System and method for controlling an operation of a machine including at least one actuator

Patent metadata

Field	Value
Publication number	US-12422824-B2
Application number	US-202318107579-A
Country	US
Kind code	B2
Filing date	Feb 9, 2023
Priority date	Feb 9, 2023
Publication date	Sep 23, 2025
Grant date	Sep 23, 2025

Abstract

The present disclosure discloses a system and a method for controlling an operation of a machine including at least one actuator. The method comprises obtaining a time period of an operation of the at least one actuator, collecting an energy level of the at least one actuator, and determining one or more hyperparameters of a time bound function such that a value of the time bound function is greater than or equal to the time period of the operation of the at least one actuator. The method further comprises solving an optimal control problem optimizing a cost function of the operation of the at least one actuator using an adaptive gradient descent method that is initialized with the collected energy level and a constant defined based on the one or more hyperparameters and controlling the at least one actuator based on a solution of the optimal control problem.

First claim

The invention claimed is:

1. A controller for controlling an operation of a machine including at least one actuator, the controller comprising: a processor; and a memory having instructions stored thereon that, when executed by the processor, cause the controller to:
obtain a time period of an operation of the at least one actuator;
collect an energy level of the at least one actuator, wherein the energy level of the at least one actuator corresponds to a difference between a current state of the at least one actuator and a desired state of the at least one actuator;
determine values of one or more hyperparameters of a time bound function such that a value of the time bound function is greater than or equal to the time period of the operation of the at least one actuator;
solve an optimal control problem optimizing a cost function of the operation of the at least one actuator using an adaptive gradient descent method, wherein the adaptive gradient descent method is initialized with the collected energy level and a constant defined based on the values of one or more hyperparameters, and wherein the adaptive gradient descent method includes a varying step size selected based on a derivative of an energy function of the optimal control problem defined such that the derivative of the energy function of the optimal control problem is negative definite and polynomially decreasing; and
control the at least one actuator based on the solution of the optimal control problem.

2. The controller of claim 1 , wherein the varying step-size is inversely proportional to a 2-norm of a gradient of the cost function.

3. The controller of claim 1 , wherein the varying step-size is a function of a component-wise sign function of a gradient of the cost function.

4. The controller of claim 1 , wherein the processor is further configured to switch between the varying step-size and a constant step-size, based on a value of a state-dependent switching constant.

5. The controller of claim 4 , wherein the value of the state-dependent switching constant is based on a 2-norm of a gradient of the cost function.

6. The controller of claim 5 , wherein the value of the state-dependent switching constant corresponds to a numerical constant if the 2-norm of the gradient of the cost function is less than a positive threshold coefficient.

7. The controller of claim 6 , wherein the state-dependent switching constant corresponds to a state-dependent function if the 2-norm of the gradient of the cost function is greater than the positive threshold coefficient.

8. The controller of claim 1 , wherein the optimal control problem is a constrained optimization problem.

9. The controller of claim 8 , wherein the processor is further configured to transform the constrained optimization problem into an unconstrained optimization problem.

10. The controller of claim 1 , wherein the processor is further configured to compute a gradient of the cost function based on numerical differentiation of the cost function.

11. The controller of claim 1 , wherein the processor is further configured to compute a gradient of the cost function based on a gradient computation filter.

12. The controller of claim 1 , wherein the machine includes a plurality of robots for performing a sequence of operations, and wherein the processor is configured to control an operation of each robot based on a solution of the corresponding optimal control problem to synchronously perform the sequence of operations.

13. A method for controlling an operation of a machine including at least one actuator, the method comprising:
obtaining a time period of an operation of the at least one actuator;
collecting an energy level of the at least one actuator, wherein the energy level of the at least one actuator corresponds to a difference between a current state and a desired state of the at least one actuator;
determining values of one or more hyperparameters of a time bound function such that a value of the time bound function is greater than or equal to the time period of the operation of the at least one actuator;
solving an optimal control problem optimizing a cost function of the operation of the at least one actuator using an adaptive gradient descent method, wherein the adaptive gradient descent method is initialized with the collected energy level and a constant defined based on the values of one or more hyperparameters, and wherein the adaptive gradient descent method includes a varying step size selected based on a derivative of an energy function of the optimal control problem defined such that the derivative of the energy function of the optimal control problem is negative definite and polynomially decreasing; and
controlling the at least one actuator based on the solution of the optimal control problem.

14. The method of claim 13 , wherein the varying step-size is inversely proportional a 2-norm of a gradient of the cost function.

15. The method of claim 13 , wherein the varying step-size is a function of a component-wise sign function of a gradient of the cost function.

16. The method of claim 13 , wherein the method further comprises switching between the varying step-size and a constant step-size, based on a value of a state-dependent switching constant.

17. The method of claim 16 , wherein the value of the state-dependent switching constant is based on a 2-norm of a gradient of the cost function.

18. The method of claim 17 , wherein the value of the state-dependent switching constant corresponds to a numerical constant if the 2-norm of the gradient of the cost function is less than a positive threshold coefficient.

19. The method of claim 18 , wherein the state-dependent switching constant corresponds to a state-dependent function if the 2-norm of the gradient of the cost function is greater than the positive threshold coefficient.

20. A non-transitory computer-readable storage medium embodied thereon a program executable by a processor for performing a method for controlling an operation of a machine including at least one actuator, the method comprising:
obtaining a time period of an operation of the at least one actuator;
collecting an energy level of the at least one actuator, wherein the energy level of the at least one actuator corresponds to a difference between a current state and a desired state of the at least one actuator;
determining values of one or more hyperparameters of a time bound function such that a value of the time bound function is greater than or equal to the time period of the operation of the at least one actuator;
solving an optimal control problem optimizing a cost function of the operation of the at least one actuator using an adaptive gradient descent method, wherein the adaptive gradient descent method is initialized with the collected energy level and a constant defined based on the values of one or more hyperparameters, and wherein the adaptive gradient descent method includes a varying step size selected based on a derivative of an energy function of the optimal control problem defined such that the derivative of the energy function of the optimal control problem is negative definite and polynomially decreasing; and
controlling the at least one actuator based on the solution of the optimal control problem.

Assignees

• Mitsubishi Electric Res Laboratories Inc

Inventors

• Benosman Mouhacine
• Zhang Siqi

Classifications

• G05B13/0235

  using steepest descent or ascent method · CPC title

• G05B2219/31372

  Mes manufacturing execution system · CPC title

• G05B19/4155 Primary

  characterised by program execution, i.e. part program or machine function execution, e.g. selection of a program · CPC title