This thesis introduces a new measure of balance for bipedal robotics called the foot placement estimator (FPE). To develop this measure, stability first is defined for a simple biped. A proof of the stability of a simple biped in a controls sense is shown to exist using classical methods for nonlinear systems. With the addition of a contact model, an analytical solution is provided to define the bounds of the region of stability. This provides the basis for the FPE which estimates where the biped must step in order to be stable. By using the FPE in combination with a state machine, complete gait cycles are created without any precalculated trajectories. This includes gait initiation and termination. The bipedal model is then advanced to include more realistic mechanical and environmental models and the FPE approach is verified in a dynamic simulation. From these results, a 5-link, point-foot robot is designed and constructed to provide the final validation that the FPE can be used to provide closed-loop gait control. In addition, this approach is shown to demonstrate significant robustness to external disturbances. Finally, the FPE is shown in experimental results to be an unprecedented estimate of where humans place their feet for walking and jumping, and for stepping in response to an external disturbance.

This thesis introduces a new measure of balance for bipedal robotics called the foot placement estimator (FPE). To develop this measure, stability first is defined for a simple biped. A proof of the stability of a simple biped in a controls sense is shown to exist using classical methods for nonlinear systems. With the addition of a contact model, an analytical solution is provided to define the bounds of the region of stability. This provides the basis for the FPE which estimates where the biped must step in order to be stable. By using the FPE in combination with a state machine, complete gait cycles are created without any precalculated trajectories. This includes gait initiation and termination. The bipedal model is then advanced to include more realistic mechanical and environmental models and the FPE approach is verified in a dynamic simulation. From these results, a 5-link, point-foot robot is designed and constructed to provide the final validation that the FPE can be used to provide closed-loop gait control. In addition, this approach is shown to demonstrate significant robustness to external disturbances. Finally, the FPE is shown in experimental results to be an unprecedented estimate of where humans place their feet for walking and jumping, and for stepping in response to an external disturbance.

Pronking is a legged locomotory gait in which all legs are used in synchrony, usually resulting in slow speeds but long flight phases and large jumping heights that may potentially be useful for mobile robots locomoting in cluttered natural environments. Instantiations of this gait for robotic systems suffer from severe pitch instability either due to underactuated leg designs, or the open-loop nature of proposed controllers. Nevertheless, both the kinematic simplicity of this gait and its dynamic nature suggest that the Spring-Loaded Inverted Pendulum Model (SLIP), a very successful predictive model for both natural and robotic runners, would be a good basis for more robust and maneuverable robotic pronking. In the scope of thesis, we describe a novel controller to achieve stable and controllable pronking for a planar, underactuated hexapod model, based on the idea of &ldquo / template-based control&rdquo / , a controller structure based on the embedding of a simple dynamical template within a more complex anchor system. In this context, high-level control of the gait is regulated through speed and height commands to the SLIP template, while the embedding controller based on approximate inverse-dynamics and carefully designed passive robot morphology ensures the stability of the remaining degrees of freedom. We show through extensive simulation experiments that unlike existing open-loop alternatives, the resulting control structure provides stability, explicit maneuverability and significant robustness against sensor noise.

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