  In this paper, we improve upon a method for optimal control of quadrupedal
robots which utilizes a full-order model of the system. The original method
utilizes offline nonlinear optimal control to synthesize a control scheme which
exponentially orbitally stabilizes the closed-loop system. However, it is not
able to handle the overactuated phases which frequently occur during
quadrupedal locomotion as a result of the multi-contact nature of the system.
We propose a modified method, which handles overactuated gait phases in a way
that utilizes the full range of available actuators to minimize torque
expenditure without requiring output trajectories to be modified. It is shown
that the system under the proposed controller exhibits the same properties,
i.e. exponential orbital stability, with the same or lower point-wise torque
magnitude. A simulation study demonstrates that the reduction in torque may in
certain cases be substantial.
