Unscented model predictive control of chance constrained nonlinear systems

Abstract

This paper introduces an unscented model predictive approach for the control of constrained nonlinear systems under uncertainty. The main contribution of this paper is related to incorporation of statistical linearization, rather than commonly used analytical linearization, of the process and measurement models to provide a closer approximation of belief space propagation. Specifically, the state transition is approximated using an unscented transform to obtain a Gaussian belief space. This approximation allows for realization of closed-form solutions, which are otherwise available to linear systems only. Subsequently, the proposed approach is used to develop a model predictive motion control scheme that yields optimal control policies in presence of nonholonomic constraints as well as state estimation and collision avoidance chance constraints. As an example, successful kinematic control of a two-wheeled mobile robot is demonstrated in unstructured environments. Finally, the superiority of the proposed unscented model predictive control (MPC) over the traditional linearization-based MPC is discussed.