Stable Model-Based Predictive Control for Wheeled Mobile Robots using Linear Matrix Inequalities

Abstract

This paper presents practical results from the application of a new synthesis methodology based on model predictive control (MPC) applied to a three-wheeled omnidirectional mobile robot seeking to follow pre-established trajectories. The approach is based on the definition of an objective function with a finite future time horizon. The resulting optimization problem is declared in the form of linear matrix inequalities (LMIs). The closed loop stability of the system is guaranteed through constraints related to the non-increasing monotonicity of the objective function. Constraints are also implemented in the manipulated variables with the objective of adapting the control system to the physical limitations of the robot. Additionally, methods are described to handle the computational delay in the robot model and to adjust the control law to improve the global performance of the system.