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 .
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 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.
Claims 1-2, 4, 7-11, and 18-19 are rejected under 35 U.S.C. 103 as being unpatentable over Raghuraman (“Tube-based robust MPC with adjustable uncertainty sets using zonotopes”) in view of Straub (US 20160355252 A1)
Regarding claim 1, Raghuraman teaches A feedback controller for controlling an operation of a mechanical system subject to uncertainty on a state of the operation of the system, the feedback controller comprising: (Abstract A tube-based robust Model Predictive Control (MPC) formulation with adjustable uncertainty sets is presented where the size of the uncertainty set is optimized as part of the underlying optimization problem)
collect a feedback signal indicative of a current state of the operation of the system subject to constraints and current uncertainty on the current state of the operation of the system, wherein the current uncertainty lies in a symmetric bounded set and includes one or a combination of uncertainty on dynamics of the system, uncertainty on a state of the system, uncertainty on control commands to the system, and uncertainty on constraints on the state of the operation of the system; (III. ROBUST MPC BACKGROUND Page 463-464 Consider the discrete linear time-invariant system x(k + 1) = Ax(k) + Bu(k) + w(k), (1) where x ∈ R n are the states, u ∈ R m are the inputs, and w ∈ R n are the additive disturbances…Based on the solution to (3), the control input applied to (1) is u(k) = uˆ ∗ (k|k) + K (x(k) − xˆ ∗ (k|k)), (4) where xˆ ∗ (k|k) and uˆ ∗ (k|k) denote the optimal state and input at time step k and K is a stabilizing feedback control law, often chosen as the infinite-horizon, discrete-time LQR controller. This stabilizing control law ensures that the difference, x(k) − xˆ(k|k), between the true and nominal state trajectories satisfying (1) and (3b) respectively, always stays within a bounded set, E, given the bounded disturbances, w(k) ∈ W)
determine a robust controllable set for maintaining the state of the system employing closed-form expressions on a constrained zonotope defining the constraints on the state of the operation of the system and an affine transformation of the symmetric bounded set inclosing the current uncertainty into space of the constrained zonotope, wherein the closed-form expressions include a closed-form approximation of a Pontryagin difference between the constrained zonotopic representation and the zonotopic transformation of the symmetric bounded set; (abstract Zonotopes are used to represent the set containment conditions that define RPI sets and constraint tightening as linear constraints. IV. ROBUST MPC WITH INTEGRATED RPI SET COMPUTATION AND CONSTRAINT TIGHTENING Usually, in constrained robust MPC, desired performance is achieved by letting the state and input trajectories operate close to the bounds of the tightened state and input constraints… there exists a trade-off between the size of the uncertainty set and system performance, which must be optimized. The main contribution of this paper lies in showing that despite the introduction of scaling variables, Φ, as decision variables, all of the point and set containment conditions in (11c)-(11h) can be represented as linear constraints. V. BACKGROUND ON ZONOTOPES AND ZONOTOPIC SET OPERATIONS Theorem 3: (Theorem 7 of [16]) Given Z1 = {G1, c1} and Z2 = {G2, c2}, then Z˜ d = {GdΦ, cd}, with Φ = diag(φ), φi > 0, ∀i ∈ {1, · · · , ngd }, is an inner approximation of the Pontryagin difference Zd = Z1 Z2 such that Z˜ d ⊆ Zd if there exists Γ ∈ R ng1×(ngd+ng2 ) and β ∈ R ng1 such that GdΦ G2 = G1Γ, (16a) c1 − (cd + c2) = G1β, (16b) |Γ|1 + |β| ≤ 1. (16c) The set Z˜ d with maximal volume is typically desired and can be computed by solving an optimization problem formulated with the constraints from (16) and an objective function that maximizes the scaling variables in Φ. With cd, Φ, Γ, and β as decision variables in this optimization problem, (16) consists of only linear constraints and thus a LP or QP can be formulated based on the p-norm used to maximize the vector φ, where Φ = diag(φ))
Raghuraman does not expressly disclose but Straub discloses at least one processor; and a non-transitory memory having instructions stored thereon that, when executed by the at least one processor, cause the feedback controller to: ([0032] Machine (e.g., computer system, cyberphysical system) 500 may include a hardware processor 510, where the hardware processor 510 may include a central processing unit (CPU), a graphics processing unit (GPU), a hardware processor core, or any combination thereof. Machine 500 may also include a main memory 520 and a non-volatile storage 530. Components of machine 500 may communicate with each other via an interlink 505 (e.g., bus).)
