  This paper presents a layered control approach for real-time trajectory
planning and control of robust cooperative locomotion by two holonomically
constrained quadrupedal robots. A novel interconnected network of reduced-order
models, based on the single rigid body (SRB) dynamics, is developed for
trajectory planning purposes. At the higher level of the control architecture,
two different model predictive control (MPC) algorithms are proposed to address
the optimal control problem of the interconnected SRB dynamics: centralized and
distributed MPCs. The distributed MPC assumes two local quadratic programs that
share their optimal solutions according to a one-step communication delay and
an agreement protocol. At the lower level of the control scheme, distributed
nonlinear controllers are developed to impose the full-order dynamics to track
the prescribed reduced-order trajectories generated by MPCs. The effectiveness
of the control approach is verified with extensive numerical simulations and
experiments for the robust and cooperative locomotion of two holonomically
constrained A1 robots with different payloads on variable terrains and in the
presence of disturbances. It is shown that the distributed MPC has a
performance similar to that of the centralized MPC, while the computation time
is reduced significantly.
