Sampling-Based Model Predictive Control Focusing on the Asymmetry of Kullback-Leibler Divergence

Abstract

Model Predictive Control (MPC) is one of the effective control methods for complex systems such as automatic driving and robotics. As one of the MPC solvers, the cross-entropy method (CEM) is well known as the most flexible and general method. Although CEM can be applied to most systems, it requires a sufficient (theoretically infinite) number of samples and updates for convergence, resulting in extremely high computational cost. Therefore, we focus on the asymmetry of the Kullback-Leibler divergence used in the minimization problem of CEM, and propose a new algorithm for CEM by redefining its minimization problem, so-called risk aversion CEM (RA-CEM). RA-CEM allows the function that can be regarded as a weight for the sampled trajectory to take negative values, so that even with a small iteration, the algorithm actively avoids trajectories with poor performance and prioritizes convergence to trajectories with good performance. In a highway driving simulation, RA-CEM improved the success rate from the standard CEM.