Distributed Quadratic Programming-Based Nonlinear Controllers for Periodic Gaits on Legged Robots

Quadratic programming (QP)-based nonlinear controllers have gained increasing popularity in the legged locomotion community. This letter presents a formal foundation to systematically decompose QP-based centralized nonlinear controllers into a network of lower-dimensional local QPs, with application to legged locomotion. The proposed approach formulates a feedback structure between the local QPs and assumes a one-step communication delay protocol. The properties of local QPs are analyzed, wherein it is established that their steady-state solutions on periodic orbits (representing gaits) coincide with that of the centralized QP. The asymptotic convergence of local QPs’ solutions to the steady-state solution is studied via Floquet theory. The effectiveness of the analytical results is evaluated through rigorous numerical simulations and various experiments on a quadrupedal robot, with the result being robust locomotion on different terrains and in the presence of external disturbances. This letter shows that the proposed distributed QPs have considerably less computation time and reduced noise propagation sensitivity than the centralized QP.