path, a path for the object and movements for the object to perform the determined path. The claim does not include any control that actually causes the object to move. Under Step 2A Prong 2, the additional element is “a system comprising: one or more processors to:” perform the claimed steps. The additional element does not integrate the abstract idea into a practical application because the it is merely a tool to apply the abstract idea in a generic or general purpose computer. Similarly, under Step 2B, the claim does not include additional elements are sufficient to amount to significantly more than the judicial exception because the system is merely a tool to apply the abstract idea in a generic or general purpose computer. Additionally, accessing the memory can be an additional element of mere data gathering and is insignificant extra-solution activity (MPEP 2106.05(g)). Re Claim 16, the limitation “wherein the updated stored past path signature associated with the past path indicates one or more geometric characteristics of the past path comprising one or more of a shift invariance property, a tree-like equivalency property, a universality property, a concatenation property, and a time parameterization invariance property” is also part of the abstract idea of Step 2A Prong 1. The claim limitation describes the path signature, however, a human could still practically perform the steps mentally using the described path signature. Under Step 2A Prong 2 and Step 2B, the use of “the system” as an additional element does not add more as already described in the analysis of independent Claim 15. Re Claim 17, the limitation “wherein the one or more actions to be performed are identified based on evaluating a cost defined over an overall path that includes the updated stored past path signature and a path-to-go relative to the reference path, and wherein evaluating the cost is used to select the one or more actions to guide the autonomous vehicle along the reference path” is also part of the abstract idea of Step 2A Prong 1. The claim limitation describes what is used to identify the action(s), however, a human could still practically perform the steps mentally using a calculated cost of the past path, a path-to-go, and the reference path. Under Step 2A Prong 2 and Step 2B, the use of “the system” as an additional element does not add more as already described in the analysis of independent Claim 15. Re Claim 19, the limitation “wherein the updated stored past path signature is determined based on a subpath of the past path corresponding to an interval of time between successive observed current states of the autonomous vehicle” is also part of the abstract idea of Step 2A Prong 1. The claim limitation describes what is used to determine the updated path signature, however, a human could still practically perform the steps mentally using the described sub-path. Under Step 2A Prong 2 and Step 2B, the use of “the system” as an additional element does not add more as already described in the analysis of independent Claim 15. Claim Rejections - 35 USC § 103 In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status. The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action: A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made. The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows: 1. Determining the scope and contents of the prior art. 2. Ascertaining the differences between the prior art and the claims at issue. 3. Resolving the level of ordinary skill in the pertinent art. 4. Considering objective evidence present in the application indicating obviousness or nonobviousness. Claim(s) 1-2, 4-6, 8, 11-13, 15-16, 18-19, and 25 is/are rejected under 35 U.S.C. 103 as being unpatentable over Tong (US 20210208596 A1) in view of Barcelos (NPL: “Path Signatures for Diversity in Probabilistic Trajectory Optimisation”). Regarding Claim 1, Tong teaches A computer-implemented method comprising: (“a method for controlling an autonomous vehicle device to repeatedly follow a same predetermined trajectory” See at least [0007]; “the present embodiments relate to a computer program product including a program code for executing the above-described method for controlling an autonomous vehicle device when run on at least one computer.” See at least [0072]) accessing from memory a stored past path signature associated with a past path traveled by an object in accordance with a reference path; (“In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration.” See at least [0022]; “act e) includes recording the actual trajectory signal in a memory device while the autonomous vehicle device is being steered, and at least act f) is carried out after the autonomous vehicle device has been steered in act c). In other words, the iterative learning control device may be used off-line (e.g., after steering the autonomous vehicle device along the predetermined trajectory has been completed), so as to prepare for a subsequent iteration of steering the autonomous vehicle device along the predetermined trajectory.” See at least [0028]) observing a current state associated with the object; (“The measuring of act d) may refer to using a location device such as a GPS receiver, using radio communication with sign posts distributed along the predetermined trajectory or the like, to acquire two-dimensional and or three-dimensional coordinate values.” See at least [0020]; “While the car is steered along the predetermined trajectory, for each discretized time k, the measuring device 32 measures current coordinates of the actual trajectory followed by the car in response to being steered according to the control signal u in act S32. The current coordinates are provided to the memory device 33 to be stored therein. Thereby, an actual trajectory signal y may be recorded in the memory device 33 (act S33, FIG. 1).” See at least [0108]) between successive observations, updating the stored past path signature (“the measuring in act d) and the recording in act e) may also be performed repeatedly for at least some of the plurality of time instances. In other words, acts d) and e) may be performed in parallel to and/or synchronous with act c).” See at least [0019]; “act e) includes recording the actual trajectory signal in a memory device while the autonomous vehicle device is being steered … For example, the actual trajectory signal may be recorded by storing, for each of the at least some of the plurality of time instances for which the actual trajectory is measured, a position value (e.g., coordinate values) in the memory device.” See at least [0028-0030]) and identifying one or more actions to be performed by the object based on the updated stored past path signature and the reference path. (“In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration. More particularly, “based on the control signal and the target trajectory signal” may provide “based on an actual tracking error signal indicative of a tracking error between the actual trajectory signal and the target trajectory signal”. The actual tracking error signal may be obtained by subtracting