GMPC: Geometric Model Predictive Control for Wheeled Mobile Robot Trajectory Tracking

TL;DR

This paper introduces a geometric model predictive control framework for wheeled mobile robots that respects the manifold constraints of robot configurations, leading to smoother trajectory tracking and efficient problem solving.

Contribution

It develops a Lie group-based MPC approach that considers manifold and kinematic constraints, improving trajectory tracking performance over existing methods.

Findings

More smooth trajectory tracking demonstrated in simulations and experiments.

Efficient convexification of the control problem using Lie algebra.

Publicly available Python simulation platform.

Abstract

The configuration of most robotic systems lies in continuous transformation groups. However, in mobile robot trajectory tracking, many recent works still naively utilize optimization methods for elements in vector space without considering the manifold constraint of the robot configuration. In this letter, we propose a geometric model predictive control (MPC) framework for wheeled mobile robot trajectory tracking. We first derive the error dynamics of the wheeled mobile robot trajectory tracking by considering its manifold constraint and kinematic constraint simultaneously. After that, we utilize the relationship between the Lie group and Lie algebra to convexify the tracking control problem, which enables us to solve the problem efficiently. Thanks to the Lie group formulation, our method tracks the trajectory more smoothly than existing nonlinear MPC. Simulations and physical experiments verify the effectiveness of our proposed methods. Our pure Python-based simulation platform is publicly available to benefit further research in the community.