Prosecution Insights
Last updated: October 26, 2026
Application No. 18/203,097

OBJECT-AGNOSTIC FAST GRASPING-POINTS ESTIMATION VIA GEOMETRIC-ALGEBRA

Non-Final OA §101§103
Filed
May 30, 2023
Examiner
PIERRE LOUIS, ANDRE
Art Unit
Tech Center
Assignee
Intel Corporation
OA Round
1 (Non-Final)
68%
Grant Probability
Favorable
1-2
OA Rounds
2m
Est. Remaining
83%
With Interview

Examiner Intelligence

Grants 68% — above average
68%
Career Allowance Rate
454 granted / 666 resolved
+8.2% vs TC avg
Strong +15% interview lift
Without
With
+15.1%
Interview Lift
resolved cases with interview
Typical timeline
3y 7m
Avg Prosecution
35 currently pending
Career history
704
Total Applications
across all art units

Statute-Specific Performance

§101
29.4%
-10.6% vs TC avg
§103
38.9%
-1.1% vs TC avg
§102
13.2%
-26.8% vs TC avg
§112
15.8%
-24.2% vs TC avg
Black line = Tech Center average estimate • Based on career data from 666 resolved cases

Office Action

§101 §103
DETAILED ACTION Notice of Pre-AIA or AIA Status 1. The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA . 2. Claims 1-20 are presented for examination. Claim Rejections - 35 USC § 101 3. 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. 3.1 Claims 18-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to non-statutory subject matter. The claim(s) does/do not fall within at least one of the four categories of patent eligible subject matter because the claims provide for at least one machine-readable medium including instructions; however, the specification (para [0016], [0018]) describe the medium to includes any others including signal bearing medium ([0018]) and therefore is not patent eligible under 35 USC 101. 3.2 Claims 1-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more. Step 1 Is the claim directed to a statutory category? Yes. The claims are to a system (claim 1), a robot/apparatus (claim 15), a non-transitory medium (claim 18). Step 2A- Prong One The claim(s) recite(s) a system (claim 1), a robot/apparatus (claim 15), a non-transitory medium (claim 18), comprising: The step of: “generate geometric primitives that describe composition of a robot”; “model kinematic composition of links and joints of the robot for grasping and manipulation by the robot using the geometric primitives”, under the broadest reasonable interpretation fall under a mental process or otherwise a mathematical concept / mathematical. Therefore, the claims are directed to an abstract idea, by use of generic computer components and thus are clearly directed to an abstract idea, as constructed. Step 2A Prong Two This judicial exception is not integrated into a practical application because the additional limitation such as: “processing circuitry”; and “a memory” including “instructions”, either alone or in combination, all serve to gather and process data and do not add anything more significantly to the judicial exception, but are mere instructions to apply the exception using a generic computer component that are well known, routine, and conventional activities (see specification at para [0086-0088], and fig.7A-7B) which can be of any type, including general-purpose computer (para [0088]) previously known in the industries. Merely adding a programmable computer to perform generic computer functions does not automatically overcome an eligibility rejection. Alice, 573 U.S. at 223-24. Furthermore, the use of a general-purpose computer to apply an otherwise ineligible algorithm does not qualify as a particular machine. See Ultramerciallnc. v. Hulu, LLC, 772F.3d 709, 716-17 (Fed. Cir. 20l4); In re TLI Commc 'ns LLC v. AV Automotive, LLC, 823 F.3d 607, 613 (Fed. Cir. 2016) (mere recitation of concrete or tangible components is not an inventive concept); Eon Corp. IP Holdings LLC v. AT&T Mobility LLC, 785; the step of: “use the model to determine a grasping configuration to grasp a target object and grasp the target based on the grasping configuration”, under the broadest reasonable interpretation, reasonable fall under post-solution action that are also well-known, routine and conventional activities and are not sufficient to amount to significantly more than the judicial exception (See further MPEP 2106.05(d)(i-iv)-f); thus are not patent eligible under 35 USC 101. It is further noted that to transform an abstract idea, law of nature or natural phenomenon into "a patent-eligible application", the claim must recite more than simply the judicial exception "while adding the words 'apply it.'" Mayo, 132 S. Ct. at 1294, 101 USPQ2d at 1965. Step 2B The claim(s) does/do not include additional elements that are sufficient to amount to significantly more than the judicial exception because, as previously discussed above with reference to the integration of abstract idea into a practical application, the additional elements of: “processing circuitry”; and “a memory” including “instructions”, either alone or in combination, all serve to gather and process data and do not add anything more significantly to the judicial exception, but are mere instructions to apply the exception using a generic computer component that are well known, routine, and conventional activities (see specification at para [0086-0088], and fig.7A-7B) which can be of any type, including general-purpose computer (para [0088]) previously known in the industries. Merely adding a programmable computer to perform generic computer functions does not automatically overcome an eligibility rejection. Alice, 573 U.S. at 223-24. Furthermore, the use of a general-purpose computer to apply an otherwise ineligible algorithm does not qualify as a particular machine. See Ultramerciallnc. v. Hulu, LLC, 772F.3d 709, 716-17 (Fed. Cir. 20l4); In re TLI Commc 'ns LLC v. AV Automotive, LLC, 823 F.3d 607, 613 (Fed. Cir. 2016) (mere recitation of concrete or tangible components is not an inventive concept); Eon Corp. IP Holdings LLC v. AT&T Mobility