Design of convex model predictive control for foothold optimization of quadrupedal robot

Abstract

Legged robots have been actively researched in many fields such as rescue operation or freight transport. This is based on characteristics of legged robots: the payloads of legged robots are larger than those of aerial vehicles, and they are able to perform much dynamic tasks on complex terrain compared to wheeled drones. In order to maximize the utilization of legged robots, it is necessary to control robust movement of robots even within complex terrain and various hardware constraints. Therefore, model predictive control(MPC) techniques, which are optimal control algorithms that can calculate control inputs taking into account various constraints, are being studied actively in legged robot academic. However, since the dynamics of multi-joint robots is nonlinear in general, many existing studies have used simplified models of the actual legged robot to apply the dynamics to real-time optimal control algorithms. In particular, separate controllers based on simple models, such as linear inverted pendulum model(LIPM), are generally used used to select foothold of a robot in the process of simplifying the dynamics model. However, those models for foothold selection are not suitable for walking in non-ground environments such as ramps, walls and ceilings, as they assume walking on a flat ground surface. Therefore, we proposed the MPC framework which could simultaneously optimize foothold and ground reaction forces(GRFs) of quadrupedal robots under arbitrary terrain. Through computer simulation, it was verified that the proposed MPC framework can optimize foothold and control motion of a quadrupedal robot under non-ground environment such as wall climbing or walking on a precipice.