Deployment Strategy for Mobile Robots with Energy and Timing Constraints

Yongguo Mei, Yung-Hsiang Lu, Y. Charlie Hu, and C.S. George Lee

School of Electrical and Computer Engineering, Purdue University

ICRA 2005 (IEEE International Conference On Robotics And Automation)

Outline

• Introduction• Deployment strategy :

• Overhead deployment• Area covered by one group• Number of groups and group size• Deployment algorithm

• Experimental Evaluation• Conclusions

Introduction

• Mobile robots carry limited energy sources• A lot of tasks have timing constraints

• Search survivors and rescue• Landmine detection

Motivation

• Few studies have been conducted for deploying mobile robots• The number of robots needed• Initial locations of these robots

Are affected by each robot’s energy capacity, the deadline, and the moving speed

Goals

• The desirable deployment strategy• Uses the minimum number of robots to

cover a given area• cover the area within the energy and the

timing constraints

Explains the rules to find better deployment strategies for reducing the number of robots in each group and the number of groups

Assumption

• All robots are the same• Initial energy , each robot’s power consumption is af

fected only by its speed• Sensing range is d , sensing region is 2d * 2d = 4d2

• The robots travel along scanline to cover the area• The area to be covered is a two-dimensional region

without obstacles

2d

2d

Sensing

Area

Scan-Line

2d

Overhead deployment

• Unloading time : a robot that is unloaded later has shorter time before the deadline

• Dispersing overhead : the time and the energy spent by each robot to reach its starting location after being unloaded

• Fragmentation overhead : when a robot can’t finish a scanline due to energy or timing constraints or both

Overhead deployment

• unloading time: longer time to unload m

ore robots

• dispersing overhead:

AB and AC

• fragmentation overhead: from D to E

The fragmentation overhead in terms of area is at most 2dh

Area Coverage by One Group

An area covered by a group of 12 robots

• Point A is the unloading location of the whole group

• The 5th robot spends time traveling across AB, its covered area can’t be larger than a1

Area Coverage by One Group

• Average dispersing overhead: w/2• Average fragmentation overhead: h/2• h = w minimize the total overhead

• The total dispersing distance

0 + AB + AD ≈ 0 + w/3 + 2w/3

= w

• w /ψ+ 2w /ψ +…+ (ψ -1)w/ ψ

= (ψ -1)w/ 2

Deployment Strategy

• make the minimum areas of all groups close• unload fewer robots for later groups• minimize the size of the first group

Deployment AlgorithmEach group’s size depends on only the sizes of

the previous groups

The size for the first group

The sizes of the other groups

The size of the latest assigned group

Deployment Algorithm

Because the determination of the last groupsize depends only on the comparison of minimum areas,not the area left before unloading the last group

Simulation

• A commercial robot called PPPK is used • Omni-directional wheels dr

iven by three MS492MH DC servo motors

• Energy capacity:20736J (4 AA batteries)

• P(v) = 48.31v2 – 3.37v +0.69• Optimal speed: 0.12m/s with

power consumption 0.98W

Simulation

Area covered by different number of robots with differentratios of height and width

6 hours before deadline

Simulation

• Comparing with two other solutions• Equal-number deployment by unloading

the same number of robots each time• Unloads all robots at one location

• Sensing distance used is 0.8m

Deployment for covering 6.8 * 105 m2 within four hours

Simulation

With the same conditions, the one-unloading method has to use 416 robots, and the average area per robot is 1634m2.

Conclusions

• This paper presents a method to deploy mobile robots for covering an area with energy and timing constraints.

• Our approach determines the number of robots in each group and the number of groups.