Distributionally robust model predictive control for constrained robotic manipulators based on neural network modeling

doi:10.1007/s10483-024-3191-6

Abstract

Abstract:

A distributionally robust model predictive control (DRMPC) scheme is proposed based on neural network (NN) modeling to achieve the trajectory tracking control of robot manipulators with state and control torque constraints. First, an NN is used to fit the motion data of robot manipulators for data-driven dynamic modeling, converting it into a linear prediction model through gradients. Then, by statistically analyzing the stochastic characteristics of the NN modeling errors, a distributionally robust model predictive controller is designed based on the chance constraints, and the optimization problem is transformed into a tractable quadratic programming (QP) problem under the distributionally robust optimization (DRO) framework. The recursive feasibility and convergence of the proposed algorithm are proven. Finally, the effectiveness of the proposed algorithm is verified through numerical simulation.

Key words: robotic manipulator, trajectory tracking control, neural network (NN), distributionally robust optimization (DRO), model predictive control (MPC)

2010 MSC Number:

93C85

Yiheng YANG, Kai ZHANG, Zhihua CHEN, Bin LI. Distributionally robust model predictive control for constrained robotic manipulators based on neural network modeling. Applied Mathematics and Mechanics (English Edition), 2024, 45(12): 2183-2202.

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State	Method
State	NN-RMPC	NN-DRMPC	Robot-DRMPC	Robot-FA
$q_1$	0	0	0	0
$q_2$	0	0	0	0
$\dot{q}_1$	0	0	0	1 000
$\dot{q}_2$	0	16	804	1 000
$u_1$	0	0	0	0
$u_2$	0	0	0	0
Percentage	0.0%	1.6%	80.4%	100.0%

State	Method
State	NN-RMPC	NN-DRMPC	Robot-DRMPC	Robot-FA
$q_1$	0	0	0	0
$q_2$	0	0	0	0
$\dot{q}_1$	0	47	133	464
$\dot{q}_2$	0	1	0	45
$u_1$	0	0	0	0
$u_2$	0	0	0	0
Percentage	0.0%	4.7%	13.3%	46.4%