Deployment Strategy for Mobile Robots with Energy and Timing Constraints

1. 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)

2. Outline • Introduction • Deployment strategy : • Overhead deployment • Area covered by one group • Number of groups and group size • Deployment algorithm • Experimental Evaluation • Conclusions

3. Introduction • Mobile robots carry limited energy sources • A lot of tasks have timing constraints • Search survivors and rescue • Landmine detection

4. 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

9. 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

10. Assumption • All robots are the same • Initial energy , each robot’s power consumption is affected 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

11. Scan-Line 2d Sensing Area 2d

12. 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

13. Overhead deployment • unloading time: longer time to unload more robots • dispersing overhead: AB and AC • fragmentation overhead:from D to E The fragmentation overhead in terms of area is at most 2dh

14. Area Coverage by One Group • 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 An area covered by a group of 12 robots

15. 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

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

17. Deployment Algorithm Each group’s size depends on only the sizes of the previous groups The sizes of the other groups The size of the latest assigned group The size for the first group

18. Deployment Algorithm Because the determination of the last group size depends only on the comparison of minimum areas, not the area left before unloading the last group

19. Simulation • A commercial robot called PPPK is used • Omni-directional wheels driven 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

20. Simulation 6 hours before deadline Area covered by different number of robots with different ratios of height and width

21. 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

24. Simulation Deployment for covering 6.8 * 105 m2 within four hours With the same conditions, the one-unloading method has to use 416 robots, and the average area per robot is 1634m2.

25. 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.