An Abstraction-Free Method for Multirobot Temporal Logic Optimal Control Synthesis

Abstract

The majority of existing Linear Temporal Logic (LTL) planning methods rely on the construction of a discrete product automaton, that combines a discrete abstraction of robot mobility and a Büchi automaton that captures the LTL specification. Representing this product automaton as a graph and using graph search techniques, optimal plans that satisfy the LTL task can be synthesized. However, constructing expressive discrete abstractions makes the synthesis problem computationally intractable. In this paper, we propose a new samplingbased LTL planning algorithm that does not require any discrete abstraction of robot mobility. Instead, it builds incrementally trees that explore the product state-space, until a maximum number of iterations is reached or a feasible plan is found. The use of trees makes data storing and manipulation tractable, which significantly increases the scalability of our algorithm. To accelerate the construction of feasible plans, we introduce bias in the sampling process which is guided by transitions in the Büchi automaton that belong to the shortest path to the accepting states. We show that our planning algorithm is probabilistically complete and asymptotically optimal. Finally, we present numerical experiments showing that our method outperforms relevant temporal logic planning methods. I. INTRODUCTIONM OTION planning traditionally consists of generating robot trajectories that reach a goal region from a starting point while avoiding obstacles [1]. Methods for pointto-point navigation range from using potential fields and navigation functions [2], [3] to sampling-based algorithms [4]- [6]. More recently, a new class of planning approaches emerges that can handle a richer class of tasks, than the classical pointto-point navigation, and can capture temporal goals. Such tasks can be, e.g., sequencing or coverage [7], data gathering [8], intermittent communication [9], or persistent surveillance [10], and can be captured using formal languages, such as Linear Temporal Logic (LTL) [11], developed in concurrency theory.Control synthesis for mobile robots under complex tasks, captured by Linear Temporal Logic (LTL) formulas, builds upon either bottom-up approaches when independent LTL expressions are assigned to robots [12]-[14] or top-down approaches when a global LTL formula describing a collaborative task is assigned to a team of robots [15], [16], as in this work. Common in the above works is that they rely on model

Semantic Abstraction-Guided Motion Planning for scLTL Missions in Unknown Environments

“…The second step then grows another tree rooted at this accepting state, and attempts to find a cyclic (infinite) path that satisfies the LTL specification. The same authors then introduce in [7] sampling bias guided by the automaton capturing the LTL, something that [13] also proposes in a similar fashion. Lastly, besides proposing a heuristic to guide the search, [16] integrates feedback control laws to guarantee feasibility of plans by robots with complex, possibly non-holonomic, dynamics.…”

“…If the path connecting these two points is collision-free, the sample is considered for being added to the graph. If the symbolic counterpart of the sampled transition is in bias, the sampled point is stored as a "bias frontier"; otherwise it rejects this sample with some probability p (lines [11][12][13][14]. This probability depends on how much you want to bias the sampling.…”

Safe Motion Planning for an Uncertain Non-Holonomic System with Temporal Logic Specification

“…Sampling based motion planners avoid the explicit states space construction and thus mitigate the dimensionality problem. Motivated by the success of algorithms, such as RRT [5] and its asymptotically optimal version RRT [6], several approaches have been proposed in order to enhance sampling-based algorithms with temporal logic mission specifications [7], [8], [9], [10].…”

“…Various approaches have been proposed to address this issue, mainly through heuristics for biasing of the sampling towards satisfaction of the specification [11], [8]. The biasing approaches can be classified as geometry guided and automaton guided.…”

“…It proposes a two-layer planning scheme with a high-level planning layer over a discretization of the state space and a low-level planner that is sampling based. A recent work on multi-agent path planning from temporal logic specifications using RRT uses visibility graphs as a geometrical bias for sampling [8]. While geometrical guiding is shown to significantly speed-up the search algorithm, it is restricted to two and in some cases small three dimensional environments.…”