Structure preserving simulation of monopedal jumping

This work considers the structure preserving simulation of three-dimensional multibody dynamics with contacts. The used variational integrator is based on a discrete version of the Lagrange-d'Alembert principle, which yields a symplectic momentum method. One of our main goals is to guarantee the structure preservation and the geometric correctness, thus we solve the non-smooth problem including the computation of the contact configuration, time and force instead of relying on a smooth approximation of the contact problem via a penalty potential. In addition to the formulation of non-smooth problems in forward dynamic simulations, we are interested in the optimal control of the monopedal high jump. The optimal control problem is solved using a direct transcription method transforming it into a finite dimensional constrained optimisation problem. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)