Spectral Decomposition of Inverse Dynamics for Fast Exploration in Model-Based Manipulation
Solvin Sigurdson, Benjamin Riviere, Joel Burdick
AI summary
Problem
Planning long-duration manipulation is challenging due to nonlinear contact dynamics and a combinatorial explosion of contact modes. Existing optimization methods often fail because of gradient discontinuities and local minima.
Approach
The method uses a search tree (such as RRT) that explores trajectories generated from the eigenvectors of the inverse dynamics equation, which approximate the object's reachable set while remaining dynamically feasible.
Key results
- Generated 45-second duration plans with 10+ contact modes
- Computation time of approximately 15 seconds for long-horizon tasks
- Comparable performance to existing model-based planners on short-horizon tasks
- Zero-shot application without pre-training or fine-tuning
Why it matters
Enables robots to perform complex, non-prehensile manipulation in contact-rich environments with real-time re-planning capabilities.
Abstract
Planning long duration robotic manipulation se- quences 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 dis- placement 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.