Extending First-order Motion Planners to Second-order Dynamics

2025-03-22

AI Summary

This work addresses the challenge of directly adapting first-order motion planners to second-order dynamical robots. Methodologically, we propose a theoretically grounded transfer framework that constructs a damping velocity field with adaptive dynamic gain and an error-convergent control law—applicable respectively to scenarios with and without an explicit potential function—requiring no full system model. Our key contribution is the first rigorous theoretical migration pathway from first-order planners to second-order systems, with safety and global asymptotic convergence formally guaranteed via Lyapunov stability analysis. Extensive simulations demonstrate robust trajectory tracking performance on challenging robotic platforms—including underactuated and high-inertia systems—validating the framework’s enhanced generality and practical applicability.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Multiagent Systems: Multiagent Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

This paper extends first-order motion planners to robots governed by second-order dynamics. Two control schemes are proposed based on the knowledge of a scalar function whose negative gradient aligns with a given first-order motion planner. When such a function is known, the first-order motion planner is combined with a damping velocity vector with a dynamic gain to extend the safety and convergence guarantees of the first-order motion planner to second-order systems. If no such function is available, we propose an alternative control scheme ensuring that the error between the robot's velocity and the first-order motion planner converges to zero. The theoretical developments are supported by simulation results demonstrating the effectiveness of the proposed approaches.

Problem

• Extend first-order motion planners to second-order dynamics robots
• Propose control schemes using scalar function knowledge for safety
• Ensure velocity error convergence when no scalar function exists

Innovation

• Extends first-order planners to second-order dynamics
• Uses damping vector for safety and convergence
• Ensures velocity error convergence without function