用于非完整机器人无饱和运动规划的有限时间曲率约束向量场
Finite-Time Curvature-Constrained Vector Field for Saturation-Free Motion Planning of Nonholonomic Robots
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- School of Artificial Intelligence and Robotics, Hunan University（湖南大学人工智能与机器人学院）
- College of Information Science and Engineering, Hunan Normal University（湖南师范大学信息科学与工程学院）
- College of Systems Engineering and the State Key Laboratory of Digital Intelligent Modeling and Simulation, National University of Defense Technology（国防科技大学系统工程学院和数字智能建模与仿真国家重点实验室）
- Department of Computer Engineering, Automation & Robotics, and the Institute of Mathematics (IMAG), University of Granada（格拉纳达大学计算机工程、自动化与机器人系以及数学研究所（IMAG））
机构由 AI 辅助整理，请以论文原文为准。
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中文总结 AI 辅助
针对非完整机器人运动规划问题，提出由有限时间曲率约束向量场和无饱和控制律组成的框架。通过构建FT-C2VF实现有限时间收敛并满足曲率约束，开发控制器跟踪该场，经分析和实验验证方法有效且鲁棒。
中文摘要 AI 辅助
准确地将机器人引导到目标配置在工程中至关重要，但对于非完整移动机器人来说仍然具有挑战性。向量场（VFs）提供了一个自然的框架，通过在整个工作空间中指定期望的运动方向并实现与反馈控制的直接集成。然而，大多数现有的基于VF的方法不能明确生成满足曲率约束的轨迹。因此，执行器限制通常通过输入饱和来强制执行，这在控制器设计中未考虑时可能会使稳定性保证无效并降低闭环性能。此外，这些方法通常只确保渐近收敛，没有明确的稳定时间界限。为了解决这些问题，我们提出了一个广义的运动规划和控制框架，由一个有限时间曲率约束向量场（FT-C2VF）和一个无饱和控制律组成。根据运动目标，该框架在有限时间内将机器人驱动到目标配置或使其周期性地通过目标配置。首先，使用互补增益构建FT-C2VF，以实现有限时间收敛，同时确保其积分曲线的曲率是连续的、有界的，并且随着径向比单调递减。其次，开发了一个几乎全局C1光滑的无饱和控制器，以在没有雅可比信息的情况下跟踪FT-C2VF，同时将所有控制输入保持在规定的执行器限制内。第三，动力学系统分析建立了目标平衡点的几乎全局有限时间稳定性。数值模拟显示了相对于代表性的基于VF的方法的改进性能，并且在阿克曼转向车辆上的户外实验证实了所提出方法的有效性和鲁棒性。
英文摘要
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.
