2018/10/03 by Ashkan Jasour, Jasour, Ashkan, Andreas Hofmann +3 · 1 citation
Computer Science · Decision Sciences · Engineering · #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Robotics (cs.RO) #Software Reliability and Analysis Research #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1810.01577
openalex publication_date 2018/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we address the risk estimation problem where one aims at\nestimating the probability of violation of safety constraints for a robot in\nthe presence of bounded uncertainties with arbitrary probability distributions.\nIn this problem, an unsafe set is described by level sets of polynomials that\nis, in general, a non-convex set. Uncertainty arises due to the probabilistic\nparameters of the unsafe set and probabilistic states of the robot. To solve\nthis problem, we use a moment-based representation of probability\ndistributions. We describe upper and lower bounds of the risk in terms of a\nlinear weighted sum of the moments. Weights are coefficients of a univariate\nChebyshev polynomial obtained by solving a sum-of-squares optimization problem\nin the offline step. Hence, given a finite number of moments of probability\ndistributions, risk can be estimated in real-time. We demonstrate the\nperformance of the provided approach by solving probabilistic collision\nchecking problems where we aim to find the probability of collision of a robot\nwith a non-convex obstacle in the presence of probabilistic uncertainties in\nthe location of the robot and size, location, and geometry of the obstacle.\n