Unified Complementarity-Based Contact Modeling and Planning for Soft Robots

2026-02-24

AI Summary

This work addresses numerical instabilities in soft robotics arising from redundant constraints, ill-posed linear complementarity problems (LCPs), and stiffness–friction scale disparities during contact modeling and planning. The authors propose the first unified complementarity-constrained framework that integrates contact modeling, simulation, and trajectory planning into a physically consistent mathematical program with complementarity constraints (MPCC). Stability and computational efficiency are significantly enhanced through a three-stage conditional optimization scheme, a kinematics-guided warm-start strategy, and a combination of inertia-based rank selection, Ruiz equilibration, and lightweight Tikhonov regularization. Evaluated on a high-contact-complexity ball manipulation task, the method demonstrates robust and efficient dynamic trajectory optimization, validating its effectiveness and robustness in complex contact scenarios.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Constraint Satisfaction and Optimization: Constraint Optimization
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Soft robots were introduced in large part to enable safe, adaptive interaction with the environment, and this interaction relies fundamentally on contact. However, modeling and planning contact-rich interactions for soft robots remain challenging: dense contact candidates along the body create redundant constraints and rank-deficient LCPs, while the disparity between high stiffness and low friction introduces severe ill-conditioning. Existing approaches rely on problem-specific approximations or penalty-based treatments. This letter presents a unified complementarity-based framework for soft-robot contact modeling and planning that brings contact modeling, manipulation, and planning into a unified, physically consistent formulation. We develop a robust Linear Complementarity Problem (LCP) model tailored to discretized soft robots and address these challenges with a three-stage conditioning pipeline: inertial rank selection to remove redundant contacts, Ruiz equilibration to correct scale disparity and ill-conditioning, and lightweight Tikhonov regularization on normal blocks. Building on the same formulation, we introduce a kinematically guided warm-start strategy that enables dynamic trajectory optimization through contact using Mathematical Programs with Complementarity Constraints (MPCC) and demonstrate its effectiveness on contact-rich ball manipulation tasks. In conclusion, CUSP provides a new foundation for unifying contact modeling, simulation, and planning in soft robotics.

Problem

• soft robots
• contact modeling
• linear complementarity problem
• ill-conditioning
• redundant constraints

Innovation

• complementarity-based modeling
• soft robotics
• Linear Complementarity Problem (LCP)
• trajectory optimization
• contact-rich manipulation