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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.

Risk Contours Map for Risk Bounded Motion Planning under Perception Uncertainties