contact dynamics modeling

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.

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.

Modeling collision and impact in multibody systems coupled with deformable structures remains challenging due to ambiguous constitutive relationships and the non-smooth dynamics induced by multiple unilateral constraints. Method: This paper proposes a unified dynamical modeling framework that integrates rigid-body impact theory with soft-contact constitutive laws. The framework explicitly embeds elastic connectors and unilateral constraints, enabling systematic analysis of how unilateral spring stiffness, damping, and related parameters govern impulse transmission, energy dissipation, and contact-state transitions. A hybrid numerical implementation synergizes rigid-body dynamics with continuum-based contact models to robustly resolve multi-point non-smooth impacts. Results: Validation across multiple benchmark cases demonstrates that the proposed model significantly outperforms conventional approaches in impact response accuracy, contact-state tracking fidelity, and consistency of energy evolution. It establishes a new paradigm for complex coupled impact systems—offering both physical interpretability and computational robustness.

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.

Conventional musculoskeletal models often treat the foot as a rigid body, limiting accurate representation of foot–ground contact dynamics and thereby compromising gait simulation fidelity. To address this, we propose a high-fidelity deformable human foot model that integrates multipoint contact mechanics with deformable-body dynamics, fully embedded within a comprehensive musculoskeletal system. We further design a two-stage deep reinforcement learning framework: first optimizing joint kinematics, then jointly regulating foot deformation and contact forces to generate naturalistic gait. Compared to standard rigid-foot models, our approach achieves significant improvements in key metrics—including joint angles, ground reaction forces, and gait stability—with simulation results showing strong agreement with experimental kinematic and dynamic data (average RMSE reduced by 32.7%). This work establishes a more physiologically realistic and computationally robust platform for biomechanical modeling and neuromuscular control research.

This work addresses the computational bottleneck in contact-intensive robotic simulation, where conventional physics engines suffer from superlinear scaling in contact count due to reliance on complementarity constraints or optimization-based methods, hindering high-frequency control. The authors propose a complementarity-free analytical contact engine that leverages an impedance-inspired predictor-corrector scheme within the Coulomb friction dual cone to compute contact impulses in closed form, fully decoupling contact pairs and enabling GPU parallelization. The method unifies tangential, torsional, and rolling friction into a separable 6D contact model and is efficiently accelerated via Warp, offering a plug-and-play backend compatible with MuJoCo. Experiments demonstrate near-linear runtime scaling in dense-contact scenarios, achieving 2–3× higher throughput than existing simulators while maintaining physical fidelity comparable to MJX, and enabling real-time model predictive control and dexterous manipulation with significantly improved closed-loop success rates.

Existing point contact models struggle to accurately capture the frictional and torque dynamics inherent in rich contact interactions, thereby limiting the realization of human-like dexterous manipulation. This work proposes a Force-Distributed Line Contact (FDLC) model that, for the first time, incorporates non-uniform force distributions along line contacts into trajectory optimization. A bilevel optimization framework is developed: the lower level optimizes the contact force distribution, while the upper level employs iterative Linear Quadratic Regulator (iLQR) for trajectory optimization. By transcending the representational limitations of point contact models in complex contact scenarios, the proposed approach generates highly efficient and robust trajectories—demonstrated in a box-rotation task—achieving lower control effort and reduced robot motion compared to conventional methods.

This work addresses the numerical ill-conditioning and lack of efficient, scalable solvers in contact-implicit trajectory optimization (CITO) caused by complementarity constraints. We propose a novel approach that integrates an augmented Lagrangian method with an implicit active-set strategy to dynamically identify contact mode branches during trajectory optimization iterations. This is the first method to enable online handling of complementarity constraints while guaranteeing convergence to stationary points. Our custom C++ solver achieves speedups of 2.9–70× (13.8× geometric mean) over strong baselines on standard CITO benchmarks, significantly enhancing dexterous manipulation performance in contact-implicit model predictive control (CI-MPC). The approach is successfully validated on a real robotic system performing a T-shaped object pushing task.

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.