What if there is a way to integrate prosthetics seamlessly with the human body and robots could help improve the lives of children with disabilities? With physical human-robot interaction being seen in multiple aspects of life, including industry, medical, and social, how these robots are interacting with human becomes even more important. Therefore, how smoothly the robot can interact with a person will determine how safe and efficient this relationship will be. This thesis investigates adaptive control method that allows a robot to adapt to the human's actions based on the interaction force. Allowing the relationship to become more effortless and less strained when the robot has a different goal than the human, as seen in Game Theory, using multiple techniques that adapts the system. Few applications this could be used for include robots in physical therapy, manufacturing robots that can adapt to a changing environment, and robots teaching people something new like dancing or learning how to walk after surgery.

The experience gained is the understanding of how a cost function of a system works, including the tracking error, speed of the system, the robot’s effort, and the human’s effort. Also, this two-agent system, results into a two-agent adaptive impedance model with an input for each agent of the system. This leads to a nontraditional linear quadratic regulator (LQR), that must be separated and then added together. Thus, creating a traditional LQR. This new experience can be used in the future to help build better safety protocols on manufacturing robots. In the future the knowledge learned from this research could be used to develop technologies for a robot to allow to adapt to help counteract human error.