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

• URL: http://arxiv.org/abs/2607.17542v1
• Date: Mon, 20 Jul 2026 04:36:20 GMT
• Title: Finite-Time Curvature-Constrained Vector Field for Saturation-Free Motion Planning of Nonholonomic Robots
• Abstract summary: Accurately steering a robot to a target configuration is fundamental in engineering, yet remains challenging for nonholonomic mobile robots.<n>Most existing VF-based methods cannot explicitly generate trajectories satisfying curvature constraints.<n>We propose a general motion planning and control framework consisting of a finite-time curvature-constrained vector field (FT-C2VF) and a saturation-free control law.
• Score: 32.96414771882991
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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