Hitting the sweet spot: automatic optimization of energy transfer during tool-held hits

Abstract

Tool-held hitting tasks, like hammering a nail or striking a ball with a bat, require humans, and robots, to purposely collide and transfer momentum from their limbs to the environment. Due to the vibrational dynamics, every tool has a location where a hit is most efficient results in minimal tool vibrations, and consequently maximum energy transfer to the environment. In sports, this location is often referred to as the "sweet spot" of a bat, or racquet. Our recent neuroscience study suggests that humans optimize hits by using the jerk and torque felt at their hand. Motivated by this result, in this work we first analyze the vibrational dynamics of an end-effector-held bat to understand the signature projected by a sweet spot on the jerk and torque sensed at the end-effector. We then use this analysis to develop a controller for a robotic "baseball hitter". The controller enables the robot-hitter to iteratively adjust its swing trajectory to ensure that the contact with the ball occurs at the sweet spot of the bat. We tested the controller on the DLR LWR III manipulator with three different bats. Like a human, our robot hitter is able to optimize the energy transfer, specifically maximize the ball velocity, during hits, by using its end effector position and torque sensors, and without any prior knowledge of the shape, size or material of the held bat.