Multibody Dynamics

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Overview

The field models interconnected bodies—from robot arms and closed-chain mechanisms to cables and spacecraft—to predict motion, forces, and actuator loads. Common approaches include Lagrangian and Newton–Euler equations, Featherstone’s recursive algorithms, and constrained solvers for joint loops and contact; differentiable simulators and learned graph models extend these tools to optimization and data-driven prediction. Work spans contact-rich robot control, GPU-batched simulation, and comparisons with physical robot or mechanism measurements. A central challenge is balancing physical fidelity, especially for friction and changing contacts, with the speed and reliable gradients needed for large-scale learning and control.

Latest papers

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42 papers8 papers in the last four weeks, up 14% on the four weeks before. 0.0% of all new papers.

Apr 21, 2026

Forward Dynamics of Variable Topology Mechanisms - The Case of Constraint Activation

Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is becoming an important issue in human-machine interaction. Anticipating the dynamic behavior of variable topology mechanisms requires solving a non-smooth dynamic problem. The core challenge is a physically meaningful transition condition at the topology switching events. Such a condition is presented in this paper. Two versions are reported, one using projected motion equations in terms of redundant coordinates, and another one using the Voronets equations in terms of minimal coordinates. Their computational properties are discussed. Results are shown for joint locking of a planar 3R mechanisms and a 6DOF industrial manipulator.

Andreas Mueller

Institute of Robotics, Johannes Kepler University Altenbergerstr. 69, 4040 Linz, Austria

Dynamical SystemsMultibody Dynamics
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Apr 5, 2026

frax: Fast Robot Kinematics and Dynamics in JAX

In robot control, planning, and learning, there is a need for rigid-body dynamics libraries that are highly performant, easy to use, and compatible with CPUs and accelerators. While existing libraries often excel at either low-latency CPU execution or high-throughput GPU workloads, few provide a unified framework that targets multiple architectures without compromising performance or ease-of-use. To address this, we introduce frax, a JAX-based library for robot kinematics and dynamics, providing a high-performance, pure-Python interface across CPU, GPU, and TPU. Via a fully-vectorized approach to robot dynamics, frax enables efficient real-time control and parallelization, while supporting automatic differentiation for optimization-based methods. On CPU, frax achieves low-microsecond computation times suitable for kilohertz control rates, outperforming common libraries in Python and approaching optimized C++ implementations. On GPU, the same code scales to thousands of instances, reaching upwards of 100 million dynamics evaluations per second. We validate performance on a Franka Panda manipulator and a Unitree G1 humanoid, and release frax as an open-source library.

Daniel Morton, Marco Pavone

Daniel Morton and Marco Pavone are with the Departments of Mechanical Engineering and Aeronautics & Astronautics, Stanford University, Stanford, CA 94305.

Robot KinematicsRoboticsMultibody Dynamics
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Apr 2, 2026

A Dynamic Toolkit for Transmission Characteristics of Precision Reducers with Explicit Contact Geometry

Precision reducers couple contact geometry, bearing support, structural deformation, and loading history. This paper presents a dynamic toolkit connecting distributed local contacts to the complete mechanical reaction path. Work-conjugate maps transfer displacement, reaction, and tangent contributions between contacts and rigid or reduced coordinates, with explicit allocation of contact and body elasticity. An implicit generalized-alpha solution distinguishes trial evaluations from accepted history. Contact records then support performance protocols and configured geometric or constitutive feedback. The numerical studies focus on mechanical coupling and pressure recovery. An idealized annular housing retains physical interfaces while its structural coordinates are reduced. Two reductions with similar static errors have cross-port response errors of 24.975 and 0.312 percent over the same frequency band relative to a common parent model. In a shared-pin example, a 20 micrometer radial displacement of one wheel changes the load on a second, fixed wheel by approximately 75 N. Removing cross-station compliance removes this incremental transfer on the tested sleeve-seating branch. A double-wheel cycloidal assembly relates torsional branch response to aggregate contact-load variation and normalized pressure fields. The pressure maxima remain sensitive to resolution despite small discrete force residuals. Further formulations specify how motion and contact records support precision, vibration, heat, wear, and durability models with their required inputs. The framework separates model representation and numerical resolution while retaining common definitions of motion, force, and observation.

