Stability Guaranteed MPC for Mobile Robot Navigation (Extended Abstract)

A mobile robot needs to navigate in dynamic and unstructured environments. For this, motion planning algorithms must be able to handle complex, time-varying constraints presented by the environment, and quickly generate high quality trajectories that reaches the goal. Model Predictive Control (MPC) is a receding-horizon control algorithm which optimizes the performance of the constrained systems on-line. (See (Rawlings 2000) (Mayne et al. 2000) (Lee 2011) for excellent reviews.) This can be a very useful tool for mobile robot navigation in dynamic environments due to its dynamic replanning framework, its ability to handle complex time-varying constraints, and its flexible formulation which allows the user to tune the behavior of the system to desired performance. Thus the MPC and MPC-like dynamic replanning framework are becoming more popular in robotics community, e.g. (Green and Kelly 2007) (Howard, Green, and Kelly 2009) (Dolgov et al. 2010) (Knepper and Mason 2012) (Du Toit and Burdick 2012) (Park, Johnson, and Kuipers 2012). However, it can be difficult to ensure stability and temporal consistency of solutions, especially for systems with differential constraints. In this paper, we show that it is possible to provide a stability guarantee for MPC for mobile robots that can be modeled as unicycles (e.g. differentially driven carts) with a proper estimate of the cost-to-go. This critically depends on our non-holonomic distance function, which is also a control-Lyapunov function for unicycle-type vehicles. This allows us to properly estimate the cost-to-go for unicycletype vehicles, and ensure convergence via MPC. We show theoretical and numerical analysis on the stability conditions.