  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.
