Risk Contours Map for Risk Bounded Motion Planning under Perception Uncertainties
Ashkan M.Z. Jasour, Brian P. Williams · 2019
In this paper, we introduce "risk contours map" that contains the risk information of different regions in uncertain environments.Risk is defined as the probability of collision of robots with obstacles in presence of probabilistic uncertainties in location, size, and geometry of obstacles.We use risk contours to obtain safe paths for robots with guaranteed bounded risk.We formulate the problem of obtaining risk contours as a chance constrained optimization.We leverage the theory of moments and nonnegative polynomials to provide a convex optimization in the form of sum of squares optimization.Provided approach deals with nonconvex obstacles and probabilistic bounded and unbounded uncertainties.We demonstrate the performance of the provided approach by solving risk bounded motion planning problems.Such constraint involves a multivariate integral over a nonconvex set which is computationally challenging.In this paper, we provide a systematic numerical procedure to compute outer and inner approximations of ∆-risk contours for given uncertain obstacle and probability distributions of uncertainties.Remark 1: Although unsafe obstacles are defined by just one polynomial, the approach proposed in this paper can be extended to more complex sets involving multiple polynomials.This assumption is only done to simplify the exposition.