Optimization-based motion generation for multiped robots in contact scenarios

Abstract

The introduction of legged robots into society has the potential to impact many aspects of our lives. The versatile morphology of robots with arms and legs, or multipeds, allows them to operate in a broad spectrum of environments. For example, legged robots could assist at construction sites or locomote in rocky terrain under persistent interaction with the environment through contact. These behaviors require algorithms that translate high level operator commands into movement and contact interaction with the environment, steering robots towards successful task completion. Traditional planning and control methods are limited by a core property of legged robots; they can fall. Control algorithms must respond quickly in order to keep a multiped in balance, and planners are required to respond to changes in the environment. This thesis presents a movement control framework designed to control complex contact interactions between a multiped robot and its environment. An optimal control based architecture is proposed that treats planning and control as one coherent optimization program. The lookahead capabilities of planners are combined with the reactiveness of feedback controllers in a multi-layer optimization architecture. An optimal control problem plans whole-body motion and contact forces over a lookahead while a fast feedback loop computes motor commands consistent with the current higher layer plan. At the core of our analysis we exploit the mathematical structure relating the robot’s center of mass to the contact forces between the robot and the environment, leading to a specialized algorithm combining planning and control. A trajectory optimization method is proposed to compute whole-body motion and corresponding contact force plans. It is decomposed into two sub-problems with reduced complexity and solved with a composition of specialized solvers. A reactive feedback controller tracks the high level plan using hierarchical inverse dynamics. Our control architecture successfully plans and controls a stepping task over com- plex terrain. Optimal control depends on an accurate robot model and often ignores real-world sensor noise and delay. Further, the short reaction time required to prevent legged robots from falling limits the amount of computation time permitted. Therefore, we demonstrate the validity of our approach and modeling assumptions through experimental validation on a torque controlled humanoid robot. An efficient implementation of our hierarchical inverse dynamics solver in a 1kHz control loop exhibits robust push rejection in a series of balancing experiments. The proposed controller successfully balances in a wide range of scenarios, includ- ing on a moving see-saw, on a sliding platform, and being pushed while standing on one foot and tracking a desired trajectory with the other.