The 3-D Spring–Mass Model Reveals a Time-Based Deadbeat Control for Highly Robust Running and Steering in Uncertain Environments

Over the past three decades, the spring-mass model has developed into the basic behavior model to study running in animals and robots. In the planar version, this model has helped to reveal and understand the passive stabilization of running in the horizontal and sagittal planes, and to derive from this knowledge control strategies for running robots. However, only few attempts have been made to transfer the knowledge to 3-D locomotion. Here, we show that the 3-D spring-mass model reveals a deadbeat control that does not require feedback about the actual ground level to produce highly robust running and steering in uncertain environments. The control naturally extends the time-based control derived for the planar version of this model and allows it to navigate rough terrain, while stabilizing running and steering. Using this control strategy, we demonstrate in simulation that a human-like system running at 5 ms^-1 tolerates frequent ground disturbances up to 30% of the leg length. Moreover, we find that the control outperforms a classical leg-placement strategy in terms of turning rate and disturbance rejection if the relative errors in system energy and the other model parameters stay small ( 10%). Our results suggest that the time-based control can be a powerful alternative for leg-placement strategies in highly maneuverable running robots.