the actual trajectory signal from the target trajectory signal. “Tracking error” may refer to a deviation, such as an averaged or root mean square distance, between the respective signals.” See at least [0022-0023]) Tong does not explicitly teach, but Barcelos teaches with a plurality of coefficients of a subpath signature (“The path signature transforms such multivariate sequential data (which may have missing or irregularly sampled values) into an infinite-length series of real numbers that uniquely represents a trajectory through Euclidean space. Although formally distinct and with notably different properties, one useful intuition is to think of the signature of a path as akin to a Fourier transform, where paths are summarised by an infinite series of feature space coefficients.” … PNG media_image1.png 152 322 media_image1.png Greyscale See at least pgs. 3-4, B. Path Signature) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of Tong to further include the teachings of Barcelos with a reasonable expectation of success to represent the path as path signatures defined by coefficients because the path signature uniquely represents a trajectory through Euclidean space even for paths with missing or irregularly sampled values as well as provides other beneficial properties (“The signature of a path has several interesting properties which make it inherently interesting for applications in robotics. … Canonical feature map for paths … Time-reversal … Uniqueness … Invariance under reparametrisation … Dimension is independent of path length” See at least pgs. 4-5, B. Path Signature). Regarding Claim 2, Tong does not explicitly teach, but Barcelos teaches wherein the updated stored past path signature indicates one or more geometric characteristics of a path comprising one or more of (“Invariance under reparametrisation:: An important difficulty when vying for diversity in trajectory optimisation is the potential symmetry present in the data. This is particularly true when dealing with sequential data, such as, for instance, trajectories of an autonomous vehicle. In this case, the problem is compounded as there is an infinite group of symmetries given by the reparametrisation of a path (i.e. continuous surjections in the time domain to itself), each leading to distinct similarity metrics. In contrast, the path signature acts as a filter that is invariant to reparametrisation removing these troublesome symmetries and resulting in the same features as shown in Figure 3.” See at least pgs. 5, Invariance under reparametrisation) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Barcelos with a reasonable expectation of success to represent the path as path signatures defined by coefficients because the path signature uniquely represents a trajectory through Euclidean space even for paths with missing or irregularly sampled values as well as provides other beneficial properties (“The signature of a path has several interesting properties which make it inherently interesting for applications in robotics. … Canonical feature map for paths … Time-reversal … Uniqueness … Invariance under reparametrisation … Dimension is independent of path length” See at least pgs. 4-5, B. Path Signature). Regarding Claim 4, Tong further teaches further comprising performing the one or more actions identified based, at least in part, on the updated stored past path signature to cause the object to move in accordance with the reference path. (“In any further iteration, acts c), d), e), and f) may be performed in response to the altered control signal generated in act f) as the control signal. Feeding the control signal to the autonomous vehicle device in act c) may refer to repeatedly, for each of a plurality of time instances, providing a respective of the values comprised by the control signal to the autonomous vehicle device, such as to a steering device of the autonomous vehicle device. … In act e), recording may refer to forming a signal from a plurality of the values measured in act d) for a plurality of the time instances. In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration.” See at least [0017-0022]) Regarding Claim 5, Tong further teaches wherein the updated stored past path signature includes a signature transform of a subpath of the past path between successive observations of the object, the subpath being traversed since a last time interval. (“act f) may operate using entire signals. In other words, each of the values of the altered control signal for each time instance of the plurality of time instances may be determined depending on a portion corresponding to a range of time instances or to all of the time instances of a time series of each of the control signal, the actual trajectory signal, and the target value signal and/or the actual tracking error signal.” See at least [0027]; “While the car is steered along the predetermined trajectory, for each discretized time k, the measuring device 32 measures current coordinates of the actual trajectory followed by the car in response to being steered according to the control signal u in act S32. The current coordinates are provided to the memory device 33 to be stored therein. Thereby, an actual trajectory signal y may be recorded in the memory device 33 (act S33, FIG. 1).” See at least [0108]) Regarding Claim 6, Tong further teaches wherein the object is a robot, (“The autonomous vehicle” See at least [0010]) where at least a portion of the robot is to move at least in part by causing the one or more actions based on the updated stored past path signature in accordance with the reference path to be performed. (“In any further iteration, acts c), d), e), and f) may be performed in response to the altered control signal generated in act f) as the control signal. Feeding the control signal to the autonomous vehicle device in act c) may refer to repeatedly, for each of a plurality of time instances, providing a respective of the values comprised by the control signal to the autonomous vehicle device, such as to a steering device of the autonomous vehicle device. … In act e), recording may refer to forming a signal from a plurality of the values measured in act d) for a plurality of the time instances. In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration.” See at least [0017-0022]) Regarding Claim 8, Tong teaches A non-transitory computer readable storage medium storing thereon executable instructions that, as a result of being executed by one or more processors of a computer system, cause the computer system to: (“a method for controlling an autonomous vehicle device to repeatedly follow a same predetermined trajectory” See at least [0007]; “the present embodiments relate to a computer program product including a program code for executing the above-described method for controlling an autonomous vehicle device when run on at least one computer. A computer program product, such as a computer program means, may be embodied as a memory card, USB stick, CD-ROM, DVD, or as a file that may be downloaded from a server in a network. For example, such a file may be provided