A Novel Model Predictive Control Framework Using Dynamic Model Decomposition Applied to Dynamic Legged Locomotion

Dynamic locomotion for legged robots is difficult because the system dynamics are highly nonlinear and complex, nominally underactuated and unstable, multi-input and multi-output, as well as time-variant and hybrid. One usually faces the choice between the intricate full-body dynamics which remains computationally expensive and sometimes even intractable, and the empirically simplified model which inevitably limits the locomotion capability. In this paper, we explore the legged robot dynamics from a different perspective. By decomposing the robot into the body and the legs, with interaction forces and moments connecting them, we enjoy a novel method called Dynamic Model Decomposition that involves lower-dimensional dynamics for each subsystem while their composition maintaining the equivalence to the original full-order robot model. Based on that, we further propose a corresponding model predictive control framework via quadratic programming, which con-siders linearly approximated body dynamics with constrained leg reaction forces as inputs. The overall methodology was successfully applied to a planar five-link biped robot. The simulation results show that the robot is capable of body reference tracking, push recovery, velocity tracking, and even blind locomotion on fairly rough terrain. This suggests a promising dynamic motion control scheme in the future.