# Efficient Probabilistic Collision Detection for Non-Gaussian Noise Distributions

## TL;DR

This paper introduces an efficient algorithm for computing tight upper bounds on collision probabilities between objects with non-Gaussian positional uncertainties, improving accuracy and speed for robotic motion planning.

## Contribution

The paper presents a novel method for probabilistic collision detection with non-Gaussian noise, extending to non-convex shapes and demonstrating significant improvements over prior methods.

## Key findings

- Tighter collision probability bounds (10x)
- Faster computation (3x)
- Effective motion planning for robot arms in uncertain environments

## Abstract

We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy datasets from depth sensors, whose distributions may correspond to Truncated Gaussian, Weighted Samples, or Truncated Gaussian Mixture Model. We derive tight probability bounds for convex shapes and extend them to non-convex shapes using hierarchical representations. We highlight the benefits of our approach over prior probabilistic collision detection algorithms in terms of tighter bounds ($10$x) and improved running time ($3$x). Moreover, we use our tight bounds to design an efficient and accurate motion planning algorithm for a 7-DOF robot arm operating in tight scenarios with sensor and motion uncertainties.