Finite-Time Curvature-Constrained Vector Field for Saturation-Free Motion Planning of Nonholonomic Robots
This work addresses the challenge of motion planning for nonholonomic robots by explicitly incorporating curvature constraints and actuator saturation, which is critical for practical applications but often ignored in vector-field-based methods.
The authors propose a finite-time curvature-constrained vector field (FT-C2VF) and a saturation-free control law for nonholonomic robots, achieving finite-time convergence to a target configuration while respecting curvature constraints and actuator limits. Simulations and outdoor experiments on an Ackermann-steered vehicle demonstrate improved performance over existing methods.
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.