determine a control command for controlling the operation of the system subject to the robust controllable set; and ([0026] The movement model updated by motion feedback 300 can facilitate adapting to changes of the control model (e.g., due to control surface damage, etc.) far more rapidly than a human would be able to, allowing the human pilot's commands (being issued based on the normal control model) to be translated into commands that produce the desired actions under an altered control model. As a part of this process, the movement model updated by motion feedback 300 would monitor the pilot and/or autopilot commands 320, where the commands are monitored relative to an existing movement model 310. Using the commands and model data, the expected movement is determined 330 and compared this to the actual movement 340 to determine the difference 350. A difference weighting factor 360 and existing movement model weighting factor 370 may be applied to the computed difference 350 and the existing movement model 310, respectively. Weighting factors 360 may be used to balance the need for responsiveness to changing conditions against the potential for sensor failure and other errors. A new movement model 380 may be created by combining these values. This new movement model would then be used for the control of the aircraft.)
submit the control command to an actuator of the system causing a change in the state of the operation of the system. (Claim 1 generating one or more actuator instructions to effect the movement goal using the movement determination processing module; sending the one or more actuator instructions from the movement determination processing module to a hardware-implemented movement command processing module; and instructing, using the movement command processing module, the one or more actuators to execute the one or more actuator instructions)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Straub with a reasonable expectation of success by creating and updating the movement model allows the ADCS to respond to changing conditions that affect the movement model as taught by Straub ([0011]).
Regarding claim 2, Raghuraman teaches The feedback controller of claim 1, wherein the closed-form approximation of the Pontryagin difference is an inner approximation determined by scaling the affine transformation and equality constraints describing the constrained zonotope as a constrained zonotopic minuend based on characteristics of a convex, compact, and symmetric subtrahend. (V. BACKGROUND ON ZONOTOPES AND ZONOTOPIC SET OPERATIONS A zonotope is the Minkowski sum of a finite set of line segments or, equivalently, the image of a hypercube under an affine transformation [20], [21]. Theorem 3: (Theorem 7 of [16]) Given Z1 = {G1, c1} and Z2 = {G2, c2}, then Z˜ d = {GdΦ, cd}, with Φ = diag(φ), φi > 0, ∀i ∈ {1, · · · , ngd }, is an innerapproximation of the Pontryagin difference Zd = Z1 Z2 such that Z˜ d ⊆ Zd if there exists Γ ∈ R ng1×(ngd+ng2 ) and β ∈ R ng1 such that GdΦ G2 = G1Γ, (16a) c1 − (cd + c2) = G1β, (16b) |Γ|1 + |β| ≤ 1. (16c))
Regarding claim 4, Raghuraman teaches The feedback controller of claim 2, wherein the symmetric bounded set is transformed into the space of the constrained zonotope using higher-dimensional affine transformation. (V. BACKGROUND ON ZONOTOPES AND ZONOTOPIC SET OPERATIONS A zonotope is the Minkowski sum of a finite set of line segments or, equivalently, the image of a hypercube under an affine transformation [20], [21]. Theorem 3: (Theorem 7 of [16]) Given Z1 = {G1, c1} and Z2 = {G2, c2}, then Z˜ d = {GdΦ, cd}, with Φ = diag(φ), φi > 0, ∀i ∈ {1, · · · , ngd }, is an innerapproximation of the Pontryagin difference Zd = Z1 Z2 such that Z˜ d ⊆ Zd if there exists Γ ∈ R ng1×(ngd+ng2 ) and β ∈ R ng1 such that GdΦ G2 = G1Γ, (16a) c1 − (cd + c2) = G1β, (16b) |Γ|1 + |β| ≤ 1. (16c))
