Moment-Sum-of-Squares Approach for Fast Risk Estimation in Uncertain Environments
Name
1810.01577.pdf
Description
Submitted version
Size
808.27 KB
Format
Adobe PDF
Checksum (MD5)
6674a56734031ae80c67853a5e629a69
Author(s)
Jasour, Ashkan M.
Hofmann, Andreas
Williams, Brian C
Date Issued
January 21, 2019
Publisher
Institute of Electrical and Electronics Engineers
Citation
Jasour, Ashkan M. et al. "Moment-Sum-of-Squares Approach for Fast Risk Estimation in Uncertain Environments," 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, December 2018, Institute of Electrical and Electronics Engineers, 2019.
Version
Original manuscript
Abstract
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 nonconvex 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. Keywords: Probability distribution; Uncertainty; Chebyshev approximation; Optimization; Probabilistic logic; Estimation; Robots; collision avoidance; least squares approximations; mobile robots; optimisation; polynomials; set theory; statistical distributions
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/cdc.2018.8618744
