GAME THEORY: A POTENTIAL TOOL FOR THE DESIGN AND ANALYSIS OF PATIENT ROBOT INTERACTION STRATEGIES

1. GAME THEORY: A POTENTIAL TOOL FOR THE DESIGN AND ANALYSIS OF PATIENT ROBOT INTERACTION STRATEGIES Aodhan L. Coffey, Tomás E. Ward and Richard H. Middleton Biomedical Engineering Research Group, Department of Electronic Engineering, National University of Ireland Maynooth, Ireland 1.Introduction Designing suitable robotic controllers for automating movement-based rehabilitation therapy requires an understanding of the interaction between patient and therapist. Current approaches do not take into account the highly dynamic and interdependent nature of this relationship. We feel that a better understand can be accomplished through framing the interaction as a problem in game theory. Game Theory is a branch of mathematical analysis developed to study social decision making in situations of competition and conflict. Typically these games consist of two or more competitive participants (agents) where the outcome of a participant's choice of action depends critically on the actions of others. When played iteratively participants can, through the adoption of strategies derived from the participant’s model of their opponent, achieve improved payoff over time [1]. • 2. Design • We start by defining each player’s inputs and objectives according to a basic mathematical formulation. • The patient: • A player who wants to successfully complete each motor task (Ti). • Successful completion is determined by an effort threshold En (effort needed) that must be reached. • Patient’s input is defined as Ep = (Effort patient). • The robotic actuator: • A player who will provide additional assistance to the patient ( a therapist ). • The robot’s inputs is defined as Er (Robot effort). • 3.Experimental • We now use our preliminary model to demonstrate plausible patterns of behaviour between patient-therapist. As an example, we simulate ‘learned dependency’. In this instance we model: • The patient - as ‘lazy’, wanting to complete each motor task with the minimum effort possible. Therefore, the player will offer less effort each turn once the task is co-operatively completed, Ep(i+1) = Ep(i)-delta, if T(i)=1. • The therapist - as ‘over helpful’, always providing the additional effort required to complete the task, Er= [En – Ep]. • We then model the interaction through a round based game of 100 iterations. 4. Results and Future Work Given the rules as designed, it is clear that after several iterations the patient will offer almost no effort and yet still ‘successfully’ complete the rehabilitation task thanks to the additional effort offered by the ‘over helpful’ robot. Fig 2: Example of a robotic movement aid device 5. Conclusion Game Theory was developed to treat a wide class of dynamic interactions based on social decision making. From our preliminary models we feel it will have value in understanding the types of interactions that occur between patients and therapists. Furthermore, we believe that such an approach will lead to the development of agent-based controllers which will engage in interaction strategies adapted to the behaviour of individual patients. Preliminary model simulation Fig 1: Simulation results showing learned dependency We can experiment therefore with alternative robot behaviour so as to reduce the likelihood of this occurrence. For example, basing the robot’s behaviour on its experiences of previous patient effort. Reference: [1]: Chiba, K.  Hiraishi, K.: Iterated continuous prisoner's dilemma game and its usefulness in analyzing multi-agent systems. Sch. of Inf. Sci., Japan Adv. Inst. of Sci. & Technol., Ishikawa, Japan.  [Figure 2]: Biometrics & Dexterous Manipulation Laboratory, Stanford.