Formal probabilistic analysis of a surgical robot control algorithm with different virtual fixtures

Surgical robots are increasingly being used in operation theaters involving normal or laparoscopic surgeries. The working of these surgical robots is highly dependent on their control algorithms, which require very rigorous analysis to ensure their correct functionality due to the safety-critical nature of surgeries. Traditionally, safety of control algorithms is ensured by simulations, but they provide incomplete and approximate analysis results due to their inherent sampling-based nature. We propose to use probabilistic model checking, which is a formal verification method, for quantitative analysis, to verify the control algorithms of surgical robots in this paper. As an illustrative example, the paper provides a formal analysis of a virtual fixture control algorithm, implemented in a neuro-surgical robot, using the PRISM model checker. In particular, we provide a formal discrete-time Markov chain-based model of the given control algorithm and its environment. This formal model is then analyzed for multiple virtual fixtures, like cubic, hexagonal and irregular shapes. This verification allowed us to discover new insights about the considered algorithm that allow us to design safer control algorithms.