Exact and Bounded Collision Probability for Motion Planning under Gaussian Uncertainty

TL;DR

This paper introduces an exact method and a tight upper bound for calculating collision probabilities in motion planning under Gaussian uncertainty, improving safety and computational efficiency.

Contribution

It presents the first exact collision probability computation for ellipsoidal shapes under Gaussian uncertainty, along with a faster upper bound for real-time planning.

Findings

Exact collision probability computation is feasible for ellipsoids.

The upper bound significantly reduces computation time.

Method outperforms existing approaches in simulations.

Abstract

Computing collision-free trajectories is of prime importance for safe navigation. We present an approach for computing the collision probability under Gaussian distributed motion and sensing uncertainty with the robot and static obstacle shapes approximated as ellipsoids. The collision condition is formulated as the distance between ellipsoids and unlike previous approaches we provide a method for computing the exact collision probability. Furthermore, we provide a tight upper bound that can be computed much faster during online planning. Comparison to other state-of-the-art methods is also provided. The proposed method is evaluated in simulation under varying configuration and number of obstacles.