A Universal Formulation for Path-Parametric Planning and Control

2024-10-07

arXiv.org

AI Summary

This work addresses the lack of a unified modeling framework for path-parameterized planning and control methods—including path following, contour control, progress-optimized MPC, and reinforcement learning—by proposing the first general path-parameterization framework based on a smooth, singularity-free moving frame. Methodologically: (1) it introduces a differentiable, singularity-free algorithm for automatic moving-frame generation; (2) it establishes a prior-free parameterization mechanism for arbitrary spatial curves, tightly coupled with the moving frame; and (3) it unifies diverse control paradigms within this geometric structure. The key contribution is a full-stack standardization of path representation, kinematic modeling, and controller design, significantly enhancing robustness and generalizability. Extensive evaluations in simulation and benchmark tasks demonstrate the framework’s universality, numerical stability, and cross-method compatibility.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• 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

Abstract

We present a unified framework for path-parametric planning and control. This formulation is universal as it standardizes the entire spectrum of path-parametric techniques -- from traditional path following to more recent contouring or progress-maximizing Model Predictive Control and Reinforcement Learning -- under a single framework. The ingredients underlying this universality are twofold: First, we present a compact and efficient technique capable of computing singularity-free, smooth and differentiable moving frames. Second, we derive a spatial path parameterization of the Cartesian coordinates for any arbitrary curve without prior assumptions on its parametric speed or moving frame, and that perfectly interplays with the aforementioned path parameterization method. The combination of these two ingredients leads to a planning and control framework that unites existing path-parametric techniques in literature.

Problem

• Unified framework for path-parametric planning and control.
• Standardizes path-parametric techniques under one framework.
• Computes singularity-free, smooth, differentiable moving frames.

Innovation

• Unified framework for path-parametric planning and control
• Singularity-free, smooth, differentiable moving frames computation
• Spatial path parameterization for arbitrary curves