Continuous-time Chance-constrained Stochastic Model Predictive Control using Multiple Shooting and CVaR

In this paper, we address the continuous-time chance-constrained nonlinear Stochastic Model Predictive Control (SMPC) problem using Conditional Value at Risk (CVaR). Chance constraint directly enforces a user-specified upper bound for the probability of constraint violation. However, it is known that a chance constraint may be non-convex and intractable in general. CVaR is a risk measure that provides a convex approximation of chance constraints. In this paper, we first use the multiple shooting method for the stochastic systems in order to represent a continuous-time Optimal Control Problem (OCP) in a Nonlinear Programming (NLP) form. Then we use scenario tree sampling to deal with the disturbances. Wheeled Mobile Robot (WMR) path planning with obstacle avoidance will be considered to illustrate the efficiency of the method.