LLC, 785; the step of: “use the model to determine a grasping configuration to grasp a target object and grasp the target based on the grasping configuration”, under the broadest reasonable interpretation, reasonable fall under post-solution action that are also well-known, routine and conventional activities and are not sufficient to amount to significantly more than the judicial exception (See further MPEP 2106.05(d)(i-iv)-f); thus are not patent eligible under 35 USC 101. It is further noted that to transform an abstract idea, law of nature or natural phenomenon into "a patent-eligible application", the claim must recite more than simply the judicial exception "while adding the words 'apply it.'" Mayo, 132 S. Ct. at 1294, 101 USPQ2d at 1965. Therefore, using computer components amount to no more than mere instructions to perform the abstract, and thus are not sufficient to amount to significantly more than the recited abstract, as constructed. 3.3 Dependent claims 2-14, 16-17, 19-20 merely include limitations pertaining to further mental process and/or mathematical concept, such as: (claim 2), “wherein: the geometric primitives are linked in a Boolean composition to describe the composition, the geometric primitives include oriented-planes and ellipsoids and logical combinations include union, subtraction, negation, and intersection, the kinematic composition is modeled using a logical combination of signed distances arising from the geometric primitives, and the signed distances are spatially and sequentially arranged by directed distances” (mathematical concept or otherwise a mental process). (claim 3); “determine directed distances between points, the points selected from a point at infinity and a quadric that models a cylindrical surface associated with the robot” (mathematical concept or otherwise a mental process); (claim 4); “model a gripper of the robot, and extrusions and implicit curves, as generalized quadratics” (mathematical concept or otherwise mental process); (claim 5); “decompose a gripper of the robot into closed polytopes and quadrics, and turn each robot kinematic element into a collection of interconnected geometric primitives” (mathematical concept); (claim 6); “during an off-line phase of a high-performance grasping computation process, transform frames and meshes describing a three dimensional robot model into a geometric collection of primitives with associated directed distances, the geometric collection of primitives with associated directed distances stored in a non-volatile memory for use in general tasks” (mathematical concept or otherwise a mental process); (claim 7) “during an off-line phase, extract and fit primitives for each mesh in a Universal Robot Description Format (URDF) of the robot model, the extraction and fitting of each mesh comprising: determining a geometric centroid of the mesh, recentering all vertices of the mesh, determining a bounding box that spans a minimal volume for the mesh to define clipping-oriented planes, and determining a bounding ellipsoid that constrains only a pair of axes with minimal spans in the bounding box, and determining bounding ellipsoids for non-overlapping pairs of axes” (mathematical concept or otherwise a mental process); (claim 8) “spawn sorted primitives during the off-line phase for each joint set in the URDF, the spawning for each joint set comprising: storing an implicit transformation for the bounding box, and store a center of each ellipsoid and main axes in decreasing length order to provide minimal computation when evaluating directed distances” (WURC to store data in a memory); (claim 9) “determine a noise and quantization robust directed margin radii during the off-line phase for each joint set in the URDF, the spawning for each joint set comprising for all vertices in the joint set, computing a minimal distance to a surface of each of the planes and ellipsoid primitives and sorting the minimal distances progressively in a list to form a distribution and compute a cut-off radius by a target percentile” (mathematical concept); (claim 10) “during the off-line phase: verify viability of a transformation of each robot model to form a robot link through computation of a Kurtosis of the distribution” (mathematical concept or otherwise a mental process), “in response to a determination that the Kurtosis is greater than 0 and less than 0.5, provide a warning to a user, and in response to a determination that the Kurtosis is greater than 0.5, abort the transformation of the robot model and indicate that the robot model is unable to be transformed.” (WURC post-solution activities), (claim 11) “during the off-line phase, sort the robot links by volume of an associated bounding box in descending order” (mental process); (claim 12) “during an on-line phase of a high-performance grasping computation process: compute forward kinematics of links from a Universal Robot Description Format (URDF) determined during an off-line phase and an instantaneous configuration of the robot” (mathematical concept), and “select, via a bounding box filter, a subset of geometric primitives close to objects as active geometric primitives based on a 6 dimensional state of each of the links” (mental process); (claim 13) “during an on-line phase of a high-performance grasping computation process: determine the grasping target based on at least one of: model-less using raw results of range sensing, from a plurality of sensors, without added attributes, or model-based using a computer-aided design (CAD) or computer-aided manufacturing (CAM) model in which all vertices are collected, polygons are subdivided, and implicit curves and surfaces evaluated, abstract and subsample, by a point cloud, a source of the grasping target with a radius set to half a repeatability of a gripper of the robot based on the object grasp, obtain a mapping, for each point in the point