On the Dynamic Similarity Between Bipeds and Quadrupeds: A Case Study on Bounding

In this letter, we identify passive dynamic bounding gaits of quadrupedal robots and investigate the dynamic similarities between these gaits and those of a bipedal model. For this purpose, we develop a passive dynamic bounding model of a quadruped with an extended main body. This model is based on the established SLIP model, yet has dynamic swing leg motions instead of a predefined angle of attack. We present a gait-identification framework that is based on a numerical continuation approach and that allows us to find all possible passive periodic motions that emerge from pronking and bounding in place. These gaits include forward pronking as well as forward bounding with gathered suspension, extended suspension, and with two suspensions. By conducting a parameter study on the body inertia, we can draw parallels between bipedal and quadrupedal gaits, and can also show how the structure of possible solutions changes with the main body inertia. In particular, we see sudden changes in the gait structure at certain critical values of the main body inertia. This letter shows connections between different types of quadrupedal gaits and may serve as a guideline in the design and control of gaits for energetically economical legged robots. It also sheds some light at the question why animals with different morphology use different gaits at the same Froude numbers.