by transferring the file including the computer program product from a wireless communication network.” See at least [0072-0073]) access from storage a stored past path signature associated with a past path traveled by an object in accordance with a reference path; (“In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration.” See at least [0022]; “act e) includes recording the actual trajectory signal in a memory device while the autonomous vehicle device is being steered, and at least act f) is carried out after the autonomous vehicle device has been steered in act c). In other words, the iterative learning control device may be used off-line (e.g., after steering the autonomous vehicle device along the predetermined trajectory has been completed), so as to prepare for a subsequent iteration of steering the autonomous vehicle device along the predetermined trajectory.” See at least [0028]) determine a current state associated with the object; (“The measuring of act d) may refer to using a location device such as a GPS receiver, using radio communication with sign posts distributed along the predetermined trajectory or the like, to acquire two-dimensional and or three-dimensional coordinate values.” See at least [0020]; “While the car is steered along the predetermined trajectory, for each discretized time k, the measuring device 32 measures current coordinates of the actual trajectory followed by the car in response to being steered according to the control signal u in act S32. The current coordinates are provided to the memory device 33 to be stored therein. Thereby, an actual trajectory signal y may be recorded in the memory device 33 (act S33, FIG. 1).” See at least [0108]) between successive observations, update the stored past path signature (“the measuring in act d) and the recording in act e) may also be performed repeatedly for at least some of the plurality of time instances. In other words, acts d) and e) may be performed in parallel to and/or synchronous with act c).” See at least [0019]; “act e) includes recording the actual trajectory signal in a memory device while the autonomous vehicle device is being steered … For example, the actual trajectory signal may be recorded by storing, for each of the at least some of the plurality of time instances for which the actual trajectory is measured, a position value (e.g., coordinate values) in the memory device.” See at least [0028-0030]) and identify one or more actions to be performed by the object based on the updated stored past path signature and the reference path. (“In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration. More particularly, “based on the control signal and the target trajectory signal” may provide “based on an actual tracking error signal indicative of a tracking error between the actual trajectory signal and the target trajectory signal”. The actual tracking error signal may be obtained by subtracting the actual trajectory signal from the target trajectory signal. “Tracking error” may refer to a deviation, such as an averaged or root mean square distance, between the respective signals.” See at least [0022-0023]) Tong does not explicitly teach, but Barcelos teaches with a plurality of coefficients of a subpath signature (“The path signature transforms such multivariate sequential data (which may have missing or irregularly sampled values) into an infinite-length series of real numbers that uniquely represents a trajectory through Euclidean space. Although formally distinct and with notably different properties, one useful intuition is to think of the signature of a path as akin to a Fourier transform, where paths are summarised by an infinite series of feature space coefficients.” … PNG media_image1.png 152 322 media_image1.png Greyscale See at least pgs. 3-4, B. Path Signature) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of Tong to further include the teachings of Barcelos with a reasonable expectation of success to represent the path as path signatures defined by coefficients because the path signature uniquely represents a trajectory through Euclidean space even for paths with missing or irregularly sampled values as well as provides other beneficial properties (“The signature of a path has several interesting properties which make it inherently interesting for applications in robotics. … Canonical feature map for paths … Time-reversal … Uniqueness … Invariance under reparametrisation … Dimension is independent of path length” See at least pgs. 4-5, B. Path Signature). Regarding Claim 11, Tong further teaches wherein the computer system is to cause performance of the one or more actions by the object to move in accordance with the reference path. (“In any further iteration, acts c), d), e), and f) may be performed in response to the altered control signal generated in act f) as the control signal. Feeding the control signal to the autonomous vehicle device in act c) may refer to repeatedly, for each of a plurality of time instances, providing a respective of the values comprised by the control signal to the autonomous vehicle device, such as to a steering device of the autonomous vehicle device. … In act e), recording may refer to forming a signal from a plurality of the values measured in act d) for a plurality of the time instances. In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration.” See at least [0017-0022]) Regarding Claim 12, Tong further teaches wherein the updated stored past path signature is determined based on a subpath of the past path corresponding to an interval of time between the successive observations, wherein the interval has elapsed since a previous update to the stored past path signature. (“act f) may operate using entire signals. In other words, each of the values of the altered control signal for each time instance of the plurality of time instances may be determined depending on a portion corresponding to a range of time instances or to all of the time instances of a time series of each of the control signal, the actual trajectory signal, and the target value signal and/or the actual tracking error signal.” See at least [0027]; “While the car is steered along the predetermined trajectory, for each discretized time k, the measuring device 32 measures current coordinates of the actual trajectory followed by the car in response to being steered according to the control signal u in act S32. The current coordinates are provided to the memory device 33 to be stored therein. Thereby, an actual trajectory signal y may be recorded in the memory device 33 (act S33, FIG. 1).” See at least [0108]) Regarding Claim 13, Tong further teaches wherein the object is an autonomous machine, (“The autonomous vehicle” See at least [0010]) where at least a portion of the autonomous machine is to move in accordance with the reference path. (“In any further iteration, acts c), d), e), and f) may be performed in response to the altered control signal generated in act f) as the control signal. Feeding the control signal to the autonomous vehicle device in act c) may refer to repeatedly, for each of a