Approximate convex hull based scenario truncation for chance constrained trajectory optimization

Abstract

In this paper, we study chance constrained trajectory optimization of linear systems with general ellipsoidal and polytopic state-input constraints where the constraints must be met with some prescribed confidence level. We use the sampling techniques, specifically scenario approach, due to their generality and tractability compared to the analytical methods. To address the main drawback of scenario approach, which may require large number of samples, we introduce an approximate convex hull-based method to significantly reduce the number of samples. Based on the allowable computational complexity, the prominent samples are selected in a proper mapping and the rest are truncated. The truncation error is later compensated for by adjusting (buffering) the constraint set, so that the satisfaction of constraints with the desired confidence level is still guaranteed. Simulation results confirm the theoretical predictions with solid performance of the proposed method after discarding about 99% of samples from the scenario approach, which remarkably speeds up the online computations.