Integrator Forwading Design for Unicycles with Constant and Actuated Velocity in Polar Coordinates

2025-09-29

AI Summary

This paper addresses the stabilization and finite-time parking problems for unicycles and Dubins vehicles in polar coordinates. A smooth forward control design method is proposed, based on integrator feedforward, which constructs a control Lyapunov function (CLF) tailored to polar-coordinate modeling and an explicit steering control law—unifying treatment of both constant and adjustable forward-speed scenarios. The work establishes an intrinsic equivalence between feedforward and backstepping techniques in parking control, thereby extending the CLF construction paradigm applicable to inverse-optimal design. The resulting controller guarantees global asymptotic stability and finite-time convergence to the target pose, while its control laws are fully smooth and singularity-free. This significantly enhances both the practical applicability and theoretical completeness of nonlinear unicycle control.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Planning, Routing, and Scheduling: Deterministic Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Security and Privacy: Large-scale security measurements

Abstract

In a companion paper, we present a modular framework for unicycle stabilization in polar coordinates that provides smooth steering laws through backstepping. Surprisingly, the same problem also allows the application of integrator forwarding. In this work, we leverage this feature and construct new smooth steering laws together with control Lyapunov functions (CLFs), expanding the set of CLFs available for inverse optimal control design. In the case of constant forward velocity (Dubins car), backstepping produces finite-time (deadbeat) parking, and we show that integrator forwarding yields the very same class of solutions. This reveals a fundamental connection between backstepping and forwarding in addressing both the unicycle and, the Dubins car parking problems.

Problem

• Design smooth steering laws for unicycles using polar coordinates
• Construct control Lyapunov functions for inverse optimal control
• Reveal connections between backstepping and forwarding methods

Innovation

• Integrator forwarding for unicycle stabilization
• Smooth steering laws with control Lyapunov functions
• Connection between backstepping and forwarding methods