plurality of time instances, providing a respective of the values comprised by the control signal to the autonomous vehicle device, such as to a steering device of the autonomous vehicle device. … In act e), recording may refer to forming a signal from a plurality of the values measured in act d) for a plurality of the time instances. In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration.” See at least [0017-0022]) Regarding Claim 15, Tong teaches A system comprising: one or more processors to: (“a method for controlling an autonomous vehicle device to repeatedly follow a same predetermined trajectory” See at least [0007]; “the present embodiments relate to a computer program product including a program code for executing the above-described method for controlling an autonomous vehicle device when run on at least one computer.” See at least [0072]) access a stored past path signature associated with a past path traveled by an autonomous vehicle in accordance with a reference path; (“In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration.” See at least [0022]; “act e) includes recording the actual trajectory signal in a memory device while the autonomous vehicle device is being steered, and at least act f) is carried out after the autonomous vehicle device has been steered in act c). In other words, the iterative learning control device may be used off-line (e.g., after steering the autonomous vehicle device along the predetermined trajectory has been completed), so as to prepare for a subsequent iteration of steering the autonomous vehicle device along the predetermined trajectory.” See at least [0028]) observe a current state associated with the autonomous vehicle; (“The measuring of act d) may refer to using a location device such as a GPS receiver, using radio communication with sign posts distributed along the predetermined trajectory or the like, to acquire two-dimensional and or three-dimensional coordinate values.” See at least [0020]; “While the car is steered along the predetermined trajectory, for each discretized time k, the measuring device 32 measures current coordinates of the actual trajectory followed by the car in response to being steered according to the control signal u in act S32. The current coordinates are provided to the memory device 33 to be stored therein. Thereby, an actual trajectory signal y may be recorded in the memory device 33 (act S33, FIG. 1).” See at least [0108]) between successive observations, update the stored past path signature (“the measuring in act d) and the recording in act e) may also be performed repeatedly for at least some of the plurality of time instances. In other words, acts d) and e) may be performed in parallel to and/or synchronous with act c).” See at least [0019]; “act e) includes recording the actual trajectory signal in a memory device while the autonomous vehicle device is being steered … For example, the actual trajectory signal may be recorded by storing, for each of the at least some of the plurality of time instances for which the actual trajectory is measured, a position value (e.g., coordinate values) in the memory device.” See at least [0028-0030]) and identify one or more actions to be performed by the autonomous vehicle based on the updated stored past path signature and the reference path. (“In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration. More particularly, “based on the control signal and the target trajectory signal” may provide “based on an actual tracking error signal indicative of a tracking error between the actual trajectory signal and the target trajectory signal”. The actual tracking error signal may be obtained by subtracting the actual trajectory signal from the target trajectory signal. “Tracking error” may refer to a deviation, such as an averaged or root mean square distance, between the respective signals.” See at least [0022-0023]) Tong does not explicitly teach, but Barcelos teaches with a plurality of coefficients of a subpath signature (“The path signature transforms such multivariate sequential data (which may have missing or irregularly sampled values) into an infinite-length series of real numbers that uniquely represents a trajectory through Euclidean space. Although formally distinct and with notably different properties, one useful intuition is to think of the signature of a path as akin to a Fourier transform, where paths are summarised by an infinite series of feature space coefficients.” … PNG media_image1.png 152 322 media_image1.png Greyscale See at least pgs. 3-4, B. Path Signature) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of Tong to further include the teachings of Barcelos with a reasonable expectation of success to represent the path as path signatures defined by coefficients because the path signature uniquely represents a trajectory through Euclidean space even for paths with missing or irregularly sampled values as well as provides other beneficial properties (“The signature of a path has several interesting properties which make it inherently interesting for applications in robotics. … Canonical feature map for paths … Time-reversal … Uniqueness … Invariance under reparametrisation … Dimension is independent of path length” See at least pgs. 4-5, B. Path Signature). Regarding Claim 16, Tong does not explicitly teach, but Barcelos teaches wherein the updated stored past path signature associated with the past path indicates one or more geometric characteristics of the past path comprising one or more of (“Invariance under reparametrisation:: An important difficulty when vying for diversity in trajectory optimisation is the potential symmetry present in the data. This is particularly true when dealing with sequential data, such as, for instance, trajectories of an autonomous vehicle. In this case, the problem is compounded as there is an infinite group of symmetries given by the reparametrisation of a path (i.e. continuous surjections in the time domain to itself), each leading to distinct similarity metrics. In contrast, the path signature acts as a filter that is invariant to reparametrisation removing these troublesome symmetries and resulting in the same features as shown in Figure 3.” See at least pgs. 5, Invariance under reparametrisation) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Barcelos with a reasonable expectation of success to represent the path as path signatures defined by coefficients because the path signature uniquely represents a trajectory through Euclidean space even for paths with missing or irregularly sampled values as well as provides other beneficial properties (“The signature of a path has several interesting properties which make it inherently interesting for applications in robotics. … Canonical feature map for paths … Time-reversal … Uniqueness … Invariance under reparametrisation … Dimension is independent of path length” See at least pgs. 4-5, B. Path Signature). Regarding Claim 18, Tong further teaches further comprising causing the one or more actions to be performed to move the autonomous vehicle, using one or more controls