cloud, of a point on a surface link of the gripper at a distance away from a surface point of the grasping target, and determine approximations between the gripper and the grasping target based on an x and y coordinate of each point, the distance, and the surface link” (mathematical concept); (claim 14) “during an on-line phase of a high-performance grasping computation process: determine, from the approximations, grasping quality as a ranking of grasping configurations for the gripper, the ranking based on grasp quality metrics, and select one of the grasping configurations as the grasping configuration based on the grasp quality metrics” (mental process); (claims 16 and 19) “during the off-line phase: transform frames and meshes describing a three dimensional robot model into a geometric collection of primitives with associated directed distances, extract and fit primitives for each mesh in a Universal Robot Description Format (URDF) of the robot model, the extraction and fitting of each mesh comprising: determining a geometric centroid of the mesh, recentering all vertices of the mesh, determining a bounding box that spans a minimal volume for the mesh to define clipping-oriented planes, and determining a bounding ellipsoid that constrains only a pair of axes with minimal spans in the bounding box, and determining bounding ellipsoids for non-overlapping pairs of axes, for each joint set in the URDF, computing, for all vertices in the joint set, a minimal distance to a surface of each of the planes and ellipsoid primitives and sorting the minimal distances progressively in a list to form a distribution and compute a cut-off radius by a target percentile, and verify viability of a transformation of each robot model to form a robot link through computation of a Kurtosis of the distribution, in response to a determination that the Kurtosis is greater than 0 and less than 0.5, provide a warning to a user, and in response to a determination that the Kurtosis is greater than 0.5, abort the transformation of the robot model and indicate that the robot model is unable to be transformed” (mathematical concept and/or mental process); (claims 17 and 20) “during the on-line phase: compute forward kinematics of links from the URDF and an instantaneous configuration of the robot, select, via a bounding box filter, a subset of geometric primitives close to objects as active geometric primitives based on a 6 dimensional state of each of the links, determine an object grasp based on at least one of: model-less using raw results of range sensing, from a plurality of sensors, without added attributes, or model-based using a computer-aided design (CAD) or computer-aided manufacturing (CAM) model in which all vertices are collected, polygons are subdivided, and implicit curves and surfaces evaluated, abstract and subsample, by a point cloud, a source of the grasping target with a radius set to a repeatability of the gripper based on the object grasp, obtain a mapping, for each point in the point cloud, of a point on a surface link of the gripper at a distance away from a surface point of the grasping target, and determine approximations between the gripper and the grasping target based on an x, y, and z coordinate of each point, the distance, and the surface link” (mathematical concept and/or a mental process); all of which further amount to further mathematical concept and/or mental process similar to that already recited by the independent claims and already addressed above and thus are further not patent eligible under 35 USC 101. Claim Rejections - 35 USC § 103 4. 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. 4.0 Claim(s) 1-12, 15, and 18 are rejected under 35 U.S.C. 103 as being unpatentable over Fan (USPG_PUB No. 2023/0124599), in view of Shi et al. (USPG_PUB No. 2018/0365349). 4.1 In considering claims 1, 15, and 18, Fan teaches a system comprising: processing circuitry (see para [0018] The computer 160 includes a processor and memory/storage); and memory (see para [0018] A computer 160 is in communication with the controller 150. The computer 160 includes a processor and memory/storage,)including instructions, which when executed by the processing circuitry cause the processing circuitry to: generate geometric primitives that describe composition of a robot (see para [0025], 0025] FIG. 2 is an illustrated flowchart diagram 200 of steps included in a grasp generation process used to create a grasp database which is in turn used in the machine tending system of FIG. 1, according to an embodiment of the present disclosure. Inputs to the grasp generation process include a part model 210 and a gripper model 220. [0049] The grasp database generation in the box 510 is performed in an “offline” mode, in advance of actual robotic machine tending operations.); and use the model to determine a grasping configuration to grasp a target object and grasp the target based on the grasping configuration (para [0031], Shown in box 310 is an initial configuration of gripper parts 320 and 322 and an object 330 which is to be grasped. That is, the gripper parts 320/322 may be opened (separated) and closed, and the entire gripper may be translated and rotated, to achieve a best quality grip during optimization computations. The gripper parts 320/322 are separated by a distance d.sub.0 at the initial configuration shown in the box 310. [0035] Shown in box 350 are the gripper parts 320/322 and the object 330 at the initial configuration (indicated by arrow 360), an intermediate configuration (indicated by arrow 370), and a final configuration (indicated by arrow 380). The movement of the gripper parts 320/322 in the configurations 360/370/380 depict the behavior of the iterative optimization loop in finding a quality grasp. Further see [0036-0037]). Fan provides for using as input gripper kinematic (abstract, para [0007], which would be understood