Approximate Quadratic Programming Algorithm for Nonlinear Model Predictive Tracking Control of a Wheeled Mobile Robot

Abstract

Nonlinear model predictive control (NMPC) has proven its ability to control constrained nonlinear processes. Although NMPC can achieve exemplary tracking performance, the related computation effort as well as guaranteeing tracking convergence are its main drawbacks. Indeed, constrained NMPC is a nonlinear and nonconvex optimization problem where it is difficult to find a feasible solution within a reasonable time. Motivated by these difficulties, this study proposes a procedure, using the Euler approximation, to transform the nonlinear optimization problem of NMPC into a constrained quadratic optimization problem. The proposed tracking controller is applied to the autonomous navigation problem of a wheeled mobile robot (WMR) in a constrained space. Under certain assumptions, we prove the closed-loop system stability and boundedness of the tracking error. Furthermore, we demonstrate the recursive feasibility of the solution. Simulations are performed, first to determine the adequate control parameters, and second, to demonstrate the effectiveness of the proposed algorithm, while its real-time implementation is experimentally verified using a differential drive mobile robot.

Keywords

• Nonlinear predictive control algorithm
• state and control signal constraints
• convex optimization
• stability
• and feasibility analysis
• wheeled mobile robot