gnoccoalpesto / dcs22

cooperative tasks optimization for multi agents system

PROJECT 3

distributed task assignment for robotic networks

all scripts performing monte carlo operations (distinguishable by "MC" or "mc" in their name) could need attention since some variables are hardcoded inside them; prefer the *fun version when possible.

Data saving is active (.txt saving not, since it creates files of 10MB order), pay attention that they create folder and may modify the environment they're runned into.

The single shot version of the algorithms for both tasks (maindcs22.m and task2dcs22.m) can be runned without any worries.

THEORETICAL BASIS:

TASK 1

1)N agents

solve constraint coupled linear program problem (1):

min{z1...zN} sum{1,N}(ci'zi) subj: sum{1,N} Hizi=b zi € Pi, i€{1...N}

ci € R^ni, Hi € R^Sxni, b € R^S compact polyhedron Pi={zi € R^ni | Dizi=<di, Gizi=gi } i€{1...N}

using Distributed Dual Subgradient:

contained in "Distributed optimization for smart cyber-physical networks"

2. montecarlo simulation and plots to show convergence varying N and problem size

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TASK 2

{-> possible further improvements}

N robots, N tasks scattered in a finite environment

each robot has to serve a task, each task must be served by at most one robot

min(tot robots' TRAVEL* distance) *->compenetration?

bipartite assignment graph Ga={Va,Ua;Ea} tasks Va={1...N}, agents Ua={1...N} edge (i,k) € Ea exist iff agent i assignable to tank k

-> many ramndomly select robots that can't execute task

cost cik of ende (i,k) [note cik=0 iff edge not exist]

1. euclidean distance ->2) manhattan? non compenetration (each slab occupied by a robot)

linear optimization problem:

min{x}sum{(i,k) € Ea} (cik xik) subj: 0=<x=<1 LB=0, UB=1 sum{k|(i,k) € Ea}(xik=1}, i€{1...N} NeighIn(k) sum{i|(i,k) € Ea}(xik=1}, k€{1...N} NeighOut(i)

x=[...;...,xik,...;...] X=[xt=1,...]

recast in form 1) by: zi=[...xik,...] (==xi)

ci=[...,cik...] ci=ci_average+noise(ci) random stochastic disturbance

k|(i,k) € Ea

(at most k=1...N)

Pi= {xi |0=<xi=<1, sum{k|(i,k)€ Ea}(xik=1), i€{1...N} Pi=

Hi, b vector defined suitably

1. Hi=I