This is the presentation of our paper, "Establishing Line-of-Sight Communication Via Autonomous Relay Vehicles, IEEE Military Communication Conference, Baltimore, MD, 2016" Line-of-sight(LoS) communication (by infrared or visible light) becomes a reliable ways to send information between mobile units in communication-denied environments. This form of communication is more difficult to intercept or jam, as an attacker would require to be located directly on that LoS. Mission-related movements may break a fully connected military mission by losing LoS to the Service Vehicles. Autonomous ground vehicle can recover the LoS based connectivity by moving from place to place as required.

1. Establishing Line-of-Sight
Communication Via Autonomous
Relay Vehicles
Md Mahbubur Rahman, Leonardo
Bobadilla and Brian Rapp

2. Introduction
• Line-of-sight(LoS) communication (by infrared or visible light) becomes a
reliable ways to send information between mobile units in
communication-denied environments.
• This form of communication is more difficult to intercept or jam, as an
attacker would require to be located directly on that LoS.
• Mission-related movements may break a fully connected military mission
by losing LoS to the Service Vehicles.
• Autonomous ground vehicle can recover the LoS based connectivity by
moving from place to place as required.

3. Motivation
• Other modalities of communication are not feasible.
• Significant use in military mission, patrolling, monitoring.
• LoS based communication is more reliable, secure and
efficient.
Sample MilitaryMission 2D representation

4. Research Questions
• What will be the optimal locations to place the
vehicles?
• How to know when the network gets disconnected?
• How to relocate a single vehicle to recover the units
that went out of sight?
Fully Connected Mission Vehicles are Disconnected One Unit is Disconnected

5. Related Work
Literature Not Addressed
Art Gallery problems (ORourke’87) and
landmark placement (Erickson’11)
problems.
Focused only on shortest path rather than
a path with the most visibility.Existing
Solutiondoes not respect the differential
constraintsof the robot vehicles.
path planningthat maintainsvisibility
with a single static landmark
(Bhattacharya’07,Muppirala’05).
Multipleunit tracking and optimalpath
planningwas not considered.
A mobile unit uploading, downloading,
and distributing datato static nodes are
common in data muling (Bhadauria’11,
Zavlanos’09).
Our communicationis based on line-of-
sight instead of the proximity of sensor
nodes.
Free-Space Optical Communications
(FSOC) (Juarez’06)
Complexmission scenarios with multi
robot system were not considered.

6. Problem Formulation
• The world, 𝑊 = 𝑅2
with 𝑛 vehicles, 𝐴1, 𝐴2, ⋯ 𝐴 𝑛
equipped with high-performance computing devices
that serve 𝑚 units 𝐵1, 𝐵2, ⋯ 𝐵 𝑚.
• 𝑞𝑖 = (𝑥, 𝑦) ∈ 𝐶𝑖 is the configuration for vehicle 𝐴𝑖 and
𝑏𝑗 = (𝑥, 𝑦) ∈ 𝐵𝑗 is the configuration of unit 𝐵𝑗.
• 𝑉(𝑞𝑖) is the visibility polygon of vehicle 𝐴𝑖.
Sample MilitaryMission 2D representation

7. Problem Definition
• A subset 𝑋 𝑐𝑜𝑚𝑚 ⊆ 𝑋 is considered the set of communication-valid
states if and only if each unit is visible by at least one servicing
vehicle and all the servicing vehicles form a connected graph.
• We must satisfy the following two conditions in order to have a
communication-valid state:
∀𝑗, ∃𝑖 𝑠. 𝑡. