A penalty-based approach for contact forces computation in bipedal robots

Computation of contact forces is essential for the simulation of mechanical systems with unilateral constraints, like bipedal robots. Most methods are based on the rigid body assumption. They can be categorized into constraint-based and penalty-based approaches. In the former, contact forces are computed by solving an optimization problem based on linear or nonlinear complementarity conditions. Unfortunately, these methods cannot be directly applied to articulated systems described in generalized coordinates. In the second approach, spring-damper models are used to minimize interpenetration between the surfaces in contact. The main criticism to penalty approaches are parameter tuning, static friction handling, and the difficulties to treat multiple simultaneous unilateral contacts. In this work we present a new compliant approach based on input-output feedback linearization. The main advantages of the proposed approach are, the spring-damper parameters are independent of the parameters of the system (i.e masses, inertias), no a priori-defined velocity thresholds are required to distinguish between dynamic and static friction, multiple simultaneous unilateral contacts are naturally handled. The proposition has been successfully applied to the simulation of a 3D bipedal walking robot.