Extensive analysis of Linear Complementarity Problem (LCP) solver performance on randomly generated rigid body contact problems

2012 ◽  
Author(s):  
Evan Drumwright ◽  
Dylan A. Shell
Keyword(s):  
Rigid Body ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Contact Problems ◽  
Linear Complementarity ◽  
Body Contact ◽  
Extensive Analysis ◽  
Solver Performance

Multi Rigid-Body Contact Dynamics With Regularized Friction

2015 ◽  
Author(s):  
Farnood Gholami ◽  
Mostafa Nasri ◽  
József Kövecses
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Mathematical Formulation ◽  
Contact Problems ◽  
Linear Complementarity ◽  
Contact Dynamics ◽  
Friction Forces ◽  
Body Contact ◽  
Normal Forces ◽  
Multibody Contact

A novel mathematical formulation in terms of a linear complementarity problem is introduced for multibody contact problems. In this approach, contacts are characterized based on kinematic constraints while the friction forces are simultaneously regularized and incorporated into the formulation. The variables of the resulting linear complementarity problem are only the normal forces. The main advantage of this formulation is a significant dimension reduction in the resulting linear complementarity problem in comparison with its counterpart formulations in the literature. Moreover, the dimension can be even further reduced by removing the velocity variables from the formulation. The proposed formulation is examined for benchmark examples yielding promising results.

A Recursive Hybrid Time-Stepping Scheme for Intermittent Contact in Multi-Rigid-Body Dynamics

2009 ◽  
Vol 4 (4) ◽  
Author(s):  
Kishor D. Bhalerao ◽  
Kurt S. Anderson ◽  
Jeffrey C. Trinkle
Keyword(s):  
Rigid Body ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Rigid Body Dynamics ◽  
Divide And Conquer ◽  
Double Pendulum ◽  
Time Stepping ◽  
Bilateral Constraints ◽  
Intermittent Contact

This paper describes a novel method for the modeling of intermittent contact in multi-rigid-body problems. We use a complementarity based time-stepping scheme in Featherstone’s divide and conquer framework to efficiently model the unilateral and bilateral constraints in the system. The time-stepping scheme relies on impulse-based equations and does not require explicit collision detection. A set of complementarity conditions is used to model the interpenetration constraint and a linearized friction cone is used to yield a linear complementarity problem. The divide and conquer framework ensures that the size of the resulting mixed linear complementarity problem is independent of the number of bilateral constraints in the system. This makes the proposed method especially efficient for systems where the number of bilateral constraints is much greater than the number of unilateral constraints. The method is demonstrated by applying it to a falling 3D double pendulum.

A Recursive Hybrid Time-Stepping Scheme for Intermittent Contact in Multi-Rigid-Body Dynamics

2009 ◽  
Author(s):  
Kishor D. Bhalerao ◽  
Kurt S. Anderson ◽  
Jeffery C. Trinkle
Keyword(s):  
Rigid Body ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Rigid Body Dynamics ◽  
Divide And Conquer ◽  
Double Pendulum ◽  
Time Stepping ◽  
Bilateral Constraints ◽  
Intermittent Contact

This paper describes a novel method for the modeling of intermittent contact in multi-rigid-body problems. We use a complementarity based time-stepping scheme in Featherstone’s Divide and Conquer framework to efficiently model the unilateral and bilateral constraints in the system. The time-stepping scheme relies on impulse-based equations and does not require explicit collision detection. A set of complementarity conditions is used to model the interpenetration constraint and a linearized friction cone is used to yield a linear complementarity problem. The Divide and Conquer framework ensures that the size of the resulting mixed linear complementarity problem is independent of the number of bilateral constraints in the system. This makes the proposed method especially efficient for systems where the number of bilateral constraints are much greater than the number of unilateral constraints. The method is demonstrated by applying it to a falling 3D double pendulum.

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