A framework for multi-robot motion planning from temporal logic specifications

Abstract

We propose a framework for the coordination of a network of robots with respect to formal requirement specifications expressed in temporal logics. A regular tessellation is used to partition the space of interest into a union of disjoint regular and equal cells with finite facets, and each cell can only be occupied by a robot or an obstacle. Each robot is assumed to be equipped with a finite collection of continuous-time nonlinear closed-loop dynamics to be operated in. The robot is then modeled as a hybrid automaton for capturing the finitely many modes of operation for either staying within the current cell or reaching an adjacent cell through the corresponding facet. By taking the motion capabilities into account, a bisimilar discrete abstraction of the hybrid automaton can be constructed. Having the two systems bisimilar, all properties that are expressible in temporal logics such as Linear-time Temporal Logic, Computation Tree Logic, and µ-calculus can be preserved. Motion planning can then be performed at a discrete level by considering the parallel composition of discrete abstractions of the robots with a requirement specification given in a suitable temporal logic. The bisimilarity ensures that the discrete planning solutions are executable by the robots. For demonstration purpose, a finite automaton is used as the abstraction and the requirement specification is expressed in Computation Tree Logic. The model checker Cadence SMV is used to generate coordinated verified motion planning solutions. Two autonomous aerial robots are used to demonstrate how the proposed framework may be applied to solve coordinated motion planning problems.

Mind the gap

“…However, it lacks a metric notion of time, and it is not able to express bounds on the delay between events. In LTL, one can express that an event B follows an event A, [8] TCTL Uppaal [35] CTL C-SMV [49] LTL [27] LTL [46] LTL [32] LTL [12] LTL [33] LTL [34] LTL [47] LTL [29] LTL [21] LTL Matlab [25,28,39,48] LTL Matlab [13,26] LTL Matlab [43] MTL [52] MTL CPLEX [42] MTL Matlab but it is not possible to limit the time interval between the two events by imposing, for instance, that the delay is smaller than 5 time units. Therefore, a number of authors [8,43,44] have recently considered formalisms that allow for expressing explicit time constraints, such as Metric Temporal Logic (MTL) [36], or Timed Computation Tree Logic (TCTL) [6].…”

Safe Design of Flow Management Systems Using Rebeca

“…[32] and with hybrid automata in Ref. [33]. For the latter, they show how the generated hybrid automata can be embedded into automata which can be model checked using SMV.…”

Research status of multi - robot systems task allocation and uncertainty treatment

“…Nieto-Granda, Rogers III and Christensen [17] proposed coordination algorithms of the redundant robot in the system. In addition, some scholars have researched the coordination of multirobot systems at the logic level through the finite-state machine [18][19] or Petri nets [20][21][22]. This method can deal with different athletic abilities [18] or functions of robots [20], completely from the logical level of coordination achieved by the relatively limited behavior.…”

“…In addition, some scholars have researched the coordination of multirobot systems at the logic level through the finite-state machine [18][19] or Petri nets [20][21][22]. This method can deal with different athletic abilities [18] or functions of robots [20], completely from the logical level of coordination achieved by the relatively limited behavior. However, it is possible to participate in the control loop of the multi-robot system by supervising the control [23].…”