Regarding claim 7, Raghuraman teaches The feedback controller of claim 1, wherein the feedback controller is configured for fault-tolerant control by tightening the constraints represented by the constrained zonotope and maintaining a nominal trajectory of the operation of the mechanical system within the robust controllable set approximated using the constrained zonotope. (VI. ONE-STEP RPI SET COMPUTATION AND CONSTRAINT TIGHTENING When analyzing (11), the addition of scalable sets introduces the need to 1) enforce point containment within a scaled tightened constraint set (e.g. xˆ(j|k) ∈ X˜(Φx)) and 2) set containment for inner-approximations of the tightened constraint set (e.g. X˜(Φx) ⊕ E˜(Φε) ⊆ X ) and the outer approximation of the mRPI set (e.g. AKE˜(Φε)⊕W(Φw) ⊆ E˜(Φε)). Then, (18a) readily satisfies the definition of a zonotope with ˆξx ∈ [−1, 1]. The Pontryagin difference containment conditions from Theorem 3 are satisfied by (18b)-(18d). Fig. 2. Simulation results for uncertainty weightings λ ∈ {101 , 2 × 105 , 106} with the dashed lines denoting the reference trajectories for the position state and the acceleration/deceleration input.)
Regarding claim 8, Raghuraman teaches The feedback controller of claim 7, wherein a containment of the nominal trajectory in a constrained zonotopic inner-approximation of the robust controllable set is given by tightening the constraints based on nominal dynamics, nominal uncertainty model, and the constrained zonotope. (VI. ONE-STEP RPI SET COMPUTATION AND CONSTRAINT TIGHTENING When analyzing (11), the addition of scalable sets introduces the need to 1) enforce point containment within a scaled tightened constraint set (e.g. xˆ(j|k) ∈ X˜(Φx)) and 2) set containment for inner-approximations of the tightened constraint set (e.g. X˜(Φx) ⊕ E˜(Φε) ⊆ X ) and the outer approximation of the mRPI set (e.g. AKE˜(Φε)⊕W(Φw) ⊆ E˜(Φε)). Then, (18a) readily satisfies the definition of a zonotope with ˆξx ∈ [−1, 1]. The Pontryagin difference containment conditions from Theorem 3 are satisfied by (18b)-(18d).)
Regarding claim 9, Raghuraman teaches The feedback controller of claim 8, wherein tightening the constraints is further based on post-failure dynamics, post-failure safety constraints, and a post-failure uncertainty model. (VI. ONE-STEP RPI SET COMPUTATION AND CONSTRAINT TIGHTENING When analyzing (11), the addition of scalable sets introduces the need to 1) enforce point containment within a scaled tightened constraint set (e.g. xˆ(j|k) ∈ X˜(Φx)) and 2) set containment for inner-approximations of the tightened constraint set (e.g. X˜(Φx) ⊕ E˜(Φε) ⊆ X ) and the outer approximation of the mRPI set (e.g. AKE˜(Φε)⊕W(Φw) ⊆ E˜(Φε)). Then, (18a) readily satisfies the definition of a zonotope with ˆξx ∈ [−1, 1]. The Pontryagin difference containment conditions from Theorem 3 are satisfied by (18b)-(18d))
Regarding claim 10, Raghuraman teaches The feedback controller of claim 7, wherein the robust controllable set is determined from a stochastic controllable set, by enforcing the constraints as containment in a second non-stochastic constrained zonotope that inner-approximates the Pontryagin difference between a first constrained zonotope and a convex, compact, and symmetric set based on a nominal uncertainty model that contains a given probability mass. (Abstract Zonotopes are used to represent the set containment conditions that define RPI sets and constraint tightening as linear constraints. The Hausdorff distance metric is shown to reduce conservatism when optimizing the size of these tightened constraint sets. Finally, a numerical example demonstrates the ability to optimize the size of the uncertainty set within a robust MPC formulation and highlights the benefits and limitations of this approach.)