as modeling the kinematic of the model, but does not specifically show model kinematic composition of links and joints of the robot for grasping and manipulation by the robot using the geometric primitives. Fan further teaches the Offline and online aspect of claim 15 (see Fan para The conveyor 140 is merely exemplary; the robot 100 may place the finished part in another bin, in a shipping container or elsewhere after removal from the machining station 130. After dropping off the finished part, the robot 100 then returns to the bin 110 to select another raw part to load into the machining station 130. The next raw part grasp is determined based on new image data provided by the 3D camera(s) 170. [0049] The grasp database generation in the box 510 is performed in an “offline” mode, in advance of actual robotic machine tending operations. The grasp database generation does not require a robot, a vision system or a machining station, and is typically done by a computer other than a robot controller, such as the computer 160 of FIG. 1. [0050] Box 520 includes the steps performed during actual “online” robotic machine tending operations, as shown in fig.1.). Shi et al. teaches step to model kinematic composition of links and joints of the robot for grasping and manipulation by the robot using the geometric primitives (see para [0026], The above method is accurate and complete for the nature of the verification, since correctness is verified using mathematical methods. In addition, CGA can perform the modeling and processing on geometric elements such as points, lines, planes, circles, and spheres, and the rotation and translation of these geometric elements in a unified manner. It offers great advantages in dealing with problems of robot kinematics and motion planning, and can improve dimensions for solving problems, thus simplifying the coupling in robot computations, thereby reducing the complexity of the computations. [0048] establishing a corresponding geometric model for the basic components and motion planning constraints of a robot based on a conformal geometric algebra theory, describing the established geometric model using a higher-order logic language, and forming a basic geometric logic model system for the robot; [0050] performing formal modeling for a specific motion process of the robot based on the basic geometric logic model system, to obtain a logical model of the geometric relations involved in the motion process of the robot..), and determine a grasping configuration to grasp a target ([0052]: "forming a logic proposition using the geometric relationship logic model of the specific motion process of the robot and the constraint or attribute of the motion process to be verified;", wherein the "attribute" is further described at paragraph [0063]: "the attribute of the motior process to be verified of the robot is that the robot gripper successfully and firmly grasps the object."); grasp the target based on the grasping configuration ([0053]: "verifying whether the logic proposition is correct using a logic reasoning engine"), and the distance aspect of claim 18 (see para [0094], [0095] wherein a and b represent any two points in the three-dimensional Euclidean space, and A and B are expressions of a point a and a point b in a conformal space respectively. The above model is an expression of a point-to-point distance in conformal geometric algebra, wherein dist(a,b) represents the distance between two points, which can be represented by the inner product of geometric algebra. A point-to-line distance, a point-to-sphere distance, and a sphere-to-sphere distance also have specific expressions in conformal geometric algebra, which can be used for specific computations in robot problems.). Fan and Shi et al. are analogous art because they are from the sane field of endeavor and that the model analyzes by Shi et al. is similar to that of Fan. Therefore, it would have been obvious to a person of skilled in the art at the time of filing of the applicant’s invention to combine the method of Shi et al. with that Fan because Shi et al. teaches the improvement of accuracy of the verification and reduce the complexity of the computations (see abstract, para [0026]). 4.2 Regarding claim 2, the combined teachings of Fan and Shi et al. teaches wherein: the geometric primitives are linked in a Boolean composition to describe the composition (see Shi et al. para [0010] establishing a corresponding geometric model for the basic components and motion planning constraints of the robot according to the specific structural parameters and the motion planning parameters based on a conformal geometric algebra theory, wherein the established geometric model is described in a higher-order logic language; performing formal modeling for a motion process of the robot based on the established geometric model, to obtain a logical model of the geometric relations involved in the motion process of the robot;), the geometric primitives include oriented-planes and ellipsoids and logical combinations include union, subtraction, negation, and intersection (see Shi et al. [0015] a module for the establishing of robot basic geometric logical models, configured for establishing a corresponding geometric model for the basic components and motion planning constraints of the robot according to the specific structural parameters and the motion planning parameters based on a conformal geometric algebra theory, wherein the established geometric model is described in a higher-order logic language; [0016] a module for the establishing of a logical model of the geometric relations in the motion process of the robot, configured for performing formal modeling for a motion process of the robot based on the established geometric model, to obtain a logical model of the geometric relations in the motion process of the robot; [0017] a module for the construction