Safe Navigation using Density Functions

TL;DR

This paper introduces a new method for safe robot navigation using analytically constructed density functions, enabling safe control synthesis in complex environments and high-dimensional spaces.

Contribution

It presents an analytical construction of density functions for safe navigation, overcoming limitations of traditional navigation and potential functions.

Findings

Proven convergence of the navigation method

Effective in cluttered environments

Applicable to high-dimensional robotic systems

Abstract

This paper presents a novel approach for safe control synthesis using the dual formulation of the navigation problem. The main contribution of this paper is in the analytical construction of density functions for almost everywhere navigation with safety constraints. In contrast to the existing approaches, where density functions are used for the analysis of navigation problems, we use density functions for the synthesis of safe controllers. We provide convergence proof using the proposed density functions for navigation with safety. Further, we use these density functions to design feedback controllers capable of navigating in cluttered environments and high-dimensional configuration spaces. The proposed analytical construction of density functions overcomes the problem associated with navigation functions, which are known to exist but challenging to construct, and potential functions, which suffer from local minima. Application of the developed framework is demonstrated on simple integrator dynamics and fully actuated robotic systems.