Regarding claim 11, Raghuraman does not expressly disclose but Straub discloses The feedback controller of claim 1, wherein the mechanical system is a spacecraft, and wherein the feedback controller is a fault-tolerant controller is configured to perform an abort-safe control under the uncertainty. ([0007] FIG. 4 depicts a block diagram of a movement model updated by sensor input and motion feedback loop, in accordance with some embodiments. [0010] The subject matter described herein includes an attitude determination and control system (ADCS) and associated methods. Systems for determining attitude (e.g., orientation, angular position), may be used by airborne and space-based vehicles, such as to determine the vehicle's attitude relative to an external point of reference.)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Straub with a reasonable expectation of success by creating and updating the movement model allows the ADCS to respond to changing conditions that affect the movement model as taught by Straub ([0011]).
Regarding claim 18, Raghuraman teaches A method for feedback control of an operation of a mechanical system subject to uncertainty on a state of the operation of the system, (Abstract A tube-based robust Model Predictive Control (MPC) formulation with adjustable uncertainty sets is presented where the size of the uncertainty set is optimized as part of the underlying optimization problem)
collecting a feedback signal indicative of a current state of the operation of the system subject to constraints and current uncertainty on the current state of the operation of the system, wherein the current uncertainty lies in a symmetric bounded set and includes one or a combination of uncertainty on dynamics of the system, uncertainty on a state of the system, uncertainty on control commands to the system, and uncertainty on constraints on the state of the operation of the system; (III. ROBUST MPC BACKGROUND Page 463-464 Consider the discrete linear time-invariant system x(k + 1) = Ax(k) + Bu(k) + w(k), (1) where x ∈ R n are the states, u ∈ R m are the inputs, and w ∈ R n are the additive disturbances…Based on the solution to (3), the control input applied to (1) is u(k) = uˆ ∗ (k|k) + K (x(k) − xˆ ∗ (k|k)), (4) where xˆ ∗ (k|k) and uˆ ∗ (k|k) denote the optimal state and input at time step k and K is a stabilizing feedback control law, often chosen as the infinite-horizon, discrete-time LQR controller. This stabilizing control law ensures that the difference, x(k) − xˆ(k|k), between the true and nominal state trajectories satisfying (1) and (3b) respectively, always stays within a bounded set, E, given the bounded disturbances, w(k) ∈ W)
determining a robust controllable set for maintaining the state of the system employing closed-form expressions on a constrained zonotope defining the constraints on the state of the operation of the system and an affine transformation of the symmetric bounded set inclosing the current uncertainty into space of the constrained zonotope, wherein the closed-form expressions include a closed-form approximation of a Pontryagin difference between the constrained zonotopic representation and the zonotopic transformation of the symmetric bounded set; (abstract Zonotopes are used to represent the set containment conditions that define RPI sets and constraint tightening as linear constraints. IV. ROBUST MPC WITH INTEGRATED RPI SET COMPUTATION AND CONSTRAINT TIGHTENING Usually, in constrained robust MPC, desired performance is achieved by letting the state and input trajectories operate close to the bounds of the tightened state and input constraints… there exists a trade-off between the size of the uncertainty set and system performance, which must be optimized. The main contribution of this paper lies in showing that despite the introduction of scaling variables, Φ, as decision variables, all of the point and set containment conditions in (11c)-(11h) can be represented as linear constraints. V. BACKGROUND ON ZONOTOPES AND ZONOTOPIC SET OPERATIONS Theorem 3: (Theorem 7 of [16]) Given Z1 = {G1, c1} and Z2 = {G2, c2}, then Z˜ d = {GdΦ, cd}, with Φ = diag(φ), φi > 0, ∀i ∈ {1, · · · , ngd }, is an inner approximation of the Pontryagin difference Zd = Z1 Z2 such that Z˜ d ⊆ Zd if there exists Γ ∈ R ng1×(ngd+ng2 ) and β ∈ R ng1 such that GdΦ G2 = G1Γ, (16a) c1 − (cd + c2) = G1β, (16b) |Γ|1 + |β| ≤ 1. (16c) The set Z˜ d with maximal volume is typically desired and can be computed by solving an optimization problem formulated with the constraints from (16) and an objective function that maximizes the scaling variables in Φ. With cd, Φ, Γ, and β as decision variables in this optimization problem, (16) consists of only linear constraints and thus a LP or QP can be formulated based on the p-norm used to maximize the vector φ, where Φ = diag(φ))
Raghuraman does not expressly disclose but Straub discloses wherein the method uses a processor coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry out steps of the method, comprising: ([0032] Machine (e.g., computer system, cyberphysical system) 500 may include a hardware processor 510, where the hardware processor 510 may include a central processing unit (CPU), a graphics processing unit (GPU), a hardware processor core, or any combination thereof. Machine 500 may also include a main memory 520 and a non-volatile storage 530. Components of machine 500 may communicate with each other via an interlink 505 (e.g., bus).)
