| Bipeds are attractive examples of multibody dynamic systems in continuous interaction with the environment, for which optimization approaches are usually required to solve the numerous kinetic and kinematic redundancies. Understanding the motion, control, and stability of the human body is important in several clinical applications and may inspire the control and physical construction of humanoid robots.;The background of this dissertation is concerned with the fundamental principles of dynamic walking. The novel Dynamic Gait Measure (DGM) is developed to provide a systematic quantification of how much a given walking motion is dynamic (i.e., statically unstable), based on the normalized distance between the center of pressure and the ground projection of the center of mass. The DGM represents a measure of static balance instability of biped walking during the entire gait cycle, as well as its phases, and reveals the effect that a given gait strategy has on gait balance stability.;While the DGM is a useful measure for benchmarking human locomotion and assessing robots performance, it is not a direct fall predictor. For this reason, a general method is established in this dissertation to provide a three-dimensional balance criterion for multi-segmental legged mechanisms. The threshold between balance and falling is formulated as the balance stability boundary, in the center of mass Cartesian state space, that includes all possible balanced states of a given legged system. An optimization-based numerical algorithm is proposed to build the balance stability boundary for a given system, which quantifies the maximum allowable size of perturbation in various directions to maintain balance, without stepping. Analyzing walking trajectories in the state space with respect to the stability boundary can provide useful insights on the dynamic and balance characteristics of human and humanoid gait.;Using the DGM and balance stability boundary as quantitative tools, the dynamic and balance characteristics of walking could be studied with respect to other performance criteria, such as gait efficiency. Numerous experimental studies on both human and robotic walking suggest that there exists an optimal trade-off between gait balance stability and walking efficiency, realized through the selection of a preferred gait strategy (i.e., spatial and temporal step parameters). However, an optimization environment that can predict the preferred gait strategy and resulting dynamic, stability, and energetic characteristics of a given biped system is, so far, not available. The trajectories and control of redundant systems under unilateral constraints, such as bipeds, are coupled with contact forces distribution in time and space as an indeterminate problem, to be solved within a general optimal motion planning and control framework. Based on these motivations, a novel optimization formulation is proposed in this dissertation to concurrently solve for optimal trajectories, control inputs, contact schedule (i.e., when, where, and whether contacts happen), and contact forces for redundant mechanisms during generic tasks. The proposed approach is demonstrated through the prediction of the optimal relationships between speed and step length, energetic cost, and DGM of a given biped system during steady-state locomotion.;The established measures and optimization approaches are essential for investigating how different biped systems leverage their dynamics to achieve desired features, such as improved stability and efficiency. The synergetic use of the proposed methods can be beneficial to the analysis of normal and pathological human gait and has the potential to assist the design of robot, exoskeletons, and prosthesis. |