Jiacheng Miao, Chao Liu, Qiliang Wang +2

Intelligent Equipment Division, CRRC Qishuyan Institute Co., Ltd, Changzhou, 213011, China · School of Mechanical Engineering, Dalian Jiaotong University, Dalian, 116028, China · Research Institute, CRRC Qishuyan Institute Co., Ltd, Changzhou, 213011, China

Dynamical SystemsMultibody DynamicsReduced-Order Modeling
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Mar 24, 2026

Strain-Parameterized Coupled Dynamics and Dual-Camera Visual Servoing for Aerial Continuum Manipulators

Tendon-driven aerial continuum manipulators (TD-ACMs) combine the maneuverability of uncrewed aerial vehicles (UAVs) with the compliance of lightweight continuum robots (CRs). Existing coupled dynamic modeling approaches for TD-ACMs incur high computational costs and do not explicitly account for aerial platform underactuation. To address these limitations, this paper presents a generalized dynamic formulation of a coupled TD-ACM with an underactuated base. The proposed approach integrates a strain-parameterized Cosserat rod model with a rigid-body model of the UAV into a unified Lagrangian ordinary differential equation (ODE) framework on SE(3)\mathrm{SE}(3), thereby eliminating computationally intensive symbolic derivations. Building upon the developed model, a robust dual-camera image-based visual servoing (IBVS) scheme is introduced. The proposed controller mitigates the field-of-view (FoV) limitations of conventional IBVS, compensates for attitude-induced image motion caused by UAV lateral dynamics, and incorporates a low-level adaptive controller to address modeling uncertainties with formal stability guarantees. Extensive simulations and experimental validation on a compact custom-built prototype demonstrate the effectiveness and robustness of the proposed framework in real-world scenarios.

Niloufar Amiri, Farrokh Janabi-Sharifi

Department of Mechanical, Industrial, and Mechatronics Engineering, Toronto Metropolitan University, ON, Canada.

Aerial ManipulationAerial RoboticsContinuum Robot ControlVision-Based Robot ControlMultibody Dynamics
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Mar 18, 2026

Symmetry-Reduced Physics-Informed Learning of Tensegrity Dynamics

Tensegrity structures possess intrinsic geometric symmetries that govern their dynamic behavior. However, most existing physics-informed neural network (PINN) approaches for tensegrity dynamics do not explicitly exploit these symmetries, leading to high computational complexity and unstable optimization. In this work, we propose a symmetry-reduced physics-informed neural network (SymPINN) framework that embeds group-theory-based symmetry directly into both the solution expression and the neural network architecture to predict tensegrity dynamics. By decomposing nodes into symmetry orbits and representing free nodal coordinates using a symmetry basis, the proposed method constructs a reduced coordinate representation that preserves geometric symmetry of the structure. The full coordinates are then recovered via symmetry transformations of the reduced solution learned by the network, ensuring that the predicted configurations automatically satisfy the symmetry constraints. In this framework, equivariance is enforced through orbit-based coordinate generation, symmetry-consistent message passing, and physics residual constraints. In addition, SymPINN improves training effectiveness by encoding initial conditions as hard constraints, incorporating Fourier feature encoding to enhance the representation of dynamic motions, and employing a two-stage optimization strategy. Extensive numerical experiments on symmetric T-bars and lander structures demonstrate significantly improved prediction accuracy and computational efficiency compared to standard physics-informed models, indicating the great potential of symmetry-aware learning for structure-preserving modeling of tensegrity dynamics.

Jing Qin, Muhao Chen

Department of Mathematics, University of Kentucky, Lexington, KY · Department of Mechanical and Aerospace Engineering, University of Houston, TX

Physics-Informed MLStructural MechanicsMultibody Dynamics
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Mar 17, 2026

Kamino: GPU-based Simulation of Rigid Multi-Body Physics with Kinematic Loops

We present Kamino, a GPU-based physics solver for massively parallel simulations of heterogeneous highly-coupled mechanical systems. Implemented in Python using NVIDIA Warp and integrated into the Newton framework, it enables the application of data-driven methods, such as large-scale reinforcement learning, to complex robotic systems that exhibit strongly coupled kinematic and dynamic constraints such as kinematic loops. The latter are often circumvented by approximating the system's topology as a kinematic tree, and incorporating explicit loop-closure constraints or so-called mimic joints. Kamino aims at alleviating this burden by natively supporting these types of couplings. Moreover, Kamino supports heterogeneous worlds, allowing for batched simulation of structurally diverse robots on a single GPU. At its core lies a state-of-the-art constrained optimization algorithm based on ADMM, which computes constraint forces by solving the constrained rigid multi-body forward dynamics transcribed as a nonlinear complementarity problem. This leads to high-fidelity simulations that resolve contact dynamics without resorting to approximate models that simplify or convexify the problem. We demonstrate RL policy training on a biped with six nested kinematic loops, generating a feasible walking policy while simulating 4,0964{,}096 parallel environments on a single GPU.

