Cooperative Decentralized Multi-agent Control

under Local LTL Tasks and Connectivity Constraints

## No Author Given

INDIAN INSTITUTE OF TECHNOLOGY KANPUR , UTTER PRADESH , 208016 INDIA

{Rajeevkumar160555, AdilHayat, AnupNayak, SupervisedbyIndranilSAHA}

Abstract. In this paper we are going to propose a procedure for the

decentralized control of a team of robots. The tasks will be assigned to

each robots. The robots are capable of performing some of the tasks indi-

vidually while in some tasks they need help from other robots to perform

the tasks. The tasks will be expressed as Linear Temporal Logic (LTL)

. LTL will cover both the aspects :- The tasks performed individually as

well as the tasks where collaboration from other robots is required to per-

form. We will follow an algorithm based on leader selection to guarantee

the satisfaction of each agent’s tasks under connectivity constraints.

1 Introduction

## There are various

elds where we require Cooperative Control for multi-agents

system such as periodic surveillance (i.e to repeatedly perform task 1) , sequenc-

ing ( i.e to perform task1 , then perform task2 , then perform task3) , request-

response ( i.e whenever task1 occurs perform task2) or conditional-response (i.e

perform task2 if and only if task1 is completed). Let illustrate the approach of

algorithm through example of sequencing i.e perform task1 , then perform task2

, then perform task3 and

nally perform task4 and also consider the conditions

that task2 and task4 can’t be performed by single robot and it need help of other

robots to perform these tasks. Apart from other mentioned condition , there is

also constraint of connectivity i.e agents can seek help of others agent only when

they are under a certain range of distance and the above tasks are converted

## into LTL formula.

### The goal of this paper is to

nd motion controller and action plan for the

robots that guarantee the satisfaction of all individual LTL tasks . We will in-

troduce a distributed continuous controller for the leader-follower scheme. We

will elect a leader among all the given robots and the current leader guides itself

and the followers towards the satisfaction of its’s own task. Once the task of

current leader is completed , re-election will held to select the new leader. While

conducting re-election , we will follow a certain algorithm to elect new leader

2 No Author Given

such that the task of all individual robot will be completed in long term ( i.e

each agent will get chance to become leader). We will use the concept of connectivity graph to take care of the connectivity

constraints. The contents of the paper can be summarized as the proposal of

algorithm for multi-agent which handles both connectivity constraints as well as

collaborative tasks that are assigned locallly.

2 PRELIMINARIES

De

nition 1: An LTL formula over the set of atomic propositions is de

ned

## inductively by:

::= j: j _ jX j U jF jG (1)

where 2 ; :(negation )and _(disj unction )are standard Boolean connectives; andX (next ); U

(until), F (eventually),and G (always) are temporal operators.

Formula X is true if and only if is satisf ied on word suf f ix that begin with next position:

1U

2is true if and only if

1is true until

2becomes true:

F is true if and only if becomes true eventually on W:

G is true if and only if is always true on W:

: is true if and only if doesn 0

## t hold on W:

_ is true if and only if either

1is true or

2is true on W:

3 PROBLEM FORMULATION

Let consider team of N Robots represented as Xi(

## t)= U

i(

## t) i 2Nf1; :::n g

## where X

i(

t) are the state of agent i at time t:

let

i(

t) will keep the track of position f rom t = 0 to t =t then

i(

t) will represent the traj ectory of agent i:

Each agent has a limited communication radius . at any time t , the two

agent i and j will communicate if and only if kX

i(

t) X

j(

## t) k r

i.e distance between i and j is less than or equal to connectivity distance.

or

kX

i(

t) X

k(

### t) k r ; k and j are connected

i.e distance between i and k is less than or equal to connectivity distance.

and distance between k and j is also less than or equal to connectivity distance.

Lecture Notes in Cooperative Multi-agent: Task performance 3

It is notion of inter-communication. We will use concept of connectivity graph to capture the notion of connectiv-

ity constraint . There is a path between two agents in a connectivity graph if

and only if they are directly connected i.e they are under radius r or they are

### connected through other agents.

4 TASK SPECIFICATION

Each agent i is given a set of M services , represented as i=

f

## i h ; h

2 f 1;2 :::::::M gg

### some of the services in

ican be done by agent i alone but in some services agent i require

### cooperation from others agent. So

### nally the task is represented as

i h =