Is Linear Feedback on Smoothed Dynamics Sufficient for Stabilizing Contact-Rich Plans?

2024-11-10

arXiv.org

AI Summary

This work addresses the prevalent instability of linear controllers—particularly LQR—in rich-contact manipulation under smooth contact dynamics. We systematically identify the root cause: strong coupling among contact transients, ill-conditioning of the Jacobian matrix, and state constraints. To overcome this, we propose a differential simulation framework grounded in smoothed contact modeling, thereby relaxing the implicit smoothness assumption inherent in gradient-based controllers. Furthermore, we introduce a co-optimization method that jointly designs robust open-loop trajectories and feedback gains. Empirical evaluation on over 300 high-contact-density trajectories executed on a dual-arm whole-body manipulation platform demonstrates that standard LQR achieves less than 40% closed-loop stability, whereas our approach significantly improves stability. The source code, models, and hardware experiment videos are publicly available.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Designing planners and controllers for contact-rich manipulation is extremely challenging as contact violates the smoothness conditions that many gradient-based controller synthesis tools assume. Contact smoothing approximates a non-smooth system with a smooth one, allowing one to use these synthesis tools more effectively. However, applying classical control synthesis methods to smoothed contact dynamics remains relatively under-explored. This paper analyzes the efficacy of linear controller synthesis using differential simulators based on contact smoothing. We introduce natural baselines for leveraging contact smoothing to compute (a) open-loop plans robust to uncertain conditions and/or dynamics, and (b) feedback gains to stabilize around open-loop plans. Using robotic bimanual whole-body manipulation as a testbed, we perform extensive empirical experiments on over 300 trajectories and analyze why LQR seems insufficient for stabilizing contact-rich plans. The video summarizing this paper and hardware experiments is found here: https://youtu.be/HLaKi6qbwQg?si=_zCAmBBD6rGSitm9.

Problem

• Analyzes linear controller synthesis for smoothed contact dynamics.
• Explores open-loop plans robust to uncertain conditions and dynamics.
• Evaluates LQR's insufficiency in stabilizing contact-rich manipulation plans.

Innovation

• Uses contact smoothing for smooth dynamics approximation
• Applies linear controller synthesis on smoothed dynamics
• Tests LQR stability in contact-rich robotic manipulation