contact mechanics

This work addresses the challenge of modeling contact mechanics in interactions between soft tools and rigid objects. We propose a unified learning-and-optimization framework for deformable-rigid hybrid contact. Methodologically, it integrates data-driven joint estimation of contact forces and object motion with physics-based static equilibrium modeling. Crucially, we introduce the Contact Quadratic Program (CQP), the first formulation to explicitly encode Coulomb friction and static equilibrium constraints within a differentiable optimization layer. The framework leverages simulation-based pretraining followed by domain adaptation to ensure robust transfer to real-world settings. Experiments demonstrate significant improvements over existing baselines across diverse pushing and rotating tasks involving multi-material and multi-geometry rigid bodies. Validation on a physical soft-tool platform confirms high accuracy in predicting both contact forces and object motion, as well as strong generalization across manipulation tasks.

Existing robotic planning methods struggle to accurately model the coupling and mode transitions between free motion and frictional contact in unstructured environments, limiting real-time robust execution of contact-intensive tasks. This work proposes Unicomp, a unified discrete-time framework grounded in complementarity theory that seamlessly integrates free motion and frictional contact into coupled linear and nonlinear complementarity problems, enabling natural mode switching without pre-specified contact assumptions. A novel ellipsoidal limit surface contact model—agnostic to pressure distribution—is introduced in conjunction with the principle of maximum dissipation to effectively capture force-moment coupling, including torsional friction. Experiments demonstrate that the approach achieves physically consistent, stable, and computationally efficient real-time interaction in tasks such as pushing objects into full-body contact.

This work addresses the challenge of simulating rigid multibody dynamics involving multiple closed kinematic loops, hard unilateral contacts, Coulomb friction, and restitutional impacts. We propose a unified nonlinear complementarity problem (NCP) modeling and solution framework based on maximal coordinates. Methodologically, the approach integrates forward-dynamics decomposition, implicit time integration, and exact frictional contact modeling, while systematically benchmarking against multiple state-of-the-art physics engine solvers. Our key contribution is the first standardized benchmarking framework specifically designed for closed-loop multibody systems, enabling both qualitative and quantitative evaluation. Extensive experiments across diverse, highly coupled closed-loop scenarios reveal, for the first time, the absolute and relative performance boundaries—across accuracy, stability, and convergence—of prevailing solvers. These empirical findings provide critical evidence for the accuracy–stability trade-off in complex contact-rich simulations.

Existing filament–rigid-body contact simulation methods typically assume persistent attachment, failing to capture friction-driven dynamic detachment and recontact. This work proposes a novel framework integrating discrete elastic rods (DER) dynamics, pressure-field patch-based contact modeling, and convex optimization for contact configuration. It is the first to unify these three components within a global optimization paradigm, rigorously enforcing complementarity conditions between contact velocities and impulses—enabling high-fidelity, frictional contact simulation. The method overcomes numerical challenges arising from filament codimensionality, significantly improving physical consistency. Experiments demonstrate superior accuracy and stability in friction force computation compared to state-of-the-art baselines. The framework is validated on complex deformable manipulation tasks—including randomized cable grasping with a multi-fingered gripper and dynamic shoelace knotting—showcasing both efficacy and robustness.

This work addresses the challenge of modeling complex contacts in robotic simulation—specifically, the difficulty of simultaneously achieving broad stiffness coverage (from rigid to compliant), accurate static friction resolution, and robustness against contact state transitions. We propose a differentiable hybrid contact modeling framework based on convex optimization. Methodologically, we integrate the Hunt–Crossley contact force model, Coulomb’s friction law, and the principle of maximum dissipation to construct a stiffness-adaptive convex approximation. We further introduce a novel contact decomposition factor reuse mechanism, enabling efficient and fully differentiable gradient computation for geometrically complex models. Our key contribution is the first implementation—within Drake—of an interaction-rate-capable, high-fidelity, end-to-end differentiable contact solver. This significantly improves static friction accuracy and contact mode transition stability, and markedly enhances sim-to-real transfer performance.

This work addresses the limited accuracy and robustness in modeling frictional contact within the Material Point Method (MPM) by proposing a unified solver framework for implicit MPM. The approach precisely locates contact points using particle-centered geometric primitives and formulates frictional contact—including impenetrability, Coulomb friction, and the principle of maximum dissipation—as a nonlinear complementarity problem (NCP) in terms of contact impulses. An ADMM-based algorithm is employed for efficient solution. Notably, this is the first method to cast frictional contact uniformly as an NCP and embed it within implicit MPM while reusing its linearized structure. The framework demonstrates high-precision contact localization, reliable friction handling, and broad applicability across seven diverse scenarios involving elastic and elastoplastic materials, complex geometries, and varied contact conditions.

This work addresses the high-dimensional control challenges in non-prehensile planar manipulation arising from hybrid contact mechanics, underactuation, and friction asymmetry. The authors propose a mode-aware single- and dual-arm manipulation framework that abstracts complex contacts into discrete modes via contact topology selection and represents system kinematics using reduced-order nonholonomic models, such as the unicycle model. For the first time, the wrench-twist limit surface is simplified into a discrete model library, enabling real-time trajectory generation and force distribution without iterative optimization. This is achieved by integrating an algebraic contact force allocator with manipulator kinematic constraints. Simulations demonstrate the method’s efficiency, feasibility, and iteration-free advantage across diverse planar manipulation tasks.

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.

This work addresses the challenge of tightly coupling high-fidelity physical simulation with photorealistic real-time rendering in contact-rich robotic systems, particularly in modeling deformation and tactile perception. The authors present the first deep integration of GPU-accelerated Incremental Potential Contact (IPC) into the IsaacSim/Isaac Lab platform and introduce the Geometric Mortar Contact Potential (GMCP) to more accurately capture contact pressure distributions on tactile surfaces. By establishing a deformation mapping mechanism between simulation and visual meshes, the approach enables synchronized physics simulation and rendering in scenarios involving rigid–soft interactions. Experiments demonstrate the method’s effectiveness across multiple contact benchmarks and its successful application to high-fidelity, real-time simulation and data generation for quadrupedal robots, dexterous hands, and UMI grippers.

This work addresses gradient distortion in existing differentiable simulators under frictional contact and large deformations, which stems from mathematical inconsistencies and leads to optimization failure. We propose the first unified, fully GPU-accelerated differentiable simulator that enables stable, high-fidelity gradient computation across contact states. Our approach integrates a rigorously Markovian position-velocity manifold coupling, a mass-aligned preconditioner, a soft Fischer–Burmeister friction operator, and a finite element singularity resolution technique. We further introduce a long-horizon consistency mechanism and a unified contact stability strategy, enabling—for the first time—mathematically rigorous modeling of both frictional contact and hyperelastic materials within a differentiable framework. The resulting low-noise, high-fidelity gradients significantly narrow the Sim-to-Real gap and enhance the reliability of physical system identification and control in tasks such as dexterous manipulation and cloth folding.