of logical propositions, configured for obtaining a motion logic relationship corresponding to a constraint or attribute of a motion process to be verified of the robot, using the logical model of geometric relations), the kinematic composition is modeled using a logical combination of signed distances arising from the geometric primitives, and the signed distances are spatially and sequentially arranged by directed distances (see Shi et al. [0094] the distance model between geometries is abstracted from the metric relationship of the basic components of a robot: [0095] wherein a and b represent any two points in the three-dimensional Euclidean space, and A and B are expressions of a point a and a point b in a conformal space respectively. The above model is an expression of a point-to-point distance in conformal geometric algebra, wherein dist(a,b) represents the distance between two points, which can be represented by the inner product of geometric algebra. A point-to-line distance, a point-to-sphere distance, and a sphere-to-sphere distance also have specific expressions in conformal geometric algebra, which can be used for specific computations in robot problems.). Therefore, it would have been obvious to a person of skilled in the art at the time of filing of the applicant’s invention to combine the method of Shi et al. with that Fan because Shi et al. teaches the improvement of accuracy of the verification and reduce the complexity of the computations (see abstract, para [0026]). 4.3 As per claim 3, the combined teachings of Fan and Shi et al. teaches determine directed distances between points, the points selected from a point at infinity and a quadric that models a cylindrical surface associated with the robot (see Shi et al. para [0064] The established geometric model includes a point model abstracted from a robot joint, and a line model formed by connecting robot joint points, a distance model between geometries abstracted from the metric relationship of the basic components of a robot, and [0094] The distance model between geometries is abstracted from the metric relationship of the basic components of a robot: [0095] wherein a and b represent any two points in the three-dimensional Euclidean space, and A and B are expressions of a point a and a point b in a conformal space respectively. The above model is an expression of a point-to-point distance in conformal geometric algebra, wherein dist(a,b) represents the distance between two points, which can be represented by the inner product of geometric algebra. A point-to-line distance, a point-to-sphere distance, and a sphere-to-sphere distance also have specific expressions in conformal geometric algebra, which can be used for specific computations in robot problems. [0069], Since the conformal geometric algebra can be constructed from the geometric algebra C1.sub.4,1, its data type is defined as a real̂(4,1)multivector. s$n represents the nth element of the multidimensional vector s, the mbasis function represents the basic blade function, the dot function represents the scalar product in the Euclidean space, and the null_inf and null_zero functions respectively represent zero vectors e.sub.0 and e.sub.∞: e.sub.0=½(e.sub.−−e.sub.+), e.sub.∞=e.sub.−+e.sub.+, [0070] wherein e.sub.0 represents an origin point, e.sub.∞ represents a point at infinity, and e.sub.+, e.sub.− can be replaced by e.sub.∞, e.sub.0 to more compactly represent a point in the conformal space). Therefore, it would have been obvious to a person of skilled in the art at the time of filing of the applicant’s invention to combine the method of Shi et al. with that Fan because Shi et al. teaches the improvement of accuracy of the verification and reduce the complexity of the computations (see abstract, para [0026]). 4.4 With regards to claim 4, the combined teachings of Fan and Shi et al. teaches model a gripper of the robot (see Fan para [0019] The computer 160 provides the target grasp data to the controller 150, which controls the robot 100 and the gripper 120 to grasp a part from the bin 110. The target grasp data includes the grasp target point (x/y/z coordinates), the approach angle to be followed by the gripper 120, and the gripper angle of rotation and width. Using the grasp data, the controller 150 can compute robot motion instructions which cause the gripper 120 to grasp a part and move the part into the machining station 130. Also see Shi et al. para [0040], In addition, different robots have different geometric features, and different geometric features have an impact on the motion logic relationship. Therefore, the logical model of geometric relations for the robot needs to be used when the motion logic relationship corresponding to the constraint or attribute of each motion process of the robot is determined. For example, two gripper ends of a robot gripper can be originally opened by 180 degrees, but due to the limitation of the work space, the two gripper ends can only be opened by 120 degrees at a certain position in the space such as a position Q; otherwise, the robot gripper will collide with other objects in the work space. At this time, 120 degrees is a constraint of the robot gripper at the position Q; that is, when the robot gripper moves in the work space, if it moves to the position Q, the degree of the opening between the two gripper ends must be adjusted from 180 degrees to 120 degrees, otherwise a collision event will occur.), and extrusions and implicit curves, as generalized quadratics (see Shi et al. para [0101] computing a first target circle where the end of the robot gripper is located based on the established geometric model in a formal way; computing a second target circle where the robot gripper is located based on the established geometric model and feature points on the robot gripper in a formal way; computing a translation operator of the robot gripper according to the first target circle and the second target circle in a formal way; computing a rotation operator of the grasping of an object by the robot gripper according to the first target circle and the second target circle in a formal way; computing a new target position of the robot gripper according to the translation operator and the rotation operator in a formal way; realizing the formal modeling for the motion process of the robot.). Therefore, it would have been obvious to a person of skilled in the art at the time of filing of the applicant’s invention to combine the method of Shi et al. with that Fan because Shi et al. teaches the improvement of accuracy of the verification and reduce the complexity of the computations (see abstract, para [0026]). 