Moment-Sum-Of-Squares Approach For Fast Risk Estimation In Uncertain Environments
This addresses risk estimation for robots in uncertain environments, offering a fast method for probabilistic collision checking, though it appears incremental as it builds on existing moment-based and sum-of-squares techniques.
The paper tackles the problem of estimating the probability of safety constraint violations for robots under bounded uncertainties with arbitrary distributions, using a moment-sum-of-squares approach to compute upper and lower bounds on risk in real-time based on finite moments.
In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this problem, an unsafe set is described by level sets of polynomials that is, in general, a non-convex set. Uncertainty arises due to the probabilistic parameters of the unsafe set and probabilistic states of the robot. To solve this problem, we use a moment-based representation of probability distributions. We describe upper and lower bounds of the risk in terms of a linear weighted sum of the moments. Weights are coefficients of a univariate Chebyshev polynomial obtained by solving a sum-of-squares optimization problem in the offline step. Hence, given a finite number of moments of probability distributions, risk can be estimated in real-time. We demonstrate the performance of the provided approach by solving probabilistic collision checking problems where we aim to find the probability of collision of a robot with a non-convex obstacle in the presence of probabilistic uncertainties in the location of the robot and size, location, and geometry of the obstacle.