Mechanical Antagonism in Legged Robots

In this work, we use first principles of kinematics to provide a fundamental insight into mechanical power distribution within multi-actuator machines. Individual actuator powers—not their net sum—determine the efficiency and actuator size of a multi-joint machine. Net power delivered to the environment naturally discards important information about how that power is generated. For example, simultaneous positive and negative powers will cancel within a mechanism, wasting energy and raising peak power requirements. The same effect can bias power draw toward a single actuator while the other actuators do zero work. In general, it is best for all actuators to contribute equally to the net power demand because balance minimizes the mechanical power requirements of individual actuators. In this paper, we present the actuation power space, within which we measure the antagonism in a machine (joints working against each other due to kinematic constraints). We show the difference between the net power consumed by the task and the total power supplied by the actuators. We derive the power quality measure as a smooth objective function which encodes both antagonism and the balance of power between actuators. As a demonstration of our general framework, we apply our technique to a legged-robot design to find improved kinematics for performing a running gait. This technique finds mechanisms with optimal power distribution, regardless of actuator choice or loss models, so it can be applied early in the design process using mechanism kinematics alone. After choosing appropriate kinematics for an application, designers can independently optimize each actuator in a design to minimize local losses.