determining a control command for controlling the operation of the system subject to the robust controllable set; and ([0026] The movement model updated by motion feedback 300 can facilitate adapting to changes of the control model (e.g., due to control surface damage, etc.) far more rapidly than a human would be able to, allowing the human pilot's commands (being issued based on the normal control model) to be translated into commands that produce the desired actions under an altered control model. As a part of this process, the movement model updated by motion feedback 300 would monitor the pilot and/or autopilot commands 320, where the commands are monitored relative to an existing movement model 310. Using the commands and model data, the expected movement is determined 330 and compared this to the actual movement 340 to determine the difference 350. A difference weighting factor 360 and existing movement model weighting factor 370 may be applied to the computed difference 350 and the existing movement model 310, respectively. Weighting factors 360 may be used to balance the need for responsiveness to changing conditions against the potential for sensor failure and other errors. A new movement model 380 may be created by combining these values. This new movement model would then be used for the control of the aircraft.)
submitting the control command to an actuator of the system causing a change in the state of the operation of the system. (Claim 1 generating one or more actuator instructions to effect the movement goal using the movement determination processing module; sending the one or more actuator instructions from the movement determination processing module to a hardware-implemented movement command processing module; and instructing, using the movement command processing module, the one or more actuators to execute the one or more actuator instructions)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Straub with a reasonable expectation of success by creating and updating the movement model allows the ADCS to respond to changing conditions that affect the movement model as taught by Straub ([0011]).
Regarding claim 19, Raghuraman teaches The method of claim 18, wherein the closed-form approximation of the Pontryagin difference is an inner approximation determined by scaling the affine transformation and equality constraints describing the constrained zonotope as a constrained zonotopic minuend based on characteristics of a convex, compact, and symmetric subtrahend. (V. BACKGROUND ON ZONOTOPES AND ZONOTOPIC SET OPERATIONS A zonotope is the Minkowski sum of a finite set of line segments or, equivalently, the image of a hypercube under an affine transformation [20], [21]. Theorem 3: (Theorem 7 of [16]) Given Z1 = {G1, c1} and Z2 = {G2, c2}, then Z˜ d = {GdΦ, cd}, with Φ = diag(φ), φi > 0, ∀i ∈ {1, · · · , ngd }, is an innerapproximation of the Pontryagin difference Zd = Z1 Z2 such that Z˜ d ⊆ Zd if there exists Γ ∈ R ng1×(ngd+ng2 ) and β ∈ R ng1 such that GdΦ G2 = G1Γ, (16a) c1 − (cd + c2) = G1β, (16b) |Γ|1 + |β| ≤ 1. (16c))
Claims 3, 5-6, and 20 are rejected under 35 U.S.C. 103 as being unpatentable over Raghuraman (“Tube-based robust MPC with adjustable uncertainty sets using zonotopes”) in view of Straub (US 20160355252 A1) in further view of Yang (“Scalable Zonotopic Under-Approximation of Backward Reachable Sets for Uncertain Linear Systems”)
Regarding claim 3, Raghuraman does not expressly disclose but Yang discloses The feedback controller of claim 2, wherein the scaling is determined by the solution of a collection of linear equations determined by the affine transformation, the equality constraints describing the constrained zonotopic minuend, and the characteristics of the convex, compact, and symmetric subtrahend. (Page 1557 (3) Efficient Minkowski Difference Between Aligned Zonotopes: Next, we show that the Minkowski difference amounts to element-wise generator subtraction when the subtrahend zonotope is aligned with the minuend zonotope)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Yang with a reasonable expectation of success by solving a linear optimization problem using Minkowski difference with a zonotope as taught by Yang (Abstract).
