Mathematical certification of motion planning on uncertain terrain with limited perception: a case study

TL;DR

This paper presents a mathematical approach to certify motion planning for agents navigating uncertain terrains with limited perception, ensuring obstacle avoidance and target convergence.

Contribution

It introduces a control algorithm with formal guarantees for obstacle avoidance and convergence under uncertain and partially known environments.

Findings

Guaranteed obstacle avoidance under mild assumptions.

Proven convergence to the target.

Applicable to agents with limited perception and complex dynamics.

Abstract

We design a controller for an agent whose mission is to reach a stationary target while avoiding a family of obstacles which are not known a-priori. The agent moves in the two dimensional plane with non-trivial double integrator dynamics and receives only local information from its surroundings. Under mild assumptions on the family of obstacles (smoothness, sufficient distance from each other, bounded curvature, etc), we prove that our control algorithm yields guaranteed obstacle avoidance and convergence to the target.