We address the problem of controlling a stochastic version of a Dubins vehicle such that the probability of satisfying a temporal logic specification over a set of properties at the regions in a partitioned environment is maximized. We assume that the vehicle can determine its precise initial position in a known map of the environment. However, inspired by practical limitations, we assume that the vehicle is equipped with noisy actuators and, during its motion in the environment, it can only measure its angular velocity using a limited accuracy gyroscope. Through quantization and discretization, we construct a finite approximation for the motion of the vehicle in the form of a Markov Decision Process (MDP). We allow for task specifications given as temporal logic statements over the environmental properties, and use tools in Probabilistic Computation Tree Logic (PCTL) to generate an MDP control policy that maximizes the probability of satisfaction. We translate this policy to a vehicle feedback control strategy and show that the probability that the vehicle satisfies the specification in the original environment is bounded from below by the maximum probability of satisfying the specification on the MDP.
The application of obstacle avoidance for stochastic Dubin-type vehicles is considered within the problem of maximizing the probability of satisfying a temporal logic specification, REF however this method produces an open loop trajectory and not a feedback motion plan.
Probabilistically safe control of noisy Dubins vehicles
2012 IEEE/RSJ International Conference on Intelligent Robots and Systems
2012 IEEE/RSJ International Conference on Intelligent Robots and Systems
Computer Science Engineering