We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. We demonstrate our approach on an illustrative case study.
In this paper, we focus on formal synthesis of control policies for finite Markov decision processes with non-negative real-valued costs. We develop an algorithm to automatically generate a policy that guarantees the satisfaction of a correctness specification expressed as a formula of Linear Temporal Logic, while at the same time minimizing the expected average cost between two consecutive satisfactions of a desired property. The existing solutions to this problem are sub-optimal. By leveraging ideas from automata-based model checking and game theory, we provide an optimal solution. We demonstrate the approach on an illustrative example.
We consider a case study of the problem of deploying an autonomous air vehicle in a partially observable, dynamic, indoor environment from a specification given as a linear temporal logic (LTL) formula over regions of interest. We model the motion and sensing capabilities of the vehicle as a partially observable Markov decision process (POMDP). We adapt recent results for solving POMDPs with parity objectives to generate a control policy. We also extend the existing framework with a policy minimization technique to obtain a better implementable policy, while preserving its correctness. The proposed techniques are illustrated in an experimental setup involving an autonomous quadrotor performing surveillance in a dynamic environment.
The design of mobile autonomous robots is challenging due to the limited on-board resources such as processing power and energy. A promising approach is to generate intelligent schedules that reduce the resource consumption while maintaining best performance, or more interestingly, to trade off reduced resource consumption for a slightly lower but still acceptable level of performance. In this paper, we provide a framework that is automatic and quantitative to aid designers in exploring such resource-performance trade-offs and finding schedules for mobile robots, guided by questions such as "what is the minimum resource budget required to achieve a given level of performance?" The framework is based on a quantitative multi-objective verification technique which, for a collection of possibly conflicting objectives, produces the Pareto front that contains all the achievable optimal trade-offs. The designer then selects a specific Pareto point based on the resource constraints and desired performance level, and a correct-by-construction schedule that meets those constraints is automatically generated. We demonstrate the efficacy of this framework on several robotic scenarios in both simulations and experiments.
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