Regarding claim 5, Raghuraman does not expressly disclose but Yang discloses The feedback controller of claim 2, wherein the closed-form approximation of the Pontryagin difference is obtained by computing the Pontryagin difference between a polyhedral outer approximation of the constrained zonotopic minuend and the subtrahend intersected with a translation of the constrained zonotopic minuend by a point of symmetry of the subtrahend. (I. INTRODUCTION A variety of approaches exists in the literature, including polyhedral computation [5], interval analysis [17], HJB method [21] and polynomial optimization [15], A. Zonotopic Inner/Outer Approximation of Z EW B. Approximation of Backward Reachable Sets Eqs. (11) and (12) only involve Minkowski addition, linear transformation of zonotopes and Minkowski difference where the subtrahend zonotope is aligned with the minuend zonotope)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Yang with a reasonable expectation of success by solving a linear optimization problem using Minkowski difference with a zonotope as taught by Yang (Abstract).
Regarding claim 6, Raghuraman teaches The feedback controller of claim 5, wherein the polyhedral outer approximation of the constrained zonotopic minuend is determined by a collection of halfspaces determined by a closed-form collection of feasible solutions to a Lagrangian dual of an optimization problem describing a feasibility check of containment of a trajectory of the operation of the mechanical system in the constrained zonotope. (II. NOTATION AND PRELIMINARIES The convex polytope S ⊂ R n in H-Rep is defined as S = {s ∈ R n | Fs ≤ h} such that F ∈ R nh×n and h ∈ R nh where nh denotes the number of halfspaces. A zonotope Z = {G, c} ⊂ R n defined by Z = {Gξ + c | ||ξ||∞ ≤ 1}, where ng denotes the number of generators such that G ∈ R n×ng and c ∈ R n)
Regarding claim 20, Raghuraman does not expressly disclose but Yang discloses The method of claim 18, wherein the scaling is determined by the solution of a collection of linear equations determined by the affine transformation, the equality constraints describing the constrained zonotopic minuend, and the characteristics of the convex, compact, and symmetric subtrahend. (Page 1557 (3) Efficient Minkowski Difference Between Aligned Zonotopes: Next, we show that the Minkowski difference amounts to element-wise generator subtraction when the subtrahend zonotope is aligned with the minuend zonotope)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Yang with a reasonable expectation of success by solving a linear optimization problem using Minkowski difference with a zonotope as taught by Yang (Abstract).
Claims 12-17 are rejected under 35 U.S.C. 103 as being unpatentable over Raghuraman (“Tube-based robust MPC with adjustable uncertainty sets using zonotopes”) in view of Straub (US 20160355252 A1) in further view of Ross (US 9849785 B1)
Regarding claim 12, Raghuraman teaches the feedback controller of claim 1; (Abstract A tube-based robust Model Predictive Control (MPC) formulation with adjustable uncertainty sets is presented where the size of the uncertainty set is optimized as part of the underlying optimization problem)
Raghuraman does not expressly disclose but Ross discloses A spacecraft for moving in a multi-object celestial system while avoiding an unauthorized entry into a keep-away zone during a normal and an abnormal operation of the spacecraft, wherein the normal operation includes moving towards a target in the keep-away zone, and wherein the abnormal operation includes one or a combination of a failure to receive an authorization to enter the keep-away zone and a failure of at least one component of the spacecraft, comprising: (Col 8 Line 48-63 FIG. 1 shows two examples of potential “keep-out” regions 12 and 14 in the state space in which it is desired to avoid having the controlled system transition through the keep-out areas. In the example of missile guidance control, for instance, the keep-out areas 12 and 14 may represent locations of friendly vessels, with the target state 8 representing an enemy craft, and the initial or starting state 4 representing the assumed current position of a firing vessel. Thus, the keep-out areas 12 and 14 serve to represent uncertain trajectory or path constraints in the state space between the initial state 4 and the final state 8. FIG. 1 further illustrates three examples of possible trajectories 16, 18 and 20 beginning at different points within the uncertainty region 6 surrounding the initial state 4, and terminating at different locations within the uncertainty region 10 surrounding the target final state 8.)
