  Most animal and human locomotion behaviors for solving complex tasks involve
dynamic motions and rich contact interaction. In fact, complex maneuvers need
to consider dynamic movement and contact events at the same time. We present a
hierarchical trajectory optimization approach for planning dynamic movements
with unscheduled contact sequences. We compute whole-body motions that achieve
goals that cannot be reached in a kinematic fashion. First, we find a feasible
CoM motion according to the centroidal dynamics of the robot. Then, we refine
the solution by applying the robot's full-dynamics model, where the feasible
CoM trajectory is used as a warm-start point. To accomplish the unscheduled
contact behavior, we use complementarity constraints to describe the contact
model, i.e. environment geometry and non-sliding active contacts. Both
optimization phases are posed as Mathematical Program with Complementarity
Constraints (MPCC). Experimental trials demonstrate the performance of our
planning approach in a set of challenging tasks.
