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

Abstract

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 con-
trol that does not require feedback about the actual ground level to
produce highly robust running and steering in uncertain environ-
ments. The control naturally extends the time-based control de-
rived 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 turn-
ing 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 alter- native for leg-placement strategies in highly maneuverable running robots.