Understanding the difference between prox and complementarity formulations for simulation of systems with contact

Thorsten Schindler (1) , Binh Nguyen (2) , Jeff Trinkle (2)

1 Institute of Applied Mechanics [Garching]
2 RPI - Rensselaer Polytechnic Institute

To plan a robotic task involving intermittent contact, such as an assembly task, it is helpful to be able to simulate the task accurately and efficiently. In the past ten years, the prox formulation of the equations of motion has arisen as a competitive alternative to the well-known linear and nonlinear complementarity problem (LCP and NCP) formulations. In this paper, we compare these two formulations, showing through a set-based argument that the formulations are equivalent. Second, we provide simple examples to compare the most common approaches for solving these formulations. The prox formulation is solved by fixed-point iteration while the complementarity formulation is solved by a pivoting scheme, known as Lemke's algorithm. The well-known paradox of PAINLEVÉ is used in a case where two solutions exist to illustrate that the fixed-point scheme can fail while the pivoting scheme will succeed.

Domaines: Sciences de l'ingénieur [physics]

Thorsten Schindler, Binh Nguyen, Jeff Trinkle. Understanding the difference between prox and complementarity formulations for simulation of systems with contact. IEEE/RSJ International Conference on Intelligent Robots and Systems, Sep 2011, San Fransisco, United States. ⟨10.1109/IROS.2011.6094779⟩. ⟨hal-01309169⟩