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For a compass-like biped robot, the problem of achieving stable walking on both ideal inclined surfaces and complex environments is studied. For the case of walking on ideal inclined surfaces, a feedback-control law is obtained via feedback-linearization techniques so that the trajectory of the robot converges to a desired passive walking gait. Simulations show that it leads to a larger basin of attraction. For the case of walking in complex environments, a scheme is developed with regulable step length and walking speed. Different reference trajectories are constructed for different steps, and corresponding feedback-control laws are updated at the beginning of each step. Then, it is shown that the errors that measure the difference of the response trajectory and the reference one asymptotically converge to zero. An example of walking over stairs is given to numerically verify and demonstrate our approach. [ABSTRACT FROM AUTHOR]

Consider a biped evolving in the sagittal plane. The unexpected rotation of the supporting foot can be avoided by controlling the zero moment point (ZMP). The objective of this study is to propose and analyze a control strategy for simultaneously regulating the position of the ZMP and the joints of the robot. If the tracking requirements were posed in the time domain, the problem would be underactuated in the sense that the number of inputs would be less than the number of outputs. To get around this issue, the proposed controller is based on a path-following control strategy, previously developed for dealing with the underactuation present in planar robots without actuated ankles. In particular, the control law is defined in such a way that only the kinematic evolution of the robot's state is regulated, but not its temporal evolution. The asymptotic temporal evolution of the robot is completely defined through a one degree-of-freedom subsystem of the closed-loop model. Since the ZMP is controlled, bipedal walking that includes a prescribed rotation of the foot about the toe can also be considered. Simple analytical conditions are deduced that guarantee the existence of a periodic motion and the convergence toward this motion. [ABSTRACT FROM AUTHOR]