Unified Complementarity-Based Contact Modeling and Planning for Soft Robots

• URL: http://arxiv.org/abs/2602.21316v1
• Date: Tue, 24 Feb 2026 19:37:36 GMT
• Title: Unified Complementarity-Based Contact Modeling and Planning for Soft Robots
• Abstract summary: This letter presents a unified complementarity-based framework for soft-robot contact modeling and planning.<n>We develop a robust Linear Complementarity Problem (LCP) model tailored to discretized soft robots.<n>We also introduce a kinematically guided warm-start strategy that enables dynamic trajectory optimization through contact.
• Score: 13.597188299981312
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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