The industry needs controllers that allow smooth and natural physical Human-Robot Interaction (pHRI) to make production scenarios more flexible and user-friendly. Within this context, particularly interesting is Role Arbitration, which is the mechanism that assigns the role of the leader to either the human or the robot. This paper investigates Game-Theory (GT) to model pHRI, and specifically, Cooperative Game Theory (CGT) and Non-Cooperative Game Theory (NCGT) are considered. This work proposes a possible solution to the Role Arbitration problem and defines a Role Arbitration framework based on differential game theory to allow pHRI. The proposed method can allow trajectory deformation according to human will, avoiding reaching dangerous situations such as collisions with environmental features, robot joints and workspace limits, and possibly safety constraints. Three sets of experiments are proposed to evaluate different situations and compared with two other standard methods for pHRI, the Impedance Control, and the Manual Guidance. Experiments show that with our Role Arbitration method, different situations can be handled safely and smoothly with a low human effort. In particular, the performances of the IMP and MG vary according to the task. In some cases, MG performs well, and IMP does not. In some others, IMP performs excellently, and MG does not. The proposed Role Arbitration controller performs well in all the cases, showing its superiority and generality. The proposed method generally requires less force and ensures better accuracy in performing all tasks than standard controllers. Note to Practitioners—This work presents a method that allows role arbitration for physical Human-Robot Interaction, motivated by the need to adjust the role of leader/follower in a shared task according to the specific phase of the task or the knowledge of one of the two agents. This method suits applications such as object co-transportation, which requires final precise positioning but allows some trajectory deformation on the fly. It can also handle situations where the carried obstacle occludes human sight, and the robot helps the human to avoid possible environmental obstacles and position the objects at the target pose precisely. Currently, this method does not consider external contact, which is likely to arise in many situations. Future studies will investigate the modeling and detection of external contacts to include them in the interaction models this work addresses
