Moment-Based Model Predictive Control of Autonomous Systems

Great efforts have been devoted to the intelligent control of autonomous systems. Yet, most of existing methods fail to effectively handle the uncertainty of their environment and models. Uncertain locations of dynamic obstacles pose a major challenge for their optimal control and safety, while their linearization or simplified system models reduce their actual performance. To address them, this paper presents a new model predictive control framework with finite samples and a Gaussian model, resulting in a chance-constrained program. Its nominal model is combined with a Gaussian process. Its residual model uncertainty is learned. The resulting method addresses an efficiently solvable approximate formulation of a stochastic optimal control problem by using approximations for efficient computation. There is no perfect distribution knowledge of a dynamic obstacle's location uncertainty. Only finite samples from sensors or past data are available for moment estimation. We use the uncertainty propagation of a system's state and obstacles' locations to derive a general collision avoidance condition under tight concentration bounds on the error of the estimated moments. Thus, this condition is suitable for different obstacles, e.g., bounding box and ellipsoid obstacles. We provide proved guarantees on the satisfaction of the chance-constraints corresponding to the nominal yet unknown moments. Simulation examples of a vehicle's control are used to show that the proposed method can well realize autonomous control and obstacle avoidance of a vehicle, when it operates in an uncertain environment with moving obstacles. It outperforms the existing moment methods in both performance and computational time.