4.5 A per claims 5, 11, the combined teachings of Fan and Shi et al. teaches decompose a gripper of the robot into closed polytopes and quadrics, and turn each robot kinematic element into a collection of interconnected geometric primitives (see Shi et al. para [0040], o this end, it can be considered that the constraints or attributes of each motion process of the robot correspond to a kind of motion logic relationship. In addition, different robots have different geometric features, and different geometric features have an impact on the motion logic relationship. Therefore, the logical model of geometric relations for the robot needs to be used when the motion logic relationship corresponding to the constraint or attribute of each motion process of the robot is determined. For example, two gripper ends of a robot gripper can be originally opened by 180 degrees, but due to the limitation of the work space, the two gripper ends can only be opened by 120 degrees at a certain position in the space such as a position Q; otherwise, the robot gripper will collide with other objects in the work space. At this time, 120 degrees is a constraint of the robot gripper at the position Q; that is, when the robot gripper moves in the work space, if it moves to the position Q, the degree of the opening between the two gripper ends must be adjusted from 180 degrees to 120 degrees, otherwise a collision event will occur. [0101] computing a first target circle where the end of the robot gripper is located based on the established geometric model in a formal way; computing a second target circle where the robot gripper is located based on the established geometric model and feature points on the robot gripper in a formal way; computing a translation operator of the robot gripper according to the first target circle and the second target circle in a formal way; computing a rotation operator of the grasping of an object by the robot gripper according to the first target circle and the second target circle in a formal way; computing a new target position of the robot gripper according to the translation operator and the rotation operator in a formal way; realizing the formal modeling for the motion process of the robot.). Therefore, it would have been obvious to a person of skilled in the art at the time of filing of the applicant’s invention to combine the method of Shi et al. with that Fan because Shi et al. teaches the improvement of accuracy of the verification and reduce the complexity of the computations (see abstract, para [0026]). 4.6 Regarding claims 6, 12, the combined teachings of Fan and Shi et al. teaches that during an off-line phase of a high-performance grasping computation process (see Fan para [0049] The grasp database generation in the box 510 is performed in an “offline” mode, in advance of actual robotic machine tending operations. The grasp database generation does not require a robot, a vision system or a machining station, and is typically done by a computer other than a robot controller, such as the computer 160 of FIG. 1.), transform frames and meshes describing a three dimensional robot model into a geometric collection of primitives with associated directed distances (see Shi et al. para 0035] The currently developed conformal geometric algebra system can theoretically be extended to any dimensional space, and is mainly applied to the 5-dimensional conformal space. The conformal geometric algebra provides a Grassmann structure representing a geometry, a unified effect representing the geometric transformation, and a bracket system and an invariant system representing geometric invariants. It demonstrates significant advantages in the aspects of geometric data processing and geometric computing. Under the framework of geometric algebra, different transformation representation and computation forms have uniformity. After a geometric space transformation, the geometric meanings and geometric characteristics of the original geometric object can still be maintained. The object of robot research is a geometric relation formed by a system established based on a basic geometry.), the geometric collection of primitives with associated directed distances stored in a non-volatile memory for use in general tasks (see Shi et al. para [0036] Under the CGA framework, geometric representation and construction can be performed based on an inner product and an outer product, respectively. The geometric representation based on an outer product mainly reflects a mutually constructive relationship between the geometries of different levels, while the representation based on an inner product may be used to construct a corresponding parametric equation through metrics characterizing parameters such as a distance, an angle, and the like. [0077] The auxiliary plane on which a robot joint is located is abstracted into the plane π, and the above mathematical expression is a standard expression of a plane in conformal geometric algebra. The input variables n and d of the function plane_CGA respectively represent the normal vector of the auxiliary plane and the distance of the auxiliary plane to the origin point. [0095]). Therefore, it would have been obvious to a person of skilled in the art at the time of filing of the applicant’s invention to combine the method of Shi et al. with that Fan because Shi et al. teaches the improvement of accuracy of the verification and reduce the complexity of the computations (see abstract, para [0026]). 