Correct-by-Construction Navigation Functions with Application to Sensor Based Robot Navigation

TL;DR

This paper introduces a correct-by-construction navigation function framework combining navigation transformation and harmonic functions, enabling autonomous robot navigation in unknown environments with real-time obstacle adaptation.

Contribution

It presents a novel explicit formulation of navigation functions related to obstacle count, allowing online adjustment and fast feedback control for robot navigation.

Findings

Navigation functions are explicitly related to obstacle number.

Framework enables real-time adaptation to new obstacles.

Simulation verifies effectiveness of the navigation scheme.

Abstract

This paper brings together the concepts of navigation transformation and harmonic functions to form navigation functions that are correct-by-construction in the sense that no tuning is required. The form of the navigation function is explicitly related to the number of obstacles in the environment. This enables application of navigation functions for autonomous robot navigation in partially or fully unknown environments, with the capability of on-the-fly adjustment of the navigation function when new obstacles are discovered by the robot. Appropriate navigation controllers, applicable to robots with local, sector bounded sensing, are presented and analyzed for a~kinematic point-mass robot and then for the dynamic point-mass robot system. The closed form nature of the proposed navigation scheme provides for online, fast-feedback based navigation. In addition to the analytic guarantees, simulation studies are presented to verify the effectiveness of the methodology.