A provably safe controller for the needle-steering problem using online strategy synthesis

Abstract

Autonomous systems often address complex planning problems, which require both prospective action planning and retrospective data evaluation. Timed games could aid since they automatically synthesize strategies that, provably correct, solve those planning problems; yet, they assume a static model of the environment, which is not realistic for autonomous systems. However, many autonomous systems are control applications, which employ sensors that capture system behavior at run time and can thus compensate for incomplete knowledge at modeling time. In this paper, we propose an online strategy synthesis, which, based on offline strategy synthesis on the one hand and on sensor information about the current state of the physical world on the other hand, derives formal safety guarantees while reacting and adapting to environment changes. We formalize the needle-steering problem from medical robotics, i.e., the problem of navigating a (flexible and beveled) needle through partially unknown tissue towards a target without damaging its surroundings, by interpreting it as a timed game. Further, we introduce a new representation of its environment through different region types that determine the acceptance of action plans and trigger local correcting actions. We present an algorithm for online strategy synthesis and, for the given region representation, formally prove that it returns safe online controllers. The algorithm is implemented on top of Uppaal Stratego. For two medical applications of needle steering, peridural anesthesia and predefined needle trajectory, we demonstrate the necessity of online adjustments in a series of simulations with various degrees of initial knowledge about the environment, and show that the overhead of online synthesis remains practical.