  Applications involving humans and robots working together are spreading
nowadays. Alongside, modeling and control techniques that allow physical
Human-Robot Interaction (pHRI) are widely investigated. To better understand
its potential application in pHRI, this work investigates the Cooperative
Differential Game Theory modeling of pHRI in a cooperative reaching task,
specifically for reference tracking. The proposed controller based on
Collaborative Game Theory is deeply analyzed and compared in simulations with
two other techniques, Linear Quadratic Regulator (LQR) and Non-Cooperative
Game-Theoretic Controller. The set of simulations shows how different tuning of
control parameters affects the system response and control efforts of both the
players for the three controllers, suggesting the use of Cooperative GT in the
case the robot should assist the human, while Non-Cooperative GT represents a
better choice in the case the robot should lead the action. Finally,
preliminary tests with a trained human are performed to extract useful
information on the real applicability and limitations of the proposed method.
