Reactive Robot Navigation Using Quasi-conformal Mappings and Control Barrier Functions

TL;DR

This paper introduces a reactive robot navigation method that transforms complex obstacle environments into a simplified 'ball world' using quasi-conformal mappings, enabling safe, collision-free control with guarantees.

Contribution

The paper develops a novel mapping technique from polyhedral obstacles to ball-shaped regions, facilitating provably safe navigation with control barrier functions.

Findings

Effective obstacle transformation into ball regions

Provably safe navigation with safety guarantees

Validated through extensive simulations and experiments

Abstract

This paper presents a robot control algorithm suitable for safe reactive navigation tasks in cluttered environments. The proposed approach consists of transforming the robot workspace into the \emph{ball world}, an artificial representation where all obstacle regions are closed balls. Starting from a polyhedral representation of obstacles in the environment, obtained using exteroceptive sensor readings, a computationally efficient mapping to ball-shaped obstacles is constructed using quasi-conformal mappings and M\"obius transformations. The geometry of the ball world is amenable to provably safe navigation tasks achieved via control barrier functions employed to ensure collision-free robot motions with guarantees both on safety and on the absence of deadlocks. The performance of the proposed navigation algorithm is showcased and analyzed via extensive simulations and experiments performed using different types of robotic systems, including manipulators and mobile robots.