  Legged robots are typically in rigid contact with the environment at multiple
locations, which add a degree of complexity to their control. We present a
method to control the motion and a subset of the contact forces of a
floating-base robot. We derive a new formulation of the lexicographic
optimization problem typically arising in multitask motion/force control
frameworks. The structure of the constraints of the problem (i.e. the dynamics
of the robot) allows us to find a sparse analytical solution. This leads to an
equivalent optimization with reduced computational complexity, comparable to
inverse-dynamics based approaches. At the same time, our method preserves the
flexibility of optimization based control frameworks. Simulations were carried
out to achieve different multi-contact behaviors on a 23-degree-offreedom
humanoid robot, validating the presented approach. A comparison with another
state-of-the-art control technique with similar computational complexity shows
the benefits of our controller, which can eliminate force/torque
discontinuities.
