A Navigation Function For Uncertain Environment

TL;DR

This paper presents a new motion planning algorithm that extends navigation functions to uncertain environments by incorporating probabilistic obstacle locations and geometric considerations, enabling safer robot navigation.

Contribution

It introduces a novel probabilistic navigation function that accounts for uncertainty in obstacle positions and geometry, advancing motion planning in stochastic scenarios.

Findings

The algorithm successfully navigates uncertain environments in various scenarios.

The proposed method provides a mathematically proven navigation function.

It effectively integrates probability density functions with geometric obstacle data.

Abstract

This paper introduces a novel motion planning algorithm for stochastic scenarios. We extend the concept of a navigation function to such scenarios. Our main idea is to consider both the Gaussian distribution probabilities of the players' locations and disc (or star sets) geometry of the objects operating in the work space. We do so by formulating a probability density function that encloses both. We use the PDF to define a metric between the robot, the obstacles and the configuration space boundary. In order to define the navigation function we formulate a safe probability value for collision. By analytically investigating the PDF we find a convenient approximation for a safe distance in the sense of that metric. We prove that the resulting map is a navigation function and demonstrate our algorithm for various scenarios.