Energy-Time Optimal Trajectory Tracking Control of Wheeled Mobile Robots

This article focuses on the development of a Lyapunov stable controller for a wheeled mobile robot to track prescribed point-to-point trajectories. Exploiting the fact that the kinematic model of a wheeled mobile robot is differentially flat, a Lyapunov stable feedback controller is synthesized in the flat output space. A Tikhonov regularization based approach is proposed to deal with the potential singularity which can arise when mapping the flat space control signal to the coordinate control. Parallel parking maneuvers parameterized with Jacobi Elliptic functions serve as energy-time optimal benchmark trajectories to test and validate the performance of the proposed tracking controllers. The Pioneer 3-DX wheeled mobile robot serves as the testbed to implement the open-loop and feedback control strategies. Multiple point-to-point maneuvers are considered, and for each maneuver, multiple runs are conducted to determine the statistics of the performance of the controller. The nonlinear controller is shown to consistently outperform the linear controller.