Optimal path planning under temporal logic constraints

Abstract

Abstract-In this paper we present a method for automatically generating optimal robot trajectories satisfying high level mission specifications. The motion of the robot in the environment is modeled as a general transition system, enhanced with weighted transitions. The mission is specified by a general linear temporal logic formula. In addition, we require that an optimizing proposition 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 trajectory 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 entire formula specifies a complex (and infinite horizon) 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 path corresponding to the optimal robot trajectory. We also present an implementation for a robot performing a data gathering mission in a road network.

Leveraging Qualitative Reasoning to Learning Manipulation Tasks

“…LTL is widely used in software engineering and program verification, but it has also received attention from the autonomous robotics community since the 1990s-see [22]. So far, LTL has been applied to declarative specification and synthesis of controllers from a high-level specification [23] and it is also applied for motion planning [24][25][26]. Similar to the approach described in this paper, Kreutzmann et al [27] apply LTL to specify processes in logistics declaratively.…”

Controlling wild mobile robots using virtual gates and discrete transitions

“…As is common in many approaches, we partition the environment into a finite set of regions over which a discrete transition system is defined. Rather than develop state-feedback control laws within regions [1], [8], [12], [17], [23], [29], we do not even attempt to stabilize the robots. We instead place virtual gates along the boundaries between regions that possibly enable discrete transitions, depending on information provided by a combinatorial filter [25], [32] that maintains information states from weak sensor data.…”

“…In related work, mechanical gates were designed and demonstrated to allow various tasks to be effectively solved [4]. In that work, tasks were specified using the LTL framework (see [3], [9], [10], [12], [17], [19], [20], [21], [22], [23], [29], [34]) and then converted into solution strategies using model checking software. In the current paper, we instead explore the idea of virtual gates, which allow a different set of tasks to be solved.…”

Controlling Wild Bodies Using Linear Temporal Logic

“…Following this, we are inspired by the family of work that converts high-level specifications into low-level control laws for the hybrid system [21], [30], [36]. In particular, our work uses the Linear Temporal Logic (LTL) framework that has been developed in several recent works [3], [13], [14], [17], [22], [23], [24], [25], [26], [27], [28], [34], [37].…”

“…Whereas it is common in LTL implementations to derive state-feedback control laws within continuous regions [17], [22], [28], [34], we simply let our "vehicle" behave wildly. To control a wild body, we design gates that appear only along region boundaries and connect to other regions.…”