Lift-off dynamics in a simple jumping robot.

We study vertical jumping in a simple robot comprising an actuated mass-spring arrangement. The actuator frequency and phase are systematically varied to find optimal performance. Optimal jumps occur above and below (but not at) the robot's resonant frequency f(0). Two distinct jumping modes emerge: a simple jump, which is optimal above ff(0), is achievable with a squat maneuver, and a peculiar stutter jump, which is optimal below f(0), is generated with a countermovement. A simple dynamical model reveals how optimal lift-off results from nonresonant transient dynamics.