Hybrid Model Predictive Control for the Stabilization of Wheeled Mobile Robots Subject to Wheel Slippage

This paper studies the problem of traction control, i.e., how to stabilize a wheeled mobile robot (WMR) subject to wheel slippage to a desired configuration. The WMR is equipped with a rechargeable battery pack which powers electric drives on each wheel. The drives propel the WMR in one mode of operation or recharge the battery pack (recover energy) in a second mode. These modes of operation are controlled, whereas wheel slippage, e.g., due to ice, is an autonomous mode change. The WMR can be thus modeled as a hybrid system with both controlled and autonomous switches. Model predictive control (MPC) for such systems, although robust, typically results in numerical methods of combinatorial complexity. We show that recently developed embedding techniques can be used to formulate numerical algorithms for the hybrid MPC problem that have the same complexity as MPC for smooth systems. We also discuss the numerical techniques that lead to efficient and robust MPC algorithms in detail. Simulations illustrate the effectiveness of the approach.