Navigating Discrete Difference Equation Governed WMR by Virtual Linear Leader Guided HMPC

In this paper, we revisit model predictive control (MPC) for the classical wheeled mobile robot (WMR) navigation problem. We prove that the reachable set based hierarchical MPC (HMPC), a state-of-the-art MPC, cannot handle WMR navigation in theory due to the non-existence of non-trivial linear system with an under-approximate reachable set of WMR. Nevertheless, we propose a virtual linear leader guided MPC (VLL-MPC) to enable HMPC structure. Different from current HMPCs, we use a virtual linear system with an under-approximate path set rather than the traditional trace set to guide the WMR. We provide a valid construction of the virtual linear leader. We prove the stability of VLL-MPC, and discuss its complexity. In the experiment, we demonstrate the advantage of VLL-MPC empirically by comparing it with NMPC, LMPC and anytime RRT* in several scenarios.