Two-stage Optimization Approach to Robust Model Predictive Control with a Joint Chance Constraint
When controlling dynamic systems such as mobile robots in uncertain environments, there is a trade off between risk and reward. For example, a race car can turn a corner faster by taking a more challenging path. This paper proposes a new approach to planning a control sequence with guaranteed risk bound. Given a stochastic dynamic model, the problem is to find a control sequence that optimizes a performance metric, while satisfying chance constraints i.e. constraints on the upper bound of the probability of failure. We propose a two-stage optimization approach, with the upper stage optimizing the risk allocation and the lower stage calculating the optimal control sequence that maximizes the reward. In general, upper-stage is a non-convex optimization problem, which is hard to solve. We develop a new iterative algorithm for this stage that efficiently computes the risk allocation with a small penalty to optimality. The algorithm is implemented and tested on the autonomous underwater vehicle (AUV) depth planning problem, which demonstrates the substantial improvement in computation cost and suboptimality compared to the prior arts.