Wearable robotics is a growing sector in the robotics industry, they can increase the productivity of workers and soldiers and can restore some of the lost function to people with disabilities. Wearable robots should be comfortable, easy to use, and intuitive. Robust control methods are needed for wearable robots that assist periodic motion.

This dissertation studies a phase based oscillator constructed with a second order dynamic system and a forcing function based on the phase angle of the system. This produces a bounded control signal that can alter the damping and stiffens properties of the dynamic system. It is shown analytically and experimentally that it is stable and robust. It can handle perturbations remarkably well. The forcing function uses the states of the system to produces stable oscillations. Also, this work shows the use of the phase based oscillator in wearable robots to assist periodic human motion focusing on assisting the hip motion. One of the main problems to assist periodic motion properly is to determine the frequency of the signal. The phase oscillator eliminates this problem because the signal always has the correct frequency. The input requires the position and velocity of the system. Additionally, the simplicity of the controller allows for simple implementation.