a set of thrusters configured to change the state of a spacecraft according to a sequence of control commands produced by the feedback controller of claim 1; (Col 12 Line 19-23 the problem space equations 172 may further characterize the control variables, such as thrust and/or control surface deflections, used to launch and potentially guide the missile from the current location 164 to the target 162.)
a set of sensors configured to produce measurements indicative of the state of the spacecraft; and (Col 26 Line 39-46 The current location and attitude of spacecraft 2810 and other information related to the state of spacecraft 2810 is measured by sensors 3124 and made available to both the attitude controller 3132 which may implement a version of the control block diagram given in FIG. 30, and the guidance control computation block 31160 of the present invention.)
a circuitry configured to detect the abnormal operation of the spacecraft. (Col 21 Line 50-55 deriving a guidance control policy 170 in this manner (specifically by selecting only the nominal value for p and only the nominal initial condition) may fail to achieve the final desired state in the presence of uncertainty in the value of p and/or in the values of the initial conditions.)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Ross with a reasonable expectation of success by improving efficiency and accuracy as taught by Ross (Col 8 Line 27).
Regarding claim 13, Raghuraman does not expressly disclose but Ross discloses The spacecraft of claim 12, wherein the feedback controller is configured to execute, during the normal operation of the spacecraft, a nominal control law subject to constraints on maintaining a state of the spacecraft within a union of a plurality of control invariant sets of values of the state of the spacecraft that partially or completely enclose the keep-away zone (Col 8 Line 48-63 FIG. 1 shows two examples of potential “keep-out” regions 12 and 14 in the state space in which it is desired to avoid having the controlled system transition through the keep-out areas. In the example of missile guidance control, for instance, the keep-out areas 12 and 14 may represent locations of friendly vessels, with the target state 8 representing an enemy craft, and the initial or starting state 4 representing the assumed current position of a firing vessel. Thus, the keep-out areas 12 and 14 serve to represent uncertain trajectory or path constraints in the state space between the initial state 4 and the final state 8. FIG. 1 further illustrates three examples of possible trajectories 16, 18 and 20 beginning at different points within the uncertainty region 6 surrounding the initial state 4, and terminating at different locations within the uncertainty region 10 surrounding the target final state 8.), wherein the state of the spacecraft includes a location of the spacecraft and at least one or a combination of a velocity and an acceleration of the spacecraft (Col 25 Line 30-32 Feedforward acceleration commands, αc(t), may also be introduced as shown in FIG. 29.), wherein each of the plurality of control invariant sets is determined using constrained zonotopes computational geometry such that when the state of the spacecraft is within a control invariant set there is a control command produced by the nominal control law that maintains the state of the spacecraft within the control invariant set despite internal and external forces acting on the spacecraft; and (Col 12 Line 19-23 the problem space equations 172 may further characterize the control variables, such as thrust and/or control surface deflections, used to launch and potentially guide the missile from the current location 164 to the target 162.)
execute, upon detecting the abnormal operation of the spacecraft, an abort control law associated with the control invariant set including a current state of the spacecraft, wherein at least some different abort control laws are associated with at least some different control invariant sets, and wherein the abort control law is jointly and interdependently determined for the corresponding control invariant set to produce abort control commands moving the spacecraft while avoiding the keep-away zone for any state within the corresponding control invariant set. (Col 21 Line 50-55 deriving a guidance control policy 170 in this manner (specifically by selecting only the nominal value for p and only the nominal initial condition) may fail to achieve the final desired state in the presence of uncertainty in the value of p and/or in the values of the initial conditions.)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Ross with a reasonable expectation of success by improving efficiency and accuracy as taught by Ross (Col 8 Line 27).
