Minimal Coordinate Formulation of Contact Dynamics in Operational Space

Jain, Abhinandan; Crean, Cory; Kuo, Calvin; Bremen, Hubertus F. von; Myint, Steven

doi:10.15607/rss.2012.viii.020

Cited by 7 publications

(13 citation statements)

References 13 publications

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“…implicit [17] Convex model convex solvers [1] MODELLING COORDINATES Using minimal coordinates, or "reduced coordinates," bilateral constraints are implicitly constrained by using joint frames. The constraints on positions, velocities, and accelerations are satisfied during the numerical integration so that stabilization is not required to correct any violations in the constraints [26,27].…”

Section: Formulations and Solversmentioning

confidence: 99%

A Framework for Problem Standardization and Algorithm Comparison in Multibody System

Williams

Trinkle

et al. 2014

Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

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The underlying dynamic model of multibody systems takes the form of a differential Complementarity Problem (dCP), which is nonsmooth and thus challenging to integrate. The dCP is typically solved by discretizing it in time, thus converting the simulation problem into the problem of solving a sequence of complementarity problems (CPs). Because the CPs are difficult to solve, many modelling options that affect the dCPs and CPs have been tested, and some reformulation and relaxation options affecting the properties of the CPs and solvers have been studied in the hopes to find the “best” simulation method. One challenge within the existing literature is that there is no standard set of benchmark simulations. In this paper, we propose a framework of Benchmark Problems for Multibody Dynamics (BPMD) to support the fair testing of various simulation algorithms. We designed and constructed a BPMD database and collected an initial set of solution algorithms for testing. The data stored for each simulation problem is sufficient to construct the CPs corresponding to several different simulation design decisions. Once the CPs are constructed from the data, there are several solver options including the PATH solver, nonsmooth Newton methods, fixed-point iteration methods for nonlinear problems, and Lemke’s algorithm for linear problems. Additionally, a user-friendly interface is provided to add customized models and solvers. As an example benchmark comparison, we use data from physical planar grasping experiments. Using the input from a physical experiment to drive the simulation, uncertain model parameters such as friction coefficients are determined. This is repeated for different simulation methods and the parameter estimation error serves as a measure of the suitability of each method to predict the observed physical behavior.

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Section: Formulations and Solversmentioning

confidence: 99%

A Framework for Problem Standardization and Algorithm Comparison in Multibody System

Williams

Trinkle

et al. 2014

Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

View full text Add to dashboard Cite

show abstract

“…The Darts multibody dynamics code, winner of 1997 NASA Software of the Year Award, can handle closed loops with constraint embedding so that a minimum number of coordinates are used [4], [5]. Darts can also model bodies that are flexible using modal descriptions of the flexible-body dynamics.…”

Section: Simulations With Dsends (How Does It Work?) E What Kindmentioning

confidence: 99%

Next Generation Simulation Framework for Robotic and Human Space Missions

Cameron

Balaram

Jain

et al. 2012

AIAA SPACE 2012 Conference &Amp; Exposition

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The Dartslab team at NASA's Jet Propulsion Laboratory (JPL) has a long history of developing physics-based simulations based on the Darts/Dshell simulation framework that have been used to simulate many planetary robotic missions, such as the Cassini spacecraft and the rovers that are currently driving on Mars. Recent collaboration efforts between the Dartslab team at JPL and the Mission Operations Directorate (MOD) at NASA Johnson Space Center (JSC) have led to significant enhancements to the Dartslab DSENDS software framework. The new version of DSENDS is now being used for new planetary mission simulations at JPL. JSC is using DSENDS as the foundation for a suite of software known as COMPASS that is the basis for their new human space mission simulations and analysis. In this paper, we will describe the collaborative process with the JPL Dartslab and the JSC MOD team that resulted in the redesign and enhancement of the DSENDS software. We will outline the improvements in DSENDS that simplify creation of new high-fidelity robotic/spacecraft simulations. We will illustrate how DSENDS simulations are assembled and show results from several mission simulations.

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“…Complementarity methods use impulsive dynamics to handle collision and contact interactions. They avoid the small time step and stiffening issues encountered in penalty methods by impulsively "stepping" over non-smooth events [4]. There are two variants of the complementarity formulation -the linear complementarity problem (LCP) formulation and the nonlinear complementarity problem (NCP) formulation.…”

Section: Introductionmentioning

confidence: 99%

“…Considerable research effort [2,[4][5][6] has been devoted to efficiently posing contact dynamics problems as solvable LCPs. Nevertheless, the LCP method can lead to inaccuracies because it relies on a discretized approximation of the friction cone.…”

Section: Introductionmentioning

confidence: 99%

“…We use a minimal coordinates approach [6,11] to set up the contact dynamics problem of the multibody system. Additionally, the operational space formulation [12] is employed to take advantage of low order structure based recursive algorithms that significantly reduce computational costs [4]. The linear and nonlinear complementarity problems are reformulated as unconstrained optimization problems which are handled using Levenberg-Marquardt type of optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of Complementarity Techniques for Minimal Coordinate Contact Dynamics

Mylapilli

Jain

2014

Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

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In this article, the non-smooth contact dynamics of multi-body systems is formulated as a complementarity problem. Minimal coordinates operational space formulation is used to derive the dynamics equations of motion. Depending on the approach used for modeling Coulomb’s friction, the complementarity problem can be posed either as a linear or a nonlinear problem. Both formulations are studied in this paper. An exact modeling of the friction cone leads to a nonlinear complementarity problem (NCP) formulation whereas a polyhedral approximation of the friction cone results in a linear complementarity problem (LCP) formulation. These complementarity problems are further recast as non-smooth unconstrained optimization problems, which are solved by employing a class of Levenberg-Marquardt algorithms. The necessary theory detailing these techniques is discussed and five schemes are implemented to solve contact dynamics problems. A simple test case of a sphere moving on a plane surface is used to validate these schemes, while a twelve-link pendulum example is chosen to compare the speed and accuracy of the schemes presented in this paper.

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Minimal Coordinate Formulation of Contact Dynamics in Operational Space

Cited by 7 publications

References 13 publications

A Framework for Problem Standardization and Algorithm Comparison in Multibody System

A Framework for Problem Standardization and Algorithm Comparison in Multibody System

Next Generation Simulation Framework for Robotic and Human Space Missions

Evaluation of Complementarity Techniques for Minimal Coordinate Contact Dynamics

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