of the autonomous vehicle, along a trajectory corresponding to the reference path. (“In any further iteration, acts c), d), e), and f) may be performed in response to the altered control signal generated in act f) as the control signal. Feeding the control signal to the autonomous vehicle device in act c) may refer to repeatedly, for each of a plurality of time instances, providing a respective of the values comprised by the control signal to the autonomous vehicle device, such as to a steering device of the autonomous vehicle device. … In act e), recording may refer to forming a signal from a plurality of the values measured in act d) for a plurality of the time instances. In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration.” See at least [0017-0022]) Regarding Claim 19, Tong further teaches wherein the updated stored past path signature is determined based on a subpath of the past path corresponding to an interval of time between successive observed current states of the autonomous vehicle. (“act f) may operate using entire signals. In other words, each of the values of the altered control signal for each time instance of the plurality of time instances may be determined depending on a portion corresponding to a range of time instances or to all of the time instances of a time series of each of the control signal, the actual trajectory signal, and the target value signal and/or the actual tracking error signal.” See at least [0027]; “While the car is steered along the predetermined trajectory, for each discretized time k, the measuring device 32 measures current coordinates of the actual trajectory followed by the car in response to being steered according to the control signal u in act S32. The current coordinates are provided to the memory device 33 to be stored therein. Thereby, an actual trajectory signal y may be recorded in the memory device 33 (act S33, FIG. 1).” See at least [0108]) Regarding Claim 25, Tong further teaches further comprising, causing one or more control signals to be generated to cause the object to perform the one or more actions. (“In any further iteration, acts c), d), e), and f) may be performed in response to the altered control signal generated in act f) as the control signal. Feeding the control signal to the autonomous vehicle device in act c) may refer to repeatedly, for each of a plurality of time instances, providing a respective of the values comprised by the control signal to the autonomous vehicle device, such as to a steering device of the autonomous vehicle device. … In act e), recording may refer to forming a signal from a plurality of the values measured in act d) for a plurality of the time instances. In act f), the iterative learning control device may be a device configured to use Iterative Learning Control (ILC) to provide an altered (e.g., updated, improved, optimized) control signal for a subsequent iteration based on the control signal and the actual trajectory signal (e.g., recorded actual trajectory signal) of a current iteration.” See at least [0017-0022]) Claim(s) 3 and 10 is/are rejected under 35 U.S.C. 103 as being unpatentable over Tong (US 20210208596 A1) in view of Barcelos (NPL: “Path Signatures for Diversity in Probabilistic Trajectory Optimisation”), Schmitt (Translated EP 3530418 A1), and Kogushi (US 20230109876 A1). Regarding Claim 3, Modified Tong does not explicitly teach, but Schmitt teaches wherein identifying the one or more actions to be performed is based on a calculated cost defined over an overall path that includes the updated stored past path signature and a path-to-go that represents a candidate future trajectory (“A sequence of movements composed of several movement sections can have a total cost function, which is a sum of the cost functions of the individual movement sections of the movement sequence. … Determining a first course of motion based on the simulated movement sections; Determining a motion progression part comprising at least two motion sections; Calculating the cost function of the movement progress part; … At each step can be a movement section be appended to the existing movement sequence part and checked whether the cost function of the resulting motion sequence portion exceeds a predetermined value. The predetermined value may be the cost function of a previously determined movement sequence, namely the first movement sequence. If the cost function of the movement sequence part is already greater than the cost function of the first movement sequence, this movement sequence part in particular will not be pursued further. This means, for example, that no further movement sections are attached in order to obtain a complete movement sequence. In particular, it can be ensured that only movement sequence parts which are good in terms of the cost function are pursued further. … the cost function contains an indication of: a quality of the simulated motion section; a length of a path corresponding to the simulated moving section.” See at least page 6, paragraphs 3-6; Examiner Interpretation: The cost of the existing/previously simulated movement sequence is the calculated cost of the past path. The cost that is compared to the cost of the simulated movement sequence is the cost of the reference path. The cost of the movement sequence parts that are pursued further is the cost of a path-to-go. The total cost function is the calculated cost defined over an overall path.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Schmitt with a reasonable expectation of success such that “a solution for the optimized movement with little computational effort can be found.” (See at least page 6, paragraph 5) Schmitt also does not explicitly teach, but Kogushi teaches a path-to-go that represents a candidate future trajectory based, at least in part, on a most recent observed state of the object relative to the reference path (“In Step S101, the motion-route calculation program 5 of the controller 3 determines a motion route for moving the robot 1 from a current teach point (i.e., a current position of the robot 1) to the target teach point, by using the information included in the route information map 6. … if a plurality of routes along which the robot 1 can move from the current teach point to the target teach point exists in the route information map 6, the motion-route calculation program 5 evaluates the plurality of routes (candidates) and determines an optimum route of the plurality of routes, as a motion route.” See at least [0095-0096], wherein the determined optimum route is the path-to-go signature and the current position is a most recent observed state of the object.