Implicit nonlinear complementarity: A new approach to contact dynamics

摘要: 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 pyramid approximations the friction cone, and inefficient lack of convexity coupled with large number auxiliary variables. Here we propose new approach: implicit complementarity. Instead treating contact velocities forces independent variables subject explicit constraints, express them functions minimal set unconstrained variables, design these so that constraints automatically satisfied. We then solve equations motion via non-smooth Gauss-Newton method augmented an original linesearch procedure which exploits problem structure. This enables us represent cone exactly reduce unknowns by about factor 3. Numerical tests suggest that, in usage scenarios typical for robotics, solver takes only 5 iterations even without warm starts. More extensive side-by-side comparisons remain done, but nevertheless potential clear.