  Bipedal walking is one of the most important hallmarks of human that robots
have been trying to mimic for many decades. Although previous control
methodologies have achieved robot walking on some terrains, there is a need for
a framework allowing stable and robust locomotion over a wide range of
compliant surfaces. This work proposes a novel biomechanics-inspired controller
that adjusts the stiffness of the legs in support for robust and dynamic
bipedal locomotion over compliant terrains. First, the 3D Dual-SLIP model is
extended to support for the first time locomotion over compliant surfaces with
variable stiffness and damping parameters. Then, the proposed controller is
compared to a Linear-Quadratic Regulator (LQR) controller, in terms of
robustness on stepping on soft terrain. The LQR controller is shown to be
robust only up to a moderate ground stiffness level of 174 kN/m, while it fails
in lower stiffness levels. On the contrary, the proposed controller can produce
stable gait in stiffness levels as low as 30 kN/m, which results in a vertical
ground penetration of the leg that is deeper than 10% of its rest length. The
proposed framework could advance the field of bipedal walking, by generating
stable walking trajectories for a wide range of compliant terrains useful for
the control of bipeds and humanoids, as well as by improving controllers for
prosthetic devices with tunable stiffness.
