  Optimal control approaches in combination with trajectory optimization have
recently proven to be a promising control strategy for legged robots.
Computationally efficient and robust algorithms were derived using simplified
models of the contact interaction between robot and environment such as the
linear inverted pendulum model (LIPM). However, as humanoid robots enter more
complex environments, less restrictive models become increasingly important. As
we leave the regime of linear models, we need to build dedicated solvers that
can compute interaction forces together with consistent kinematic plans for the
whole-body. In this paper, we address the problem of planning robot motion and
interaction forces for legged robots given predefined contact surfaces. The
motion generation process is decomposed into two alternating parts computing
force and motion plans in coherence. We focus on the properties of the momentum
computation leading to sparse optimal control formulations to be exploited by a
dedicated solver. In our experiments, we demonstrate that our motion generation
algorithm computes consistent contact forces and joint trajectories for our
humanoid robot. We also demonstrate the favorable time complexity due to our
formulation and composition of the momentum equations.
