Curvature-Constrained Vector Field for Motion Planning of Nonholonomic Robots

2025-03-25

arXiv.org

AI Summary

To address the challenges of unbounded trajectory curvature and lack of guaranteed convergence in motion planning for nonholonomic robots, this paper proposes a co-design framework integrating curvature-constrained vector fields (CVFs) with dynamically scheduled gain-saturated control laws. We introduce a novel CVF modeling framework grounded in the forward limit set of the target configuration, which synthesizes elementary flow fields to construct globally curvature-bounded vector fields. Leveraging Lyapunov stability analysis, we rigorously prove asymptotic convergence of the closed-loop system to the desired configuration under explicit curvature bounds. The method is experimentally validated on both an Ackermann-steering autonomous ground vehicle and a hardware-in-the-loop fixed-wing UAV platform. Compared with existing vector-field approaches, our solution ensures strict adherence to prescribed curvature limits, provides theoretical convergence guarantees, and demonstrates enhanced robustness against disturbances and model uncertainties.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Computer Vision: Learning & Optimization for CV

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Vector fields are advantageous in handling nonholonomic motion planning as they provide reference orientation for robots. However, additionally incorporating curvature constraints becomes challenging, due to the interconnection between the design of the curvature-bounded vector field and the tracking controller under underactuation. In this paper, we present a novel framework to co-develop the vector field and the control laws, guiding the nonholonomic robot to the target configuration with curvature-bounded trajectory. First, we formulate the problem by introducing the target positive limit set, which allows the robot to converge to or pass through the target configuration, depending on different dynamics and tasks. Next, we construct a curvature-constrained vector field (CVF) via blending and distributing basic flow fields in workspace and propose the saturated control laws with a dynamic gain, under which the tracking error's magnitude decreases even when saturation occurs. Under the control laws, kinematically constrained nonholonomic robots are guaranteed to track the reference CVF and converge to the target positive limit set with bounded trajectory curvature. Numerical simulations show that the proposed CVF method outperforms other vector-field-based algorithms. Experiments on Ackermann UGVs and semi-physical fixed-wing UAVs demonstrate that the method can be effectively implemented in real-world scenarios.

Problem

• Develops a curvature-constrained vector field for nonholonomic robot motion planning
• Co-designs vector field and control laws to ensure bounded trajectory curvature
• Guides robots to target configurations with guaranteed tracking and convergence

Innovation

• Co-develop vector field and control laws
• Construct curvature-constrained vector field via blending
• Propose saturated control laws with dynamic gain