Optimality and robustness in multi-robot path planning with temporal logic constraints

In this paper we present a method for automatically generating optimal robot paths satisfying high-level mission specifications. The motion of the robot in the environment is modeled as a weighted transition system. The mission is specified by an arbitrary linear temporal-logic (LTL) formula over propositions satisfied at the regions of a partitioned environment. The mission specification contains an optimizing proposition, which must be repeatedly satisfied. The cost function that we seek to minimize is the maximum time between satisfying instances of the optimizing proposition. For every environment model, and for every formula, our method computes a robot path that minimizes the cost function. The problem is motivated by applications in robotic monitoring and data-gathering. In this setting, the optimizing proposition is satisfied at all locations where data can be uploaded, and the LTL formula specifies a complex data-collection mission. Our method utilizes Büchi automata to produce an automaton (which can be thought of as a graph) whose runs satisfy the temporal-logic specification. We then present a graph algorithm that computes a run corresponding to the optimal robot path. We present an implementation for a robot performing data collection in a road-network platform.This work was supported in part by the Office of Naval Research (grant number MURI N00014-09-1051), Army Research Office (grant number W911NF-09-1-0088), Air Force Office of Scientific Research (grant number YIP FA9550-09-1-020), National Science Foundation (grant number CNS-0834260), Singapore-MIT Alliance for Research and Technology (SMART) Future of Urban Mobility Project and by Natural Sciences and Engineering Research Council of Canada. (MURI N00014-09-1051 - Office of Naval Research; W911NF-09-1-0088 - Army Research Office; YIP FA9550-09-1-020 - Air Force Office of Scientific Research; CNS-0834260 - National Science Foundation; Singapore-MIT Alliance for Research and Technology (SMART); Natural Sciences and Engineering Research Council of Canada

Robust Model Predictive Control for Signal Temporal Logic Synthesis

Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain

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.Comment: Submitted to American Control Conference 201

Receding Horizon Temporal Logic Control for Finite Deterministic Systems

This paper considers receding horizon control of finite deterministic systems, which must satisfy a high level, rich specification expressed as a linear temporal logic formula. Under the assumption that time-varying rewards are associated with states of the system and they can be observed in real-time, the control objective is to maximize the collected reward while satisfying the high level task specification. In order to properly react to the changing rewards, a controller synthesis framework inspired by model predictive control is proposed, where the rewards are locally optimized at each time-step over a finite horizon, and the immediate optimal control is applied. By enforcing appropriate constraints, the infinite trajectory produced by the controller is guaranteed to satisfy the desired temporal logic formula. Simulation results demonstrate the effectiveness of the approach.Comment: Technical report accompanying a paper to be presented at ACC 201