  This paper aims to develop distributed feedback control algorithms that allow
cooperative locomotion of quadrupedal robots which are coupled to each other by
holonomic constraints. These constraints can arise from collaborative
manipulation of objects during locomotion. In addressing this problem, the
complex hybrid dynamical models that describe collaborative legged locomotion
are studied. The complex periodic orbits (i.e., gaits) of these sophisticated
and high-dimensional hybrid systems are investigated. We consider a set of
virtual constraints that stabilizes locomotion of a single agent. The paper
then generates modified and local virtual constraints for each agent that allow
stable collaborative locomotion. Optimal distributed feedback controllers,
based on nonlinear control and quadratic programming, are developed to impose
the local virtual constraints. To demonstrate the power of the analytical
foundation, an extensive numerical simulation for cooperative locomotion of two
quadrupedal robots with robotic manipulators is presented. The numerical
complex hybrid model has 64 continuous-time domains, 192 discrete-time
transitions, 96 state variables, and 36 control inputs.
