On the Dynamics of Bounding and Extensions: Towards the Half-Bound and Gallop Gaits

This paper examines how simple control laws stabilize complex running behaviors such as bounding. First, we discuss the unexpectedly different local and global forward speed versus touchdown angle relationships in the self-stabilized Spring Loaded Inverted Pendulum. Then we show that, even for a more complex energy conserving unactuated quadrupedal model, many bounding motions exist, which can be locally open loop stable! The success of simple bounding controllers motivated the use of similar control laws for asymmetric gaits resulting in the first experimental implementations of the half-bound and the rotary gallop on Scout II.