Novel design of a Model Reference Adaptive Controller for soft tissue operations

Model Reference Adaptive Controllers (MRAC) have dual functionality: besides guaranteeing precise trajectory tracking of the controlled system, they have to provide an “external control loop” with the illusion that it controls a physical system of prescribed dynamic properties, i.e., the “reference system”. The MRACs are designed traditionally by Lyapunov´s 2^nd method that is mathematically complicated, requiring strong skills from the designer. Adaptive controllers alternatively designed by the use of Robust Fixed Point Transformations (RFPT) operate according to Banach´s Fixed Point Theorem, and are normally simple iterative constructions that also have a standard variant for MRAC design. This controller assumes a single actuator that is driven adaptively. Master-Slave Systems form a distinct class of practical applications, in which two arms-the master and the slave-operate simultaneously. The movement of the master must be tracked precisely by the slave in spite of the quite different forces exerted by them. In the present paper, a soft tissue-cutting operation by a master-slave structure is simulated. The master arm has a simple torque-reference friction model, and is driven by the surgeon. The obtained master arm trajectory has to be precisely tracked by the electric DC motor driven slave system, which is in dynamic interaction with the actual tissue under operation. It is shown via simulations that the RFPT-based design can efficiently solve such tasks without considerable mathematical complexity.