Method and apparatus for preconditioned predictive control of vehicle movement

Patent metadata

Field	Value
Publication number	US-10877445-B2
Application number	US-201916540368-A
Country	US
Kind code	B2
Filing date	Aug 14, 2019
Priority date	Feb 5, 2018
Publication date	Dec 29, 2020
Grant date	Dec 29, 2020

Abstract

A predictive controller controls a vehicle subject to equality and inequality constraints on state and control variables of the vehicle and solves a matrix equation of necessary optimality conditions to produce control inputs to control the vehicle. The controller represents the state variables as a function of the control variables using discrete-time dynamics and determines the control inputs iteratively using two levels of iterations. The first level of iterations selects active inequality constraints, updates a constraint Jacobian matrix with a low-rank update for a change in the set of active inequality constraints to include the active inequality constraints, and updates a preconditioning matrix with a low-rank factorization update, in response to the low-rank update of the constraint Jacobian matrix. The second level of iterations, nested in the first level, solves the matrix equation with the updated constraint Jacobian matrix using the updated preconditioning matrix to produce the control inputs.

First claim

We claim:

1. A predictive controller for controlling a movement of a vehicle subject to constraints including equality and inequality constraints on state variables and control variables of the vehicle, the predictive controller including a processor configured to execute components of the predictive controller, comprising:
an estimator to estimate a current state of the vehicle using measurements of the movement of the vehicle; and
a controller to solve, at each control step, a matrix equation of necessary optimality conditions to produce control inputs as values of the control variables in a control solution and to control the movement of the vehicle using the control inputs to change a state of the vehicle,
wherein the controller represents the state variables as a function of the control variables using discrete-time dynamics and determines the control inputs iteratively using two levels of iterations including a first level of iterations and a second level of iterations performed within an iteration of the first level of iterations,
wherein the first level of iterations, performed until a first termination condition is met,
selects active inequality constraints for each point of time within a control horizon,
updates a constraint Jacobian matrix of the matrix equation with a low-rank update for a change in the set of active inequality constraints, to include the active inequality constraints, and
updates a preconditioning matrix, with a low-rank factorization update, in response to the low-rank update of the constraint Jacobian matrix,

wherein the second level of iterations, performed until a second termination condition is met, solves the matrix equation with the updated constraint Jacobian matrix using the updated preconditioning matrix to produce the control inputs.

2. The predictive controller of claim 1 , wherein an inequality constraint is active at a point of time when a constraint function of the inequality constraint is equal to a constraint bound of the inequality constraint at the point of time, wherein the first level of iterations selects the set of active inequality constraints based on the current state of the vehicle and a current sequence of control inputs.

3. The predictive controller of claim 2 , wherein the first termination condition includes a feasibility of the control solution and an optimality of the control solution,
wherein the controller tests the optimality and the feasibility of the control solution and exits the first level of iterations when the first termination condition is met, otherwise,
wherein the control solution is not optimal, the controller removes the active inequality constraint having a negative dual variable that prevents optimality of the control solution and repeats the first level of iterations, and otherwise,
wherein the control solution is not feasible, the controller updates the current sequence of control inputs with feasible portion of the control solution, adds a blocking inequality constraint in the set of active inequality constraints, and repeats the first level of iterations.

4. The predictive controller of claim 3 , wherein the controller, in response to adding the blocking inequality constraint, adds a row in the constraint Jacobian matrix with a first function of coefficients of the blocking inequality constraint and updates the preconditioning matrix with a second function of the coefficients of the blocking inequality constraint.

5. The predictive controller of claim 4 , wherein the controller, in response to removing the active inequality constraint, removes a row in the constraint Jacobian matrix that corresponds to the removed active inequality constraint and updates the preconditioning matrix with a reverse of the second function.

6. The predictive controller of claim 1 , wherein each change in the set of active inequality constraints corresponds to only one constraint being either added or removed, which leads to a rank-one factorization update for the preconditioning matrix, in response to the rank-one update of the constraint Jacobian matrix.

7. The predictive controller of claim 1 , wherein the preconditioning matrix is updated or evaluated using a reduced arithmetic precision, compared to the arithmetic precision that is used for the matrix equation.

8. The predictive controller of claim 1 , wherein the preconditioning matrix has a sparsity structure, wherein the controller updates the factorization of the preconditioning matrix while preserving the sparsity structure.

9. The predictive controller of claim 1 , wherein the low-rank factorization update is a low-rank update of a Cholesky factorization.

10. The predictive controller of claim 1 , wherein, for a current control step, the controller initializes the Jacobian matrix and the factorization of the preconditioning matrix with values of the Jacobian matrix and the factorized preconditioning matrix determined during a previous control step.

11. The predictive controller of claim 1 , wherein the preconditioning matrix is an augmented Lagrangian block-diagonal matrix, and wherein the second level of iterations solves the matrix equation using a minimal residual method.

12. The predictive controller of claim 1 , wherein the preconditioning matrix is a Schur complement block-diagonal matrix, and wherein the second level of iterations solves the matrix equation using a minimal residual method.

13. The predictive controller of claim 12 , wherein the controller regularizes a Hessian of the matrix of the matrix equation to produce a positive definite approximation of the Hessian of the matrix, and wherein the controller determines elements of the Schur complement block-diagonal matrix based on the approximation of the Hessian of the matrix.

14. The predictive controller of claim 1 , wherein the preconditioning matrix is a constraint preconditioner, and wherein the second level of iterations solves the matrix equation using a projected conjugate gradient method.

15. The predictive controller of claim 14 , wherein the controller regularizes a Hessian of the matrix of the matrix equation to produce a positive definite approximation of the Hessian of the matrix, and wherein the controller determines elements of the constraint preconditioner based on the approximation of the Hessian of the matrix.

16. The predictive controller of claim 1 , wherein the control inputs to the vehicle includes one or a combination of a velocity of the vehicle, an acceleration of the vehicle, a torque of one or more engines of the vehicle, a torque of one or more electric propulsion motors of the vehicle, a steering angle of one or more wheels of the vehicle, a torque of a power steering system of a vehicle, and a driving torque of one or more wheels of the vehicle.

17. A vehicle including the predictive controller of claim 1 .

18. The vehicle of claim 17 , further comprising:
a low-level controller to accept the control inputs form the predictive controller to control at least one actuator of the vehicle, wherein the low-level controller includes one or combination of a steering controller to control a steering of the vehicle, a brake controller to control deceleration of the vehicle, a throttle controller to control an acceleration or a propulsion torque of the vehicle.

19. The vehicle of claim 17 , further comprising:
a motion planner configured to submit a desired motion command to the predictive controller, such that the control inputs determined by the predictive controller cause the vehicle to follow the desired motion command.

Assignees

• Mitsubishi Electric Res Laboratories Inc

Inventors

• Quirynen Rien
• Kniazev Andrei
• Di Cairano Stefano

Classifications

• G05B13/048 Primary

  using a predictor · CPC title

• G06F17/16

  Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)} · CPC title

• G06F17/11

  for solving equations {, e.g. nonlinear equations, general mathematical optimization problems (optimization specially adapted for a specific administrative, business or logistic context G06Q10/04)} · CPC title

• B25J9/1607

  Calculation of inertia, jacobian matrixes and inverses · CPC title

• G06F16/23

  Updating · CPC title