Moment-Sum-Of-Squares Approach For Fast Risk Estimation In Uncertain Environments

10/03/2018
by   Ashkan Jasour, et al.
0

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.

READ FULL TEXT
research
10/01/2021

Real-Time Risk-Bounded Tube-Based Trajectory Safety Verification

In this paper, we address the real-time risk-bounded safety verification...
research
03/23/2021

Scenario-Based Trajectory Optimization in Uncertain Dynamic Environments

We present an optimization-based method to plan the motion of an autonom...
research
05/26/2023

Convex Risk Bounded Continuous-Time Trajectory Planning and Tube Design in Uncertain Nonconvex Environments

In this paper, we address the trajectory planning problem in uncertain n...
research
10/24/2021

Integrated Conditional Estimation-Optimization

Many real-world optimization problems involve uncertain parameters with ...
research
03/17/2020

Fast Certification of Collision Probability Bounds with Uncertain Convex Obstacles

To operate reactively in uncertain environments, robots need to be able ...
research
02/15/2023

RADIUS: Risk-Aware, Real-Time, Reachability-Based Motion Planning

Deterministic methods for motion planning guarantee safety amidst uncert...
research
06/26/2023

Probabilistic Risk Assessment of an Obstacle Detection System for GoA 4 Freight Trains

In this paper, a quantitative risk assessment approach is discussed for ...

Please sign up or login with your details

Forgot password? Click here to reset