Vassilios Tsounis, Guirec Maloisel, Christian Schumacher +6

Disney Research, Zurich, Switzerland · NVIDIA, Zurich, Switzerland

Robotics SimulationPhysics-Based SimulationMultibody Dynamics
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Mar 16, 2026

Dual Quaternion Based Contact Modeling for Fast and Smooth Collision Recovery of Quadrotors

Unmanned aerial vehicles (UAVs) operating in cluttered environments require efficient and accurate impact modeling to maintain stability post collisions, however classical impulse contact models decouple the normal and tangential components. This letter presents a dual quaternion impulse reset map directly on the SE(3) manifold. By operating on the unified spatial twist (unified linear and angular velocities), the proposed formulation retains the cross-coupling between normal and tangential impulse components in a single closed-form expression, and recovers the classical decoupled Newton impulse model as a special case. A recovery controller is designed that couples linear and angular momentum to enforce kinetic energy dissipation across impacts. Hardware-in-the-loop benchmarks demonstrate a 24% reduction in execution latency compared to an optimized matrix-based implementation, and a 20% reduction relative to a position-plus-quaternion (PQ) formulation. MuJoCo simulations across Monte Carlo sweeps over impact angles and friction coefficients show a 50.8%-75.1% reduction in position root-mean-square error (RMSE) and a 68.7%-85% decrease in peak kinetic energy compared to published linear-admittance baselines.

Valentin Gaucher, Wenlong Zhang

School of Manufacturing Systems and Networks, Ira A. Fulton Schools of Engineering, Arizona State University, Mesa, AZ, 85212, USA.

Robot Failure RecoveryQuadrotor ControlMultibody Dynamics
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Mar 12, 2026

ComFree-Sim: A GPU-Parallelized Analytical Contact Physics Engine for Scalable Contact-Rich Robotics Simulation and Control

Physics simulation for contact-rich robotics is often bottlenecked by contact resolution: mainstream engines enforce non-penetration and Coulomb friction via complementarity constraints or constrained optimization, requiring per-step iterative solves whose cost grows superlinearly with contact density. We present ComFree-Sim, a GPU-parallelized analytical contact physics engine built on complementarity-free contact modeling. ComFree-Sim computes contact impulses in closed form via an impedance-style prediction--correction update in the dual cone of Coulomb friction. Contact computation decouples across contact pairs and becomes separable across cone facets, mapping naturally to GPU kernels and yielding near-linear runtime scaling with the number of contacts. We further extend the formulation to a unified 6D contact model capturing tangential, torsional, and rolling friction, and introduce a practical dual-cone impedance heuristic. ComFree-Sim is implemented in Warp and exposed through a MuJoCo-compatible interface as a drop-in backend alternative to MuJoCo Warp (MJWarp). Experiments benchmark penetration, friction behaviors, stability, and simulation runtime scaling against MJWarp, demonstrating near-linear scaling and 2--3 times higher throughput in dense contact scenes with comparable physical fidelity. We deploy ComFree-Sim in real-time MPC for in-hand dexterous manipulation on a real-world multi-fingered LEAP hand and in dynamics-aware motion retargeting, demonstrating that low-latency simulation yields higher closed-loop success rates and enables practical high-frequency control in contact-rich tasks.

Chetan Borse, Zhixian Xie, Wei-Cheng Huang +1

Intelligent Robotics and Interactive Systems (IRIS) Lab, Arizona State University · Siebel School of Computing and Data Science, University of Illinois at Urbana-Champaign

Robotics SimulationPhysics-Based SimulationMultibody DynamicsContact-Rich Robotic Manipulation
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Feb 25, 2026

The Port-Hamiltonian Structure of Vehicle Manipulator Systems

This paper presents a port-Hamiltonian formulation of vehicle-manipulator systems (VMS), a broad class of robotic systems including aerial manipulators, underwater manipulators, space robots, and omnidirectional mobile manipulators. Unlike existing Lagrangian formulations that obscure the underlying energetic structure, the proposed port-Hamiltonian formulation explicitly reveals the energy flow and conservation properties of these complex mechanical systems. We derive the port-Hamiltonian dynamics from first principles using Hamiltonian reduction theory. Two complementary formulations are presented: a standard form that directly exposes the energy structure, and an inertially-decoupled form that leverages the principal bundle structure of the VMS configuration space and is particularly suitable for control design and numerical simulation. The coordinate-free geometric approach we follow avoids singularities associated with local parameterizations of the base orientation. We rigorously establish the mathematical equivalence between our port-Hamiltonian formulations and existing reduced Euler-Lagrange and Boltzmann-Hamel equations found in the robotics and geometric mechanics literature.

