Proofs of the Technical Results Justifying an Algorithm for Collision Avoidance in Dynamic Environments with Moving and Deforming Obstacles

TL;DR

This paper provides rigorous proofs for a new reactive navigation algorithm enabling differential drive robots to safely navigate dynamic, deformable, and uncertain environments using minimal information, specifically only the nearest obstacle distance.

Contribution

It offers the first formal proofs for an algorithm that guarantees collision avoidance without requiring obstacle shape, velocity, or environment mapping.

Findings

Proves convergence and safety of the navigation algorithm.

Shows effectiveness in environments with deformable and moving obstacles.

Does not rely on obstacle shape or velocity data.

Abstract

This text presents the proofs of the technical facts underlying theoretical justification of the convergence and performance of the novel algorithm for reactive navigation of differential drive wheeled robots in dynamic uncertain environments. The algorithm restricts neither the natures nor the motions of the obstacles, they need not be rigid but conversely may deform. It does not consume data about the velocities, shapes, sizes, or orientations of the obstacles, and does not need a map of the environment or recognition of individual obstacles. The only information about the scene is the current distance to the nearest obstacle.