Implicit nonlinear complementarity: A new approach to contact dynamics

— Contact dynamics are commonly formulated as a linear complementarity problem. While this approach is superior to earlier spring-damper models, it can be inaccurate due to pyramid approximations to the friction cone, and inefficient due to lack of convexity coupled with a large number of auxiliary variables. Here we propose a new approach: implicit complementarity. Instead of treating contact velocities and forces as independent variables subject to explicit complementarity constraints, we express them as functions of a minimal set of unconstrained variables, and design these functions so that the complementarity constraints are automatically satisfied. We then solve the equations of motion via a non-smooth Gauss-Newton method augmented with an original linesearch procedure which exploits the problem structure. This enables us to represent the friction cone exactly and to reduce the number of unknowns by about a factor of 3. Numerical tests suggest that, in usage scenarios typical...

• Type: Journal
• Year: 2010
• Where: ICRA
• Authors: Emanuel Todorov
• Keywords: Complementarity Constraints, Friction Cone, ICRA 2010, Linear Complementarity Problem, Robotics