Unified Complementarity-Based Contact Modeling and Planning for Soft Robots

Researchers Milad Azizkhani and Yue Chen have introduced a groundbreaking framework called CUSP (Complementarity-Based Unified Soft Robot Planning) that addresses one of the most persistent challenges in soft robotics: modeling and planning contact-rich interactions. Published on arXiv, their work presents a unified complementarity-based approach that brings contact modeling, manipulation, and planning into a single, physically consistent formulation. This solves fundamental problems where dense contact candidates along a soft robot's body create redundant constraints and rank-deficient Linear Complementarity Problems (LCPs), while the disparity between high stiffness and low friction introduces severe ill-conditioning. Existing approaches have relied on problem-specific approximations or penalty-based treatments, but CUSP offers a more robust foundation.

The technical innovation centers on a three-stage conditioning pipeline specifically tailored for discretized soft robots. This includes 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 this robust LCP model, the researchers also developed a kinematically guided warm-start strategy. This enables dynamic trajectory optimization through contact using Mathematical Programs with Complementarity Constraints (MPCC), which they demonstrated effectively on complex, contact-rich ball manipulation tasks. The framework provides a new, unified foundation that could significantly accelerate the development of soft robots capable of safe, adaptive, and dexterous interaction with unstructured environments.