Index-3 divide-and-conquer algorithm for efficient multibody system dynamics simulations: theory and parallel implementation

[Abstract] There has been a growing attention to efficient simulations of multibody systems, which is apparently seen in many areas of computer-aided engineering and design both in academia and in industry. The need for efficient or real-time simulations requires high fidelity techniques and formulations that should significantly minimize computational time. Parallel computing is one of the approaches to achieve this objective. This paper presents a novel index-3 divide-and-conquer algorithm for efficient multibody dynamics simulations that elegantly handles multibody systems in generalized topologies through the application of the augmented Lagrangian method. The proposed algorithm exploits a redundant set of absolute coordinates. The trapezoidal integration rule is embedded into the formulation and a set of nonlinear equations need to be solved every time instant. Consequently, the Newton–Raphson iterative scheme is applied to find the system coordinates and joint constraint loads in an efficient and highly parallelizable manner. Two divide-and-conquer based mass-orthogonal projections are performed then to circumvent the effect of constraint violation errors at the velocity and acceleration level. Sample open- and closed-loop multibody system test cases are investigated in the paper to confirm the validity of the approach. Challenging simulations of multibody systems featuring long kinematic chains are also performed in the work to demonstrate the robustness of the algorithm. The details of OpenMP-based parallel implementation on an eight-core shared memory computer are presented in the text and the parallel performance results are extensively discussed. Significant speedups are obtained for the simulations of small- to large-scale multibody open-loop systems. The mentioned features make the proposed algorithm a good general purpose approach for high-fidelity, efficient or real-time multibody dynamics simulations.Ministerio de Economía y Competitividad; JCI-2012-12376Poland. National Science Center; DEC-2012/07/B/ST8/0399

Stable Constrained Dynamics

International audienceWe present a unification of the two main approaches to simulate deformable solids, namely elasticity and constraints. Elasticity accurately handles soft to moderately stiff objects, but becomes numerically hard as stiffness increases. Constraints efficiently handle high stiffness, but when integrated in time they can suffer from instabilities in the nullspace directions, generating spurious transverse vibrations when pulling hard on thin inextensible objects or articulated rigid bodies. We show that geometric stiffness, the tensor encoding the change of force directions (as opposed to intensities) in response to a change of positions, is the missing piece between the two approaches. This previously neglected stiffness term is easy to implement and dramatically improves the stability of inextensible objects and articulated chains, without adding artificial bending forces. This allows time step increases up to several orders of magnitude using standard linear solvers

Solving variational inequalities and cone complementarity problems in nonsmooth dynamics using the alternating direction method of multipliers

This work presents a numerical method for the solution of variational inequalities arising in nonsmooth flexible multibody problems that involve set-valued forces. For the special case of hard frictional contacts, the method solves a second order cone complementarity problem. We ground our algorithm on the Alternating Direction Method of Multipliers (ADMM), an efficient and robust optimization method that draws on few computational primitives. In order to improve computational performance, we reformulated the original ADMM scheme in order to exploit the sparsity of constraint jacobians and we added optimizations such as warm starting and adaptive step scaling. The proposed method can be used in scenarios that pose major difficulties to other methods available in literature for complementarity in contact dynamics, namely when using very stiff finite elements and when simulating articulated mechanisms with odd mass ratios. The method can have applications in the fields of robotics, vehicle dynamics, virtual reality, and multiphysics simulation in general

ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor

Model-based coupling for co-simulation of robotic contact tasks

[Abstract] Co-simulation of complex robotic systems allows the different components to be modelled and simulated independently using methods and tools tailored to their nature and time-scale, which makes the implementation process more modular and flexible. Some applications require the use of non-iterative coupling schemes for optimal performance, such as real-time interactive environments and human and hardware-in-the-loop setups. Stability of non-iterative schemes is challenging due to the restricted and delayed information that is exchanged between subsystems, and robust prediction of interface variables is key. Here, we propose a framework for exchanging model information between mechanical systems with contact, where reduced-order models approximate the interface dynamics of the subsystems. Effective mass and force terms are formulated using a reduced representation of the model, which can then be exchanged between subsystems and integrated in their simulation. The analysis of several simulations of challenging robotic contact tasks, such as grasping and insertion with jamming, shows that model-based coupling allows for stable co-simulation with larger interface stiffness values, resulting in stronger coupling and higher simulation accuracy.MINECO; RYC-2016-2022

An overview of Forward Dynamics Algorithms and their use in Open Source Dynamics Engines

Simulation of real-world dynamics is of major importance in testing and verifying developed industrial concepts and solutions, developing and verifying potential control paradigms, scientific research, learning and training tools, or the entertainment industry as a basis for a game engine. The module of the 3D virtual simulator that achieves simulation of the real-world behaviour such as rigid and elastic body dynamics, particle dynamics, fluid dynamics, electrodynamics, magnetism, etc., is often referred to as a dynamics engine or physics engine. The core of the rigid body dynamics (physics) engine is the solution to the forward dynamics problem, which is defined as finding a rigid body's path, velocity, and acceleration for a given input actuating torque and external forces. The past few decades saw a considerable amount of research in robot dynamics modelling, and there are many methods for robot dynamic model development available in the literature. The most commonly used algorithms for solving robot forward dynamics problem are the Composite-Rigid-Body Algorithm (CRBA) [1] and the Articulated-Body Algorithm (ABA) [2]. CRBA and ABA are reduced coordinate methods where known constraints, such as joints, are embedded in the formulation of the equations of motion. Besides reduced coordinate methods, there are maximal coordinate methods using Lagrange multipliers [3-4] to enforce constraints using constraint reaction forces

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Modeling and Control of Adjustable Articulated Parallel Compliant Actuation Arrangements in Articulated Robots

Considerable advances in robotic actuation technology have been made in recent years. Particularly the use of compliance has increased, both as series elastic elements as well as in parallel to the main actuation drives. This work focuses on the model formulation and control of compliant actuation structures including multiple branches and multi-articulation, and significantly contributes by proposing an elegant modular formulation that describes the energy exchange between the compliant elements and articulated multi-body robot dynamics using the concept of power flows, and a single matrix that describes the entire actuation topology. Using this formulation, a novel gradient descent based control law is derived for torque control of compliant actuation structures with adjustable pretension, with proven convexity for arbitrary actuation topologies. Extensions towards handling unidirectionality of elastic elements and joint motion compensation are also presented. A simulation study is performed on a 3-DoF leg model, where series-elastic main drives are augmented by parallel elastic tendons with adjustable pretension. Two actuation topologies are considered, one of which includes a biarticulated tendon. The data demonstrate the effectiveness of the proposed modelling and control methods. Furthermore, it is shown the biarticulated topology provides significant benefits over the monoarticulated arrangement