Inverse Kinematics on Guiding Vector Fields for Robot Path Following

2025-02-24

AI Summary

This paper addresses high-precision path following for autonomous mobile robots, including fixed-wing UAVs. Methodologically, it introduces a novel paradigm that extends inverse kinematics principles to guidance vector field (GVF) design: a geometric error signal is derived from an implicit path representation (zero-level set), mapped via inverse kinematics to construct the GVF, and integrated with nonlinear feedback linearization and feedforward control to achieve error dynamics linearization and transient response shaping. Key contributions include: (i) the first theoretical linkage between inverse kinematics and GVF design; (ii) explicit accommodation of constant-speed unicycle dynamics—beyond the conventional single-integrator assumption; (iii) rigorous proof of global asymptotic convergence; and (iv) experimental validation on a fixed-wing UAV, demonstrating centimeter-level 2D path tracking accuracy and tunable transient performance.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Computer Vision: Motion & Tracking

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services

Abstract

Inverse kinematics is a fundamental technique for motion and positioning control in robotics, typically applied to end-effectors. In this paper, we extend the concept of inverse kinematics to guiding vector fields for path following in autonomous mobile robots. The desired path is defined by its implicit equation, i.e., by a collection of points belonging to one or more zero-level sets. These level sets serve as a reference to construct an error signal that drives the guiding vector field toward the desired path, enabling the robot to converge and travel along the path by following such a vector field. We start with the formal exposition on how inverse kinematics can be applied to guiding vector fields for single-integrator robots in an m-dimensional Euclidean space. Then, we leverage inverse kinematics to ensure that the level-set error signal behaves as a linear system, facilitating control over the robot's transient motion toward the desired path and allowing for the injection of feed-forward signals to induce precise motion behavior along the path. We then propose solutions to the theoretical and practical challenges of applying this technique to unicycles with constant speeds to follow 2D paths with precise transient control. We finish by validating the predicted theoretical results through real flights with fixed-wing drones.

Problem

• Extend inverse kinematics to guiding vector fields
• Enable precise path following for mobile robots
• Validate technique with fixed-wing drone flights

Innovation

• Inverse kinematics for path following
• Guiding vector fields control
• Level-set error signal linearization