Regarding claim 14, Raghuraman does not expressly disclose but Ross discloses The spacecraft of claim 13, wherein each of the control invariant sets is a stochastic reachable set determined for a possible abnormal operation defined by the first likelihood of the unbounded stochastic uncertainty. (Col 13 Line 57-67 One non-limiting example will seek to reduce or minimize the stochastic uncertainty of the terminal state (i.e. the deviation from the selected target location 162 in FIG. 15 and point 8 in FIGS. 1 and 2), for example by computing the trace of the terminal covariance. That is, obtain a guidance and control policy 170 that minimizes J=trace(
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(t)=cov(x(t)) is the time varying covariance of the nominal state. In another possible embodiment, the user may seek to minimize the integrated trace of the covariance, i.e. j=∫ trace(
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(t))dt. )
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Ross with a reasonable expectation of success by improving efficiency and accuracy as taught by Ross (Col 8 Line 27).
Regarding claim 15, Raghuraman does not expressly disclose but Ross discloses The spacecraft of claim 13, wherein each of the control invariant sets is a robust control invariant set determined for the nominal control law with a bounded non-stochastic uncertainty corresponding to the first likelihood on the unbounded stochastic uncertainty. (Col 13 Line 57-67 One non-limiting example will seek to reduce or minimize the stochastic uncertainty of the terminal state (i.e. the deviation from the selected target location 162 in FIG. 15 and point 8 in FIGS. 1 and 2), for example by computing the trace of the terminal covariance. That is, obtain a guidance and control policy 170 that minimizes J=trace(
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(tf)), where
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(t)=cov(x(t)) is the time varying covariance of the nominal state. In another possible embodiment, the user may seek to minimize the integrated trace of the covariance, i.e. j=∫ trace(
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42
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(t))dt. )
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Ross with a reasonable expectation of success by improving efficiency and accuracy as taught by Ross (Col 8 Line 27).
Regarding claim 16, Raghuraman does not expressly disclose but Ross discloses The feedback controller of claim 1, wherein the feedback controller is configured for model predictive control that determines the robust controllable set for maintaining the state of the system, starting from the current state of the system, within a prediction horizon defining a number of future control steps. (Col 30 Line 10-16 A guidance control policy obtained using the method of the present invention has thus provided a solution in which the chance of encountering a singularity is small so that feedback authority can be maintained despite the presence of system and other uncertainties.)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Ross with a reasonable expectation of success by improving efficiency and accuracy as taught by Ross (Col 8 Line 27).
Regarding claim 17, Raghuraman does not expressly disclose but Straub discloses The feedback controller of claim 16, wherein the system is a vehicle. ([0010] The subject matter described herein includes an attitude determination and control system (ADCS) and associated methods. Systems for determining attitude (e.g., orientation, angular position), may be used by airborne and space-based vehicles, such as to determine the vehicle's attitude relative to an external point of reference. For example, an airplane navigation system may determine the roll, pitch, and yaw of the aircraft relative to the earth. In another example, a spacecraft (e.g., space vehicle, satellite) may use an ADCS to determine and maintain a selected attitude, such as to keep a space-based camera facing Earth. This disclosure describes embodiments of the ADCS with respect to a vehicle. The present subject matter may apply to manned or unmanned spacecraft (e.g., space vehicles), Unmanned Aerial Vehicles (UAVs), aircraft, terrestrial vehicles, submersible vehicles, or other vehicles)
Therefore, it would have been obvious to a person having ordinary skill in the art before the effective filling date of the claimed invention to modify Raghuraman with the teachings of Straub with a reasonable expectation of success by creating and updating the movement model allows the ADCS to respond to changing conditions that affect the movement model as taught by Straub ([0011]).
Conclusion
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/S.A.T./Examiner, Art Unit 3656
/KHOI H TRAN/
Supervisory Patent Examiner, Art Unit 3656