Optimal path planning for surveillance with temporal-logic constraints

Abstract

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 which 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 which computes a run corresponding to the optimal robot path. We present an implementation for a robot performing data collection in a road network platform.

Optimal Control with Weighted Average Costs and Temporal Logic Specifications

“…The weighted average cost function is more natural than the minimax cost function of Smith et al [20] in some application contexts. For example, consider an autonomous vehicle repeatedly picking up people and delivering them to a destination.…”

“…Chatterjee et al [5] create control policies that minimize an average cost function in the presence of an adversary. The approach in [20] is the most closely related to our work. Motivated by surveillance tasks, they minimize the maximum cost between visiting specific regions.…”

“…Motivated by surveillance tasks, they minimize the maximum cost between visiting specific regions. Our work is complementary to [20] in that we instead minimize a weighted average cost function.…”

Optimal Control of Nonlinear Systems with Temporal Logic Specifications

“…The product automaton might also be quite large due to the size of the abstraction and the Büchi automaton. Finally, although optimal controllers can be computed for the discrete abstraction [22,27], optimality is only with respect to the abstraction's level of refinement or asymptotic [15].…”

LTL receding horizon control for finite deterministic systems

“…In Kloetzer and Belta (2008a), the authors considered a simple cost function that penalized the combined cost of the prefix and suffix of an infinite run satisfying an LTL formula. This idea was extended in Smith, Tůmová, Belta, and Rus (2011), where the goal was to minimize the maximum distance in between successful satisfactions of a given proposition, while satisfying an LTL specification.…”