  This manuscript presents a model of compliant contacts for time-critical
humanoid robot motion control. The proposed model considers the environment as
a continuum of spring-damper systems, which allows us to compute the equivalent
contact force and torque that the environment exerts on the contact surface. We
show that the proposed model extends the linear and rotational springs and
dampers - classically used to characterize soft terrains - to the case of large
contact surface orientations. The contact model is then used for the real-time
whole-body control of humanoid robots walking on visco-elastic environments.
The overall approach is validated by simulating walking motions of the iCub
humanoid robot. Furthermore, the paper compares the proposed whole-body control
strategy and state of the art approaches. In this respect, we investigate the
terrain compliance that makes the classical approaches assuming rigid contacts
fail. We finally analyze the robustness of the presented control design with
respect to non-parametric uncertainty in the contact-model.