4.7 As per claim 7, the combined teachings of Fan and shi et al. teaches that during an off-line phase, extract and fit primitives for each mesh in a Universal Robot Description Format (URDF) of the robot model (see Fan para [0049] The grasp database generation in the box 510 is performed in an “offline” mode, in advance of actual robotic machine tending operations. The grasp database generation does not require a robot, a vision system or a machining station, and is typically done by a computer other than a robot controller, such as the computer 160 of FIG. 1. Shi et al. para Step 30: extracting feature points of an object and a robot gripper, respectively.), the extraction and fitting of each mesh comprising: determining a geometric centroid of the mesh, recentering all vertices of the mesh (see shi et al. para [0074] The reachable range of an end of a robot joint is abstracted into a sphere S, whose center is the joint and whose radius is a connecting rod. The above mathematical expression is the standard expression of a sphere in conformal geometric algebra. The input variables p, r of the function sphere_CGA respectively represent the center and the radius, wherein the center can be represented by a three-dimensional vector in the Euclidean space., determining a bounding box that spans a minimal volume for the mesh to define clipping-oriented planes (see Fan para [0044] A constraint function (Eq. 1 e) in box 436 dictates that the transformed gripper finger surface should not penetrate the object; that is, the distance should be greater than or equal to zero. This constraint in the box 436 leads to improved collision avoidance in the next iteration, as shown in box 460. Finally, Equation (1f) indicates that the transformations (R,t,q) are elements of the feasible set X of transformations (in one embodiment, R may have any rotational value, t must be within a bounding box size of the object, and q is limited by the grasp range defined in the gripper model 220)., and determining a bounding ellipsoid that constrains only a pair of axes with minimal spans in the bounding box, and determining bounding ellipsoids for non-overlapping pairs of axes (see Fan para [0044] A constraint function (Eq. 1 e) in box 436 dictates that the transformed gripper finger surface should not penetrate the object; that is, the distance should be greater than or equal to zero. This constraint in the box 436 leads to improved collision avoidance in the next iteration, as shown in box 460. Finally, Equation (1f) indicates that the transformations (R,t,q) are elements of the feasible set X of transformations (in one embodiment, R may have any rotational value, t must be within a bounding box size of the object, and q is limited by the grasp range defined in the gripper model 220). Therefore, it would have been obvious to a person of skilled in the art at the time of filing of the applicant’s invention to combine the method of Shi et al. with that Fan because Shi et al. teaches the improvement of accuracy of the verification and reduce the complexity of the computations (see abstract, para [0026]). 4.8 Regarding claim 8, the combined teachings of Fan and Shi et al. teaches spawn sorted primitives during the off-line phase for each joint set in the URDF (see Fan para [0049] The grasp database generation in the box 510 is performed in an “offline” mode, in advance of actual robotic machine tending operations. The grasp database generation does not require a robot, a vision system or a machining station, and is typically done by a computer other than a robot controller, such as the computer 160 of FIG. 1.), the spawning for each joint set comprising: storing an implicit transformation for the bounding box, and store a center of each ellipsoid and main axes in decreasing length order to provide minimal computation when evaluating directed distances (see Fan para [0024], The advance generation of the database of quality grasps enables the computer 160 (or the controller 150) to perform the real-time grasp computations quickly and efficiently during actual robotic machine tending operations. [0025], FIG. 2 is an illustrated flowchart diagram 200 of steps included in a grasp generation process used to create a grasp database which is in turn used in the machine tending system of FIG. 1, according to an embodiment of the present disclosure. Also see Shi et al. para [0135] It is known that the length of translation should be a distance between the center of the target circle Z.sub.t and the center of the circle Z.sub.h where the robot gripper is located, and that the translation axis is a straight line passing through two centers. First, the center of the target circle Z.sub.t is computed: P.sub.t=Z.sub.te.sub.∞Z.sub.t [0136] Since the translation axis is determined by two centers, the translation axis l*.sub.T can be computed by a direct expression: which in turn can be stored within the database). Therefore, it would have been obvious to a person of skilled in the art at the time of filing of the applicant’s invention to combine the method of Shi et al. with that Fan because Shi et al. teaches the improvement of accuracy of the verification and reduce the complexity of the computations (see abstract, para [0026]). 