Finite-Time Curvature-Constrained Vector Field for Saturation-Free Motion Planning of Nonholonomic Robots

2026-07-20

AI Summary

This work addresses the challenge of achieving finite-time accurate pose control for nonholonomic mobile robots under curvature constraints and actuator limitations. Existing vector field approaches typically guarantee only asymptotic convergence and rely on input saturation, which can compromise stability. To overcome these issues, this paper proposes a framework combining a finite-time curvature-constrained vector field (FT-C²VF) with a saturation-free, smooth control law. The approach introduces, for the first time, a vector field that is curvature-continuous, bounded, and monotonically decreasing with respect to the radial ratio, ensuring finite-time convergence. A nearly globally C¹-smooth, Jacobian-free, saturation-free controller is designed to enforce actuator constraints while achieving almost global finite-time stability. Simulations and real-world experiments with an Ackermann-steered vehicle demonstrate superior performance over representative vector field methods, confirming the method’s effectiveness and robustness.

Abstract

Accurately steering a robot to a target configuration is fundamental in engineering, yet remains challenging for nonholonomic mobile robots. Vector fields (VFs) provide a natural framework by specifying desired motion directions throughout the workspace and enabling direct integration with feedback control. However, most existing VF-based methods cannot explicitly generate trajectories satisfying curvature constraints. Actuator limits are therefore often enforced by input saturation, which may invalidate stability guarantees and degrade closed-loop performance when not considered in controller design. In addition, these methods usually ensure only asymptotic convergence without an explicit settling-time bound. To address these issues, we propose a generalized motion planning and control framework consisting of a finite-time curvature-constrained vector field (FT-C2VF) and a saturation-free control law. Depending on the motion objective, the framework drives the robot to the target configuration in finite time or through it periodically. First, the FT-C2VF is constructed using complementary gains to achieve finite-time convergence while ensuring that the curvature of its integral curves is continuous, bounded, and monotonically decreasing with the radial ratio. Second, an almost globally C1-smooth, saturation-free controller is developed to track the FT-C2VF without Jacobian information, while keeping all control inputs within prescribed actuator limits. Third, dynamical-systems analysis establishes almost-global finite-time stability of the target equilibrium. Numerical simulations show improved performance over representative VF-based methods, and outdoor experiments on an Ackermann-steered vehicle confirm the effectiveness and robustness of the proposed approach.

Problem

• nonholonomic robots
• curvature constraints
• vector fields
• finite-time convergence
• actuator saturation

Innovation

• finite-time convergence
• curvature-constrained vector field
• saturation-free control
• nonholonomic robots
• almost-global stability