A Smooth Penalty-Based Feedback Law for Reactive Obstacle Avoidance with Convergence Guarantees

TL;DR

This paper introduces a smooth, penalty-based feedback control law for autonomous obstacle avoidance that guarantees safety and stability without requiring environment maps, using only local sensory data.

Contribution

It presents a novel smooth feedback controller derived from an unconstrained penalty formulation, ensuring safety and stability in obstacle-rich environments without map reliance.

Findings

Guarantees safety by construction through a smooth feedback law.

Achieves almost global asymptotic stability to the goal.

Demonstrates effectiveness in complex 2D and 3D simulations.

Abstract

This paper addresses the problem of safe autonomous navigation in unknown obstacle-filled environments using only local sensory information. We propose a smooth feedback controller derived from an unconstrained penalty-based formulation that guarantees safety by construction. The controller modifies an arbitrary nominal input through a closed-form expression. The resulting closed-form feedback has a projection structure that interpolates between the nominal control and its orthogonal projection onto the obstacle boundary, ensuring forward invariance of a user-defined safety margin. The control law depends only on the distance and bearing to obstacles and requires no map, switching, or set construction. When the nominal input is a gradient descent of a navigation potential, we prove that the closed-loop system achieves almost global asymptotic stability (AGAS) to the goal. Undesired equilibria are shown to be unstable under a mild geometric curvature condition, which compares the normal curvature of the obstacle boundary with that of the potential level sets. We refer to the proposed method as SPF (Safe Penalty-based Feedback), which ensures safe and smooth navigation with minimal computational overhead, as demonstrated through simulations in complex 2D and 3D environments.