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

2026-04-18

AI Summary

This work addresses the problem of safely and smoothly navigating a unicycle robot from any feasible initial state to a goal in obstacle-rich environments under hard input constraints. The authors propose an online optimization-free safety-aware navigation framework that constructs a $C^\infty$-smooth vector field with reduced overall curvature and turning effort. By designing an analytical nonlinear feedback controller satisfying Nagumo’s theorem, the method inherently guarantees forward invariance of the safe set and asymptotic convergence to the target. Notably, safety and convergence are preserved even under strict input saturation. Simulation results demonstrate that, compared to baseline approaches, the proposed method reduces travel time by 50% and decreases angular control effort by more than 50%.

Technology Category

• Natural Language Processing: Safety and Robustness
• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Learning to Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• unicycle robot
• obstacle avoidance
• smooth control
• safety
• input constraints

Innovation

• Cinfinity-smooth vector field
• nonlinear feedback control
• Nagumo's theorem
• input-constrained navigation
• unicycle robot