Gauss' least constraints principle and rigid body simulations

Stéphane Redon (1) , Abderrahmane Kheddar (2) , Sabine Coquillart (3)

1 Action i3D
2 LSC - Laboratoire Systèmes Complexes
3 INRIA Rocquencourt

Most of well-known approaches for rigid body simulations are formulated in the contact-space. Thanks to Gauss’ principle of least constraints, the frictionless dynamics problems are formulated in a motion-space. While the two formulations are mathematically equivalent, they are not computationally equivalent. The motion-space formulation is better conditionned, always sparse, needs less memory, and avoids some unnecessary computations. A preliminary experimental comparison suggests that an algorithm operating in the motionspace takes advantage of sparsity to perform increasingly better than a contact-space algorithm as the average number of contact points per object increases.

Domaines: Modélisation et simulation

Stéphane Redon, Abderrahmane Kheddar, Sabine Coquillart. Gauss' least constraints principle and rigid body simulations. Robotics and Automation, 2002. Proceedings. ICRA'02. IEEE International Conference on, 2002, Washington, DC, United States. pp.517--522, ⟨10.1109/ROBOT.2002.1013411⟩. ⟨hal-01147672⟩