Jana Tumova

Temporal Logic Control of Discrete-Time Piecewise Affine Systems

We present a computational framework for automatic synthesis of a feedback control strategy for a discrete-time piecewise affine (PWA) system from a specification given as a linear temporal logic (LTL) formula over an arbitrary set of linear predicates in the systems state variables. Our approach consists of two main steps. First, by defining appropriate partitions for its state and input spaces, we construct a finite abstraction of the PWA system in the form of a control transition system. Second, by leveraging ideas and techniques from LTL model checking and Rabin games, we develop an algorithm to generate a control strategy for the finite abstraction. While provably correct and robust to state measurements and small perturbations in the applied inputs, the overall procedure is conservative and expensive. The proposed algorithms have been implemented as a software package and made available for download. Illustrative examples are included.

LTL robot motion control based on automata learning of environmental dynamics

We develop a technique to automatically generate a control policy for a robot moving in an environment that includes elements with partially unknown, changing behavior. The robot is required to achieve an optimal surveillance mission, in which a certain request needs to be serviced repeatedly, while the expected time in between consecutive services is minimized. We define a fragment of Linear Temporal Logic (LTL) to describe such a mission and formulate the problem as a temporal logic game. Our approach is based on two main ideas. First, we extend results in automata learning to detect patterns of the partially unknown behavior of the elements in the environment. Second, we employ an automata-theoretic method to generate the control policy.We show that the obtained control policy converges to an optimal one when the unknown behavior patterns are fully learned. We implemented the proposed computational framework in MATLAB. Illustrative case studies are included.

A symbolic approach to controlling piecewise affine systems

We present a computational framework for automatic synthesis of a feedback control strategy for a piecewise affine (PWA) system from a specification given as a Linear Temporal Logic (LTL) formula over an arbitrary set of linear predicates in its state variables. First, by defining partitions for its state and input spaces, we construct a finite abstraction of the PWA system in the form of a control transition system. Second, we develop an algorithm to generate a control strategy for the finite abstraction. While provably correct and robust to small perturbations in both state measurements and applied inputs, the overall procedure is conservative and expensive. The proposed algorithms have been implemented and are available for download. Illustrative examples are included

Incremental sampling-based algorithm for minimum-violation motion planning

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 motion-planning 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.

ProbDiVinE-MC: Multi-core LTL Model Checker for Probabilistic Systems

We present a new version of ProbDiVinE - a parallel tool for verification of probabilistic systems against properties formulated in linear temporal logic. Unlike the previous release, the new version of the tool allows for both quantitative and qualitative model-checking. It is also strictly multi-threaded, therefore, protects users from unwanted burden of parallel computing in a distributed-memory environment.

Cooperative task planning of multi-agent systems under timed temporal specifications

In this paper the problem of cooperative task planning of multi-agent systems when timed constraints are imposed to the system is investigated. We consider timed constraints given by Metric Interval Temporal Logic (MITL). We propose a method for automatic control synthesis in a two-stage systematic procedure. With this method we guarantee that all the agents satisfy their own individual task specifications as well as that the team satisfies a team global task specification.

Attraction-based receding horizon path planning with temporal logic constraints

Our goal in this paper is to plan the motion of a robot in a partitioned environment with dynamically changing, locally sensed rewards. The robot aims to accomplish a high-level temporal logic surveillance mission and to locally optimize the collection of the rewards in the visited regions. These two objectives often conflict and only a compromise between them can be reached. We address this issue by taking into consideration a user-defined preference function that captures the trade-off between the importance of collecting high rewards and the importance of making progress towards a surveyed region. Our solution leverages ideas from the automata-based approach to model checking. We demonstrate the utilization of the suggested framework in an illustrative example.

Minimum-violation LTL planning with conflicting specifications

We consider the problem of automatic generation of control strategies for robotic vehicles given a set of high-level 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.

ProbDiVinE: A Parallel Qualitative LTL Model Checker

introduce a parallel model checker for checking Markov decision processes against linear time properties. The model checker extends the parallel model checker DiVinE and supports verification of qualitative properties.

Least-violating planning in road networks from temporal logic specifications

In this paper, we consider the problem of automated plan synthesis for a vehicle operating in a road network, which is modeled as a weighted transition system. The vehicle is assigned a set of demands, each of which involves a task specification in the form of a syntactically co-safe LTL formula, a deadline for achieving this task, and a demand priority. The demands arrive gradually, upon the run of the vehicle, and hence periodical replanning is needed. We particularly focus on cases, where all tasks cannot be accomplished within the desired deadlines and propose several different ways to measure the degree of demand violation that take into account the demand priorities. We develop a general solution to the problem of least-violating planning and replanning based on a translation to linear programming problem. Furthermore, for a particular subclass of demands, we provide a more efficient solution based on graph search algorithms. The benefits of the approach are demonstrated through illustrative simulations inspired by mobility-on-demand scenarios.