  In this paper we explore the use of block coordinate descent (BCD) to
optimize the centroidal momentum dynamics for dynamically consistent
multi-contact behaviors. The centroidal dynamics have recently received a large
amount of attention in order to create physically realizable motions for robots
with hands and feet while being computationally more tractable than full rigid
body dynamics models. Our contribution lies in exploiting the structure of the
dynamics in order to simplify the original non-convex problem into two convex
subproblems. We iterate between these two subproblems for a set number of
iterations or until a consensus is reached. We explore the properties of the
proposed optimization method for the centroidal dynamics and verify in
simulation that motions generated by our approach can be tracked by the
quadruped Solo12. In addition, we compare our method to a recently proposed
convexification using a sequence of convex relaxations as well as a more
standard interior point method used in the off- the-shelf solver IPOPT to show
that our approach finds similar, if not better, trajectories (in terms of
cost), and is more than four times faster than both approaches. Finally,
compared to previous approaches, we note its practicality due to the convex
nature of each subproblem which allows our method to be used with any
off-the-shelf quadratic programming solver.
