ON THE DIFFERENTIAL DYNAMIC LOGIC MODEL FOR HYBRID SYSTEMS

Abstract

The contribution of this paper consists in advancing of a control strategy based on the differential dynamic logic (dL) for a cooperative surgeon-robot system whose behavior depends on the interaction between discrete dynamics deriving from the control and continuous dynamics deriving from surgical instrument moving. Such systems are called hybrid systems. The dL algorithm captures the logics of superposition of both dynamics and is capable to control the system in the most natural way. In our opinion, dL can be successfully used for avoiding the collisions of the surgical instrument with a critical domain in a virtual system composed by a surgical robot, a device for visualizing and analyzing the medical images and a six degree-of-freedom robotic arm designed for use in hepatic surgery. Key words: Differential logic control; Hybrid systems; Surgical robotics; Collision avoidance.