Minimum Time Strategies for a Differential Drive Robot Escaping from a Circular Detection Region

TL;DR

This paper analyzes optimal escape strategies for a differential drive robot from a circular detection zone, considering different scenarios and using differential game theory to identify time-minimizing motions.

Contribution

It formulates the escape problem as a pursuit-evasion game and derives optimal strategies depending on speed ratios and initial positions.

Findings

The robot can always escape if it moves at maximum speed away from the center.

Optimal strategies depend on the relative speeds and initial configurations.

Previous simple strategies are sometimes optimal, but others emerge based on conditions.

Abstract

A Differential Drive Robot (DDR) located inside a circular detection region in the plane wants to escape from it in minimum time. Various robotics applications can be modeled like the previous problem, such as a DDR escaping as soon as possible from a forbidden/dangerous region in the plane or running out from the sensor footprint of an unmanned vehicle flying at a constant altitude. In this paper, we find the motion strategies to accomplish its goal under two scenarios. In one, the detection region moves slower than the DDR and seeks to prevent escape; in another, its position is fixed. We formulate the problem as a zero-sum pursuit-evasion game, and using differential games theory, we compute the players' time-optimal motion strategies. Given the DDR's speed advantage, it can always escape by translating away from the center of the detection region at maximum speed. In this work, we show that the previous strategy could be optimal in some cases; however, other motion strategies emerge based on the player's speed ratio and the players' initial configurations.