The field of prostheses and rehabilitation devices has seen tremendous advancement since the ’90s. However, the control aspect of the said devices is lacking. The need for mathematical theories to improve the control strategies is apparent. This thesis attempts to bridge the gap by introducing some dynamic system analysis and control strategies.Firstly, the human gait dynamics are assumed to be periodic. Lyapunov Floquet theory and Invariant manifold theory are applied. A transformation is obtained onto a simple single degree of freedom oscillator system. The said system is transformed back into the original domain and compared to the original system. The results are discussed and critiqued. Then the technique is applied to the kinematic and kinetic data collected from healthy human subjects to verify the technique’s feasibility. The results show that the technique successfully reconstructed the kinematic and kinetic data. Human gait dynamics are not purely periodic, so a quasi-periodic approach is adopted. Techniques to reduce the order of a quasi-periodic system are studied. Lyapunov-Peron transformation (a surrogate of Lyapunov Floquet transformation for quasi-periodic systems) is studied. The transformed system is easier to control. The inverse of the said transformation is obtained to transform back to the original domain. The application of the techniques to different cases (including externally forced systems) is studied. The reduction of metabolic cost is presented as a viable goal for applying the previously studied control techniques. An experimental protocol is designed and executed to understand periodic assistive forces' effects on human walking gait. Different tether stiffnesses are used to determine the best stiffness for a given subject population. An estimation technique is introduced to obtain the metabolic cost using the center of mass's kinematic data. Lastly, it is concluded that the mathematical techniques can be utilized in a robotic tail-like rehabilitation device. Some possible future research ideas are provided to implement the techniques mentioned in this dissertation.

In this work, different passive prosthetic ankles are studied. It is observed that complicated designs increase the cost of production, but simple designs have limited functionality. A new design for a passive prosthetic ankle is presented that is simple to manufacture while having superior functionality. This prosthetic ankle design has two springs: one mimicking Achilles tendon and the other mimicking Anterior-Tibialis tendon. The dynamics of the prosthetic ankle is discussed and simulated using Working model 2D. The simulation results are used to optimize the springs stiffness. Two experiments are conducted using the developed ankle to verify the simulation It is found that this novel ankle design is better than Solid Ankle Cushioned Heel (SACH) foot. The experimental data is used to find the tendon and muscle activation forces of the subject wearing the prosthesis using OpenSim. A conclusion is included along with suggested future work.