A new control approach to achieve robust hopping against perturbations in the sagittal plane is presented in this paper. In perturbed hopping, vertical body alignment has a significant role for stability. Our approach is based on the virtual pendulum concept, recently proposed, based on experimental findings in human and animal locomotion. In this concept, the ground reaction forces are pointed to a virtual support point, named virtual pivot point (VPP), during motion. This concept is employed in designing the controller to balance the trunk during the stance phase. New strategies for leg angle and length adjustment besides the virtual pendulum posture control are proposed as a unified controller. This method is investigated by applying it on an extension of the spring loaded inverted pendulum (SLIP) model. Trunk, leg mass and damping are added to the SLIP model in order to make the model more realistic. The stability is analyzed by Poincaré map analysis. With fixed VPP position, stability, disturbance rejection and moderate robustness are achieved, but with a low convergence speed. To improve the performance and attain higher robustness, an event-based control of the VPP position is introduced, using feedback of the system states at apexes. Discrete linear quartic regulator is used to design the feedback controller. Considerable enhancements with respect to stability, convergence speed and robustness against perturbations and parameter changes are achieved.
In this paper, we intend to show the basis of a general legged locomotion controller with the ability to integrate both posture and rhythmic motion controls and shift continuously from one control method to the other according to the walking speed. The rhythmic motion of each leg in the sagittal plane is generated by a single leg controller which controls the swing-to-stance and stanceto-swing phase transitions using respectively leg loading and unloading information. Since rolling motion induced by inverted pendulum motion during the two-legged stance phases results in the transfer of the load between the contralateral legs, leg loading/unloading involves posture information in the frontal plane. As a result of the phase modulations based on leg loading/unloading, rhythmic motion of each leg is achieved and inter-leg coordination (resulting in a gait) emerges, even without explicit coordination amongst the leg controllers, allowing to realize dynamic walking in the low-to medium-speed range. We show that the proposed method has resistance C. Maufroy ( ) ability against lateral perturbations to some extent, but that an additional ascending coordination mechanism between ipsilateral legs is necessary to withstand perturbations decreasing the rolling motion amplitude. Even without stepping reflex using vestibular information, our control system, relying on phase modulations based on leg loading/unloading and the ascending coordination mechanism between ipsilateral legs, enables low speed dynamic walking on uneven terrain with long cyclic period, which was not realized in our former studies. Details of trajectory generation, movies of simulations and movies of preliminary experiments using a real robot are available at: http://robotics.mech.kit.ac.jp/kotetsu/.
Abstract-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 stabilzed 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 acheieved.
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