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We address the problem of controlling a stochastic version of a Dubinsvehicle such that the probability of satisfying a temporal logic specificationover a set of properties at the regions in a partitioned environment ismaximized. We assume that the vehicle can determine its precise initialposition in a known map of the environment. However, inspired by practicallimitations, we assume that the vehicle is equipped with noisy actuators and,during its motion in the environment, it can only measure its angular velocityusing a limited accuracy gyroscope. Through quantization and discretization, weconstruct a finite approximation for the motion of the vehicle in the form of aMarkov Decision Process (MDP). We allow for task specifications given astemporal logic statements over the environmental properties, and use tools inProbabilistic Computation Tree Logic (PCTL) to generate an MDP control policythat maximizes the probability of satisfaction. We translate this policy to avehicle feedback control strategy and show that the probability that thevehicle satisfies the specification in the original environment is bounded frombelow by the maximum probability of satisfying the specification on the MDP.

Probabilistically Safe Control of Noisy Dubins Vehicles