Ramy Rashad

Control and Instrumentation Engineering department and Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals, Dhahran, 34464, Saudi Arabia

RoboticsPort-Hamiltonian SystemsMultibody Dynamics
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Feb 23, 2026

Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Generation

Simulating rigid-body dynamics with contact in a fast, massively vectorizable, and smoothly differentiable manner is highly desirable in robotics. An important bottleneck faced by existing differentiable simulation frameworks is contact manifold generation: representing the volume of intersection between two colliding geometries via a discrete set of properly distributed contact points. A major factor contributing to this bottleneck is that the related routines of commonly used robotics simulators were not designed with vectorization and differentiability as a primary concern, and thus rely on logic and control flow that hinder these goals. We instead propose a framework designed from the ground up with these goals in mind, by trying to strike a middle ground between: i) convex primitive based approaches used by common robotics simulators (efficient but not differentiable), and ii) mollified vertex-face and edge-edge unsigned distance-based approaches used by barrier methods (differentiable but inefficient). Concretely, we propose: i) a representative set of smooth analytical signed distance primitives to implement vertex-face collisions, and ii) a novel differentiable edge-edge collision routine that can provide signed distances and signed contact normals. The proposed framework is evaluated via a set of didactic experiments and benchmarked against the collision detection routine of the well-established Mujoco XLA framework, where we observe a significant speedup. Supplementary videos can be found at https://github.com/bekeronur/contax, where a reference implementation in JAX will also be made available at the conclusion of the review process.

Onur Beker, Andreas René Geist, Anselm Paulus +4

University of Tübingen · Idiap Research Institute · EPFL

Robotics SimulationDifferentiable PhysicsMultibody Dynamics
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Nov 11, 2025

CENIC: Convex Error-controlled Numerical Integration for Contact

State-of-the-art robotics simulators operate in discrete time. This requires users to choose a time step, which is both critical and challenging: large steps can produce non-physical artifacts, while small steps force the simulation to run slowly. Continuous-time error-controlled integration avoids such issues by automatically adjusting the time step to achieve a desired accuracy. But existing error-controlled integrators struggle with the stiff dynamics of contact, and cannot meet the speed and scalability requirements of modern robotics workflows. We introduce CENIC, a new variable-step integrator that brings together recent advances in convex time-stepping and error-controlled integration, inheriting benefits from both continuous integration and discrete time-stepping. CENIC runs at fast real-time rates comparable to discrete-time robotics simulators like MuJoCo, Drake and Isaac Sim, while also providing guarantees on accuracy and convergence.

Vince Kurtz, Alejandro Castro

Robotics SimulationMultibody Dynamics
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Sep 11, 2024

Highly-Efficient Differentiable Simulation for Robotics

Robotics simulators have improved significantly in computational speed and scalability, enabling them to generate years of simulated data for complex systems in minutes or hours. Despite these advances, efficiently and accurately computing simulation derivatives remains an open challenge. Addressing this would accelerate the convergence of reinforcement learning and trajectory optimization algorithms, particularly for contact-rich problems. This paper introduces a unifying framework for robotic simulation that accounts for all factors, including dynamics, collisions, and friction. The resulting algorithm computes analytical derivatives of the simulation by implicit differentiation, explicitly handling the intrinsic non-smoothness of the collision and frictional stages while exploiting the sparsity induced by the multi-body structure. Benchmark results demonstrate state-of-the-art performance, with timings ranging from 5 μ5\,μs for a 7-dof manipulator to 95 μ95\,μs for a 36-dof humanoid, an improvement of at least two orders of magnitude over alternative methods. Implemented in C++, the code will be open-sourced after the review process to support applications such as simulation-driven learning and real-time control.

Quentin Le Lidec, Louis Montaut, Yann de Mont-Marin +3

Inria, Ecole normale sup´erieure CNRS, PSL Research University 75005 Paris, France

Robotics SimulationMultibody DynamicsDifferentiable Physics
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