Spectral Decomposition of Inverse Dynamics for Fast Exploration in Model-Based Manipulation

2026-03-29

AI Summary

This work addresses the challenge of long-horizon robotic manipulation planning, which is hindered by the nonlinear contact dynamics and combinatorial complexity of multi-contact modes, leading to rapidly escalating computational costs over extended time horizons. The paper introduces, for the first time, a spectral decomposition of the inverse dynamics equations into trajectory generation, enabling efficient approximation of an object’s reachable set through orthogonal trajectory components. This approach preserves dynamic feasibility while substantially improving exploration efficiency. Integrated with search-based planners such as RRT, the proposed method generates 45-second manipulation plans encompassing more than ten distinct contact modes within 15 seconds, thereby achieving real-time, long-horizon planning for highly complex tasks.

Technology Category

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

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
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Planning long duration robotic manipulation sequences is challenging because of the complexity of exploring feasible trajectories through nonlinear contact dynamics and many contact modes. Moreover, this complexity grows with the problem's horizon length. We propose a search tree method that generates trajectories using the spectral decomposition of the inverse dynamics equation. This equation maps actuator displacement to object displacement, and its spectrum is efficient for exploration because its components are orthogonal and they approximate the reachable set of the object while remaining dynamically feasible. These trajectories can be combined with any search based method, such as Rapidly-Exploring Random Trees (RRT), for long-horizon planning. Our method performs similarly to recent work in model-based planning for short-horizon tasks, and differentiates itself with its ability to solve long-horizon tasks: whereas existing methods fail, ours can generate 45 second duration, 10+ contact mode plans using 15 seconds of computation, demonstrating real-time capability in highly complex domains.

Problem

• long-horizon planning
• contact dynamics
• trajectory exploration
• model-based manipulation
• inverse dynamics

Innovation

• spectral decomposition
• inverse dynamics
• long-horizon planning
• contact-rich manipulation
• trajectory generation