Controllers for robust hopping with upright trunk based on the Virtual Pendulum concept

This paper presents a new control approach to achieve robust hopping with upright trunk in the sagittal plane. It relies on an innovative concept for trunk stabilization, called Virtual Pendulum concept, recently proposed, based on experimental finding in animal locomotion. With this concept, the trunk is stabilized by redirecting the ground reaction force to a virtual support point, named Virtual Pivot Point (VPP). This concept is combined with a new leg adjustment scheme to induce stable hopping when an extended trunk is added to SLIP model. The stability is investigated by Poincaré map analysis. With fixed VPP position, stability, disturbance rejection and moderate robustness are achieved, but with low convergence speed. To improve the performances and attain higher robustness, event based control of VPP position is introduced, using feedback of the system state at apex. Dead beat control and Discrete LQR are alternatively considered to adjust the feedback gains. In both cases, considerable enhancements with respect to stability, convergence speed and robustness against perturbations are achieved.