The formulation of a stability criterion is crucial to perform safe, versatile and efficient biped gaits for robots. We here present a stability criterion for non-cyclic gait synthesis, the Predicted Step Viability, inspired by human gait and N-Step Capturability. The Predicted Step Viability defines the constraints of the current step such that future steps will be able to guarantee convergence to a stable point in finite time. In this way, it is based on the prediction of future viable steps to ensure stability. The criterion was implemented using multiphase trajectory optimization on two biped models, the Compass Gait and the five-link model RABBIT. The Compass Gait was simulated with different model parameters and gait patterns including a random non-periodic one. The five-link model was tested with linear and random reference gait patterns. The Predicted Step Viability criterion successfully generated stable non-periodic gaits under a variety of conditions. Moreover, it is possible to prescribe any gait pattern completely uncoupled from the stability criterion. If it were impossible to follow the prescribed pattern without falling, the controller would give it up, maintaining stability.

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The goals of this work are to develop a biped gait controller and an active fall recovery algorithm, both based on the capture point stability theory with the criterion of N-step capturability, validate this algorithms via simulations; and to design a biped robot that represents gait on the sagittal plane, capable of serving as a test-bed for legged locomotion research. The effectiveness of the controller and fall recovery are assessed through simulations, with the designed robot, that imposes different types of perturbations, such as: pushes, ramps and irregular terrain. The controller ability to modulate the robot's velocity is also demonstrated. The fall recovery algorithm is addressed as a solution to increase robustness without significant detriment to energy efficiency. The controller was proved successful in the simulations, it only demonstrated speed limitation on descending slopes. The fall recovery manages to significantly increase robustness of a standard, energy efficient gait.

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