  Forced variational integrators are given by the discretization of the
Lagrange-d'Alembert principle for systems subject to external forces, and have
proved useful for numerical simulation studies of complex dynamical systems. In
this paper we model a passive walker with foot slip by using techniques of
geometric mechanics, and we construct forced variational integrators for the
system. Moreover, we present a methodology for generating (locally) optimal
control policies for simple hybrid holonomically constrained forced Lagrangian
systems, based on discrete mechanics, applied to a controlled walker with foot
slip in a trajectory tracking problem.