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong and Schmitt to further include the teachings of Kogushi with a reasonable expectation of success to automatically determine a motion route that optimizes time, distance, energy, or peak current of the robot. (See at least [0097-0099]) Regarding Claim 10, Modified Tong does not explicitly teach, but Schmitt teaches wherein the one or more actions to be performed are identified at least in part, by calculating a cost based, at least in part, on the updated stored past path signature and a path-to-go that indicates a candidate trajectory (“A sequence of movements composed of several movement sections can have a total cost function, which is a sum of the cost functions of the individual movement sections of the movement sequence. … Determining a first course of motion based on the simulated movement sections; Determining a motion progression part comprising at least two motion sections; Calculating the cost function of the movement progress part; … At each step can be a movement section be appended to the existing movement sequence part and checked whether the cost function of the resulting motion sequence portion exceeds a predetermined value. The predetermined value may be the cost function of a previously determined movement sequence, namely the first movement sequence. If the cost function of the movement sequence part is already greater than the cost function of the first movement sequence, this movement sequence part in particular will not be pursued further. This means, for example, that no further movement sections are attached in order to obtain a complete movement sequence. In particular, it can be ensured that only movement sequence parts which are good in terms of the cost function are pursued further. … the cost function contains an indication of: a quality of the simulated motion section; a length of a path corresponding to the simulated moving section.” See at least page 6, paragraphs 3-6; Examiner Interpretation: The cost of the existing/previously simulated movement sequence is the calculated cost of the past path. The cost that is compared to the cost of the simulated movement sequence is the cost of the reference path. The cost of the movement sequence parts that are pursued further is the cost of a path-to-go.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Schmitt with a reasonable expectation of success such that “a solution for the optimized movement with little computational effort can be found.” (See at least page 6, paragraph 5) Schmitt also does not explicitly teach, but Kogushi teaches a candidate trajectory based on the current state of the object relative to the reference path (“In Step S101, the motion-route calculation program 5 of the controller 3 determines a motion route for moving the robot 1 from a current teach point (i.e., a current position of the robot 1) to the target teach point, by using the information included in the route information map 6. … if a plurality of routes along which the robot 1 can move from the current teach point to the target teach point exists in the route information map 6, the motion-route calculation program 5 evaluates the plurality of routes (candidates) and determines an optimum route of the plurality of routes, as a motion route.” See at least [0095-0096], wherein the determined optimum route is the path-to-go signature and the current position is a most recent observed state of the object.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong and Schmitt to further include the teachings of Kogushi with a reasonable expectation of success to automatically determine a motion route that optimizes time, distance, energy, or peak current of the robot. (See at least [0097-0099]) Claim(s) 7, 14, and 21 is/are rejected under 35 U.S.C. 103 as being unpatentable over Tong (US 20210208596 A1) in view of Barcelos (NPL: “Path Signatures for Diversity in Probabilistic Trajectory Optimisation”) and Kogushi (US 20230109876 A1). Regarding Claim 7, Modified Tong does not explicitly teach, but Kogushi teaches further comprising generating a path-to-go path signature based on identifying the one or more actions, wherein: the path-to-go path signature is concatenated with the updated stored past path signature to represent an overall path; the overall path includes a portion of the past path traversed by the object and a future path is used to determine the one or more actions; and the path-to-go path signature representing indicates, at least, a trajectory between a current location of the object and a final location of the reference path. (“In Step S101, the motion-route calculation program 5 of the controller 3 determines a motion route for moving the robot 1 from a current teach point (i.e., a current position of the robot 1) to the target teach point, by using the information included in the route information map 6. … if a plurality of routes along which the robot 1 can move from the current teach point to the target teach point exists in the route information map 6, the motion-route calculation program 5 evaluates the plurality of routes (candidates) and determines an optimum route of the plurality of routes, as a motion route.” See at least [0095-0096], wherein the determined optimum route is the generated path-to-go signature.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Kogushi with a reasonable expectation of success to automatically determine a motion route that optimizes time, distance, energy, or peak current of the robot. (See at least [0097-0099]) Regarding Claim 14, Modified Tong does not explicitly teach, but Kogushi teaches wherein the computer system is to further generate a path-to-go path signature based on identifying the one or more actions, wherein: the path-to-go path signature is concatenated with the updated stored past path signature to represent an overall path used to identify the one or more actions; the overall path includes a portion of the past path already traversed by the object and a future path implied by the one or more actions; and the path-to-go path signature represents a trajectory between a current location of the object and a final location of the reference path. (“In Step S101, the motion-route calculation program 5 of the controller 3 determines a motion route for moving the robot 1 from a current teach point (i.e., a current position of the robot 1) to the target teach point, by using the information included in the route information map 6. … if a plurality of routes along which the robot 1 can move from the current teach point to the target teach point exists in the route information map 6, the motion-route calculation program 5 evaluates the plurality of routes (candidates) and determines an optimum route of the plurality of routes, as a motion route.” See at least [0095-0096], wherein the determined optimum route is the generated path-to-go signature.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Kogushi with a reasonable expectation of success to automatically determine a motion route that optimizes time, distance, energy, or peak current of the robot. (See at least [0097-0099]) Regarding Claim 21, Tong does not explicitly teach, but Barcelos teaches wherein the plurality of coefficients of the stored past path signature encode geometric features (“The path signature transforms such multivariate sequential data (which may have missing or irregularly sampled values) into an infinite-length series of real numbers that uniquely represents a trajectory through Euclidean space. Although formally distinct and with notably different properties, one useful intuition is to think of the signature of a path as akin to a Fourier transform, where paths are summarised by an infinite series of feature space coefficients.” … PNG media_image1.png 152 322 media_image1.png Greyscale See at least pgs. 3-4, B. Path Signature; Examiner Interpretation: The coefficients encode geometric features by defining the path’s shape.