4.9 With regards to claim 9, the combined teachings of Fan and Shi et al. teaches determine a noise and quantization robust directed margin radii during the off-line phase for each joint set in the URDF (see Fan et al. para [0054], methods provide high quality, full-DOF grasps with surface contacts; thus the generated grasps are more robust to uncertainties and disturbances. The grasp generation method is easy to run, and runs automatically in an offline environment not requiring a robot and vision system. In addition, the disclosed methods generate diverse grasp data including many different grasp locations and approach directions. Finally, the disclosed grasp generation method allows for preferred and prohibited grasp regions to be defined on the part, also see shi et al. para [0074] The reachable range of an end of a robot joint is abstracted into a sphere S, whose center is the joint and whose radius is a connecting rod. The above mathematical expression is the standard expression of a sphere in conformal geometric algebra. The input variables p, r of the function sphere_CGA respectively represent the center and the radius, wherein the center can be represented by a three-dimensional vector in the Euclidean space..), the spawning for each joint set comprising for all vertices in the joint set, computing a minimal distance to a surface of each of the planes and ellipsoid primitives and sorting the minimal distances progressively in a list to form a distribution and compute a cut-off radius by a target percentile (see Shi et al. para [0094], [0095] wherein a and b represent any two points in the three-dimensional Euclidean space, and A and B are expressions of a point a and a point b in a conformal space respectively. The above model is an expression of a point-to-point distance in conformal geometric algebra, wherein dist(a,b) represents the distance between two points, which can be represented by the inner product of geometric algebra. A point-to-line distance, a point-to-sphere distance, and a sphere-to-sphere distance also have specific expressions in conformal geometric algebra, which can be used for specific computations in robot problems.). Therefore, it would have been obvious to a person of skilled in the art at the time of filing of the applicant’s invention to combine the method of Shi et al. with that Fan because Shi et al. teaches the improvement of accuracy of the verification and reduce the complexity of the computations (see abstract, para [0026]). 4.10 As per claim 10, the combined teachings of Fan and Shi et al. teaches during the off-line phase: verify viability of a transformation of each robot model to form a robot link through computation of a Kurtosis of the distribution (see Fan para 0049] The grasp database generation in the box 510 is performed in an “offline” mode, in advance of actual robotic machine tending operations. The grasp database generation does not require a robot, a vision system or a machining station, and is typically done by a computer other than a robot controller, such as the computer 160 of FIG. 1.and Shi et al. abstract, obtaining a motion logic relationship corresponding to a constraint or attribute of a motion process to be verified of the robot, and verifying whether the motion logic relationship is correct. The method and system are used for analysis to improve the accuracy of the verification and reduce the complexity of the computations. para [0012] [0012] verifying whether the logical relationship about motion is correct; if it is correct, this indicates that the logical model of the geometric relations meets the constraint of the motion process to be verified or has the attribute of the motion process to be verified; otherwise, it is indicated that the logical model of the geometric relations does not meet the constraint of the motion process to be verified or does not have the attribute of the motion process to be verified.), in response to a determination that the Kurtosis is greater than 0 and less than 0.5, provide a warning to a user, and in response to a determination that the Kurtosis is greater than 0.5, abort the transformation of the robot model and indicate that the robot model is unable to be transformed (see Shi et al. para [0012] verifying whether the logical relationship about motion is correct; if it is correct, this indicates that the logical model of the geometric relations meets the constraint of the motion process to be verified or has the attribute of the motion process to be verified; otherwise, it is indicated that the logical model of the geometric relations does not meet the constraint of the motion process to be verified or does not have the attribute of the motion process to be verified.). Allowable Subject Matter 5. Claims 13-14, 16-17, and 19-20 are objected to as being dependent upon a rejected base claim, but would be allowable if rewritten in independent form including all of the limitations of the base claim and any intervening claims. Conclusion 6. The prior art made of record and not relied upon is considered pertinent to applicant's disclosure. 6.1 Zapolsky et al. (USPG_PUB No. 2023/0330843) teaches a method and system for grasping objects. 6.2 Fan (USPG_PUB No. 2022/0072707) teaches a method for generating quality grasp poses for robot grasping of parts and, more particularly, to a method for robot grasp learning comprising a random initialization where random objects and grippers. 7. Claims 1-20 are rejected and this action is non-final. Any inquiry concerning this communication or earlier communications from the examiner should be directed to ANDRE PIERRE-LOUIS whose telephone number is (571)272-8636. The examiner can normally be reached M-F 9:00 AM-5:00 PM. 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, EMERSON C PUENTE can be reached at 571-272-3652. 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. /ANDRE PIERRE LOUIS/Primary Patent Examiner, Art Unit 2187 October 2, 2026
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Prosecution Timeline

May 30, 2023
Application Filed
Oct 06, 2026
Non-Final Rejection mailed — §101, §103 (current)

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