Abstract
In this paper, we present a novel method to model and simulate nonsmooth mechanical systems, with the intent on application for legged robots. The method uses a binary vector to keep track of the changing set of active constraints. As a result, the dynamics of the nonsmooth mechanical system is formulated into a single set of differential equations and a switching set of kinematic constraints. Compared to the conventional mode-based approach, the proposed method (i) does not require exhaustive mode enumeration, (ii) is simpler to derive, and (iii) scales better to complex, higher-dimensional systems. We demonstrate the utility of the proposed method by simulating a five-bar planar hopping robot.