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Barcelos with a reasonable expectation of success to represent the path as path signatures defined by coefficients because the path signature uniquely represents a trajectory through Euclidean space even for paths with missing or irregularly sampled values as well as provides other beneficial properties (“The signature of a path has several interesting properties which make it inherently interesting for applications in robotics. … Canonical feature map for paths … Time-reversal … Uniqueness … Invariance under reparametrisation … Dimension is independent of path length” See at least pgs. 4-5, B. Path Signature). Barcelos also does not explicitly teach, but Kogushi teaches further comprising, determining a path-to-go using one or more cost functions defined over the reference path and based at least in part on the updated stored past path signature, …, and wherein the path-to-go represents a candidate future trajectory to be followed by the object. (“In Step S101, the motion-route calculation program 5 of the controller 3 determines a motion route for moving the robot 1 from a current teach point (i.e., a current position of the robot 1) to the target teach point, by using the information included in the route information map 6. … if a plurality of routes along which the robot 1 can move from the current teach point to the target teach point exists in the route information map 6, the motion-route calculation program 5 evaluates the plurality of routes (candidates) and determines an optimum route of the plurality of routes, as a motion route. … If the cost information (i.e., various types of information such as time required for movement, distance of movement, energy required for movement, peak current) of each route is included in the route information map 6, the motion-route calculation program 5 can evaluate each route on various criteria of evaluation, by using the cost information. For example, for performing the evaluation, the motion-route calculation program 5 can select parameters, used for the evaluation, depending on an index of performance on which a user places importance for the motion of the robot performed for work; and calculate the sum of costs after weighting each parameter in accordance with the type of the parameter.” See at least [0095-0098]; Examiner Interpretation: The routes included in the route information map are reference paths and the selected routes define a path-to-go.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong and Barcelos to further include the teachings of Kogushi with a reasonable expectation of success to automatically determine a motion route that optimizes time, distance, energy, or peak current of the robot. (See at least [0097-0099]) Claim(s) 9 is/are rejected under 35 U.S.C. 103 as being unpatentable over Tong (US 20210208596 A1) in view of Barcelos (NPL: “Path Signatures for Diversity in Probabilistic Trajectory Optimisation”) and Schreiber (US 20110313573 A1). Regarding Claim 9, Modified Tong does not explicitly teach, but Schreiber teaches wherein the updated stored past path signature indicates a trajectory previously traveled by the object including one or more geometric characteristics of the past path that comprise one or more of ("comparing an acting force or movement or sequence, a first force that acts on the manipulator, a sequence of a first force and a second force that act in succession on the manipulator, a first movement of the manipulator, or a sequence of a first and a second movement of the manipulator with stored forces, movements or sequences with which a command is respectively associated." See at least [0008]; Examiner Interpretation: A sequence is a concatenation property and it is used here as a path signature because it is used to identify the trajectory with respect to stored trajectories. A sequence of movements indicates geometric characteristics of a trajectory.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Schreiber with a reasonable expectation of success to facilitate identifying/recognizing more complex movements, and to facilitate safe and intuitive robot control (see at least [0027]). Claim(s) 17 and 23 is/are rejected under 35 U.S.C. 103 as being unpatentable over Tong (US 20210208596 A1) in view of Barcelos (NPL: “Path Signatures for Diversity in Probabilistic Trajectory Optimisation”) and Schmitt (Translated EP 3530418 A1). Regarding Claim 17, Modified Tong does not explicitly teach, but Schmitt teaches wherein the one or more actions to be performed are identified based on evaluating a cost defined over an overall path that includes the updated stored past path signature and a path-to-go relative to the reference path, and wherein evaluating the cost is used to select the one or more actions to guide the autonomous vehicle along the reference path. (“A sequence of movements composed of several movement sections can have a total cost function, which is a sum of the cost functions of the individual movement sections of the movement sequence. … Determining a first course of motion based on the simulated movement sections; Determining a motion progression part comprising at least two motion sections; Calculating the cost function of the movement progress part; … At each step can be a movement section be appended to the existing movement sequence part and checked whether the cost function of the resulting motion sequence portion exceeds a predetermined value. The predetermined value may be the cost function of a previously determined movement sequence, namely the first movement sequence. If the cost function of the movement sequence part is already greater than the cost function of the first movement sequence, this movement sequence part in particular will not be pursued further. This means, for example, that no further movement sections are attached in order to obtain a complete movement sequence. In particular, it can be ensured that only movement sequence parts which are good in terms of the cost function are pursued further. … the cost function contains an indication of: a quality of the simulated motion section; a length of a path corresponding to the simulated moving section.” See at least page 6, paragraphs 3-6; Examiner Interpretation: The cost of the existing/previously simulated movement sequence is the calculated cost of the past path. The cost that is compared to the cost of the simulated movement sequence is the cost of the reference path. The cost of the movement sequence parts that are pursued further is the cost of a path-to-go.) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Schmitt with a reasonable expectation of success such that “a solution for the optimized movement with little computational effort can be found.” (See at least page 6, paragraph 5) Regarding Claim 23, Modified Tong does not explicitly teach, but Schmitt teaches wherein identifying the one or more actions comprises evaluating a cost function defined over a signature of an overall path that includes the past path and a path-to-go, wherein the overall path corresponds to a concatenation of the past path and the path-to-go. (“A sequence of movements composed of several movement sections can have a total cost function, which is a sum of the cost functions of the individual movement sections of the movement sequence. … Determining a first course of motion based on the simulated movement sections; Determining a motion progression part comprising at least two motion sections; Calculating the cost function of the movement progress part; … At each step can be a movement section be appended to the existing movement sequence part and checked whether the cost function of the resulting motion sequence portion exceeds a predetermined value. The predetermined value may be the cost function of a previously determined movement sequence, namely the first movement sequence. If the cost function of the movement sequence part is already greater than the cost function of the first movement sequence, this movement sequence part in particular will not be pursued further. This means, for example, that no further movement sections are attached in order to obtain a complete movement sequence. In particular, it can be ensured that only movement sequence parts which are good in terms of the cost function are pursued further. … the cost function contains an indication of: a quality of the simulated motion section; a length of a path corresponding to the simulated moving section.” See at least page 6, paragraphs 3-6) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Schmitt with a reasonable expectation of success such that “a solution for the optimized movement with little computational effort can be found.” (See at least page 6, paragraph 5) Claim(s) 22 is/are rejected under 35 U.S.C. 103 as being unpatentable over Tong (US 20210208596 A1) in view of Barcelos (NPL: “Path Signatures for Diversity in Probabilistic Trajectory Optimisation”) and Ye (US 20230162374 A1). Regarding Claim 22, Modified Tong does not explicitly teach, but Ye teaches wherein updating the stored past path signature includes concatenating the subpath signature with the stored past path signature using a tensor product operation. (“an observed past trajectory of an object is obtained; a spatial pointwise feature of each trajectory point in the observed past trajectory is obtained; a temporal pointwise feature of the trajectory point is obtained according to the spatial pointwise feature of the trajectory points within a preset observation time interval; a motion trajectory prediction on the object is performed according to the spatial pointwise feature and the temporal pointwise feature of the trajectory points.” See at least [0007-0010]; “The second temporal pointwise feature of the trajectory point is concatenated with the first temporal pointwise feature of the interval trajectory point through the tensor concatenation to obtain the temporal pointwise feature of all trajectory points.” See at least [0090]) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Ye with a reasonable expectation of success to improve motion trajectory prediction accuracy (See at least [0002-0004]). Claim(s) 24 is/are rejected under 35 U.S.C. 103 as being unpatentable over Tong (US 20210208596 A1) in view of Barcelos (NPL: “Path Signatures for Diversity in Probabilistic Trajectory Optimisation”) and Raste (US 20230311849 A1). Regarding Claim 24, Modified Tong also does not explicitly teach, but Raste teaches wherein the one or more actions are identified in a receding-horizon manner based on successive updates to the stored past path signature. (“an MPC controller is based on an iterative optimization with a finite horizon (constrained) of a route model. At each discrete sampling time (k), the route is sampled and the actual state x.sub.k is measured or estimated with the help of observers. The performance of the controller is expressed by a so-called cost function. Based on a dynamic model of the route, this cost function is formulated in such a way that it expresses the behavior of the MPC controller in the future for a current route state x.sub.k and a series of future inputs u.sub.k. In other words, this predicted cost function gives a numerical indicator of the quality of the control, with the assumption that the current system state is influenced by a specific sequence of inputs from the past. The question is not how the controller will perform, but what is the sequence of inputs u.sub.k that produces the best performance. In order to compute the optimal sequence of inputs, the cost function must be minimized at each sampling interval by using a numerical optimization algorithm. As in the case of most actual systems, the inputs, outputs and states can be restricted by physical boundary conditions, which can easily be included in the numerical minimization task. From the sequence of future inputs u.sub.k, only the first one is applied, then the process is repeated on the basis of brand-new measured state information. This type of repeated measure-predict-optimize-apply cycle is referred to as receding horizon control.” See at least [0046]) It would have been obvious to a person having ordinary skill in the art before the effective filing date of the invention to modify the teachings of modified Tong to further include the teachings of Raste with a reasonable expectation of success “to compute the optimal sequence of inputs” (See at least [0046]). Conclusion Any inquiry concerning this communication or earlier communications from the examiner should be directed to Karston G Evans whose telephone number is (571)272-8480. The examiner can normally be reached Mon-Fri 9:00-5:00. Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice. If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Abby Lin can be reached at (571)270-3976. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300. Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000. /KARSTON G. EVANS/Examiner, Art Unit 3657
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Prosecution Timeline

Sep 05, 2023
Application Filed
May 30, 2025
Non-Final Rejection mailed — §101, §103
Sep 30, 2025
Response Filed
Nov 06, 2025
Final Rejection mailed — §101, §103
Feb 05, 2026
Request for Continued Examination
Feb 26, 2026
Response after Non-Final Action
Mar 10, 2026
Interview Requested
Apr 01, 2026
Non-Final Rejection mailed — §101, §103 (current)

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Prosecution Projections

3-4
Expected OA Rounds
71%
Grant Probability
88%
With Interview (+17.2%)
2y 8m (~0m remaining)
Median Time to Grant
High
PTA Risk
Based on 150 resolved cases by this examiner. Grant probability derived from career allowance rate.

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