Abstract-We consider the problem of automatic generation of control strategies for robotic vehicles given a set of highlevel mission specifications, such as "Vehicle x must eventually visit a target region and then return to a base," "Regions A and B must be periodically surveyed," or "None of the vehicles can enter an unsafe region." We focus on instances when all of the given specifications cannot be reached simultaneously due to their incompatibility and/or environmental constraints. We aim to find the least-violating control strategy while considering different priorities of satisfying different parts of the mission. Formally, we consider the missions given in the form of linear temporal logic formulas, each of which is assigned a reward that is earned when the formula is satisfied. Leveraging ideas from the automata-based model checking, we propose an algorithm for finding an optimal control strategy that maximizes the sum of rewards earned if this control strategy is applied. We demonstrate the proposed algorithm on an illustrative case study.

Abstract-This paper studies the problem of control strategy synthesis for dynamical systems with differential constraints to fulfill a given reachability goal while satisfying a set of safety rules. Particular attention is devoted to goals that become feasible only if a subset of the safety rules are violated. The proposed algorithm computes a control law, that minimizes the level of unsafety while the desired goal is guaranteed to be reached. This problem is motivated by an autonomous car navigating an urban environment while following rules of the road such as "always travel in right lane" and "do not change lanes frequently". Ideas behind sampling based motionplanning algorithms, such as Probabilistic Road Maps (PRMs) and Rapidly-exploring Random Trees (RRTs), are employed to incrementally construct a finite concretization of the dynamics as a durational Kripke structure. In conjunction with this, a weighted finite automaton that captures the safety rules is used in order to find an optimal trajectory that minimizes the violation of safety rules. We prove that the proposed algorithm guarantees asymptotic optimality, i.e., almost-sure convergence to optimal solutions. We present results of simulation experiments and an implementation on an autonomous urban mobility-on-demand system.

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