Planning Smooth and Safe Control Laws for a Unicycle Robot Among Obstacles

TL;DR

This paper introduces a novel control framework for safe, smooth navigation of a unicycle robot among obstacles, ensuring convergence to a goal with reduced effort and faster arrival times.

Contribution

It develops a new QP-based smooth vector field and an analytic controller that guarantees safety and convergence without online optimization.

Findings

Controller safely converges to the goal under input limits.

Simulations show twice faster arrival time and over 50% lower control effort.

Framework effectively navigates among obstacles in various scenarios.

Abstract

This paper presents a framework for safe navigation of a unicycle point robot to a goal position in an environment populated with obstacles from almost any admissible state, considering input limits. We introduce a novel QP formulation to create a Cinfinity-smooth vector field with reduced total bending and total turning. Then we design an analytic, non-linear feedback controller that inherently satisfies the conditions of Nagumo's theorem, ensuring forward invariance of the safe set without requiring any online optimization. We have demonstrated that our controller, even under hard input limits, safely converges to the goal position. Simulations confirm the effectiveness of the proposed framework, resulting in a twice faster arrival time with over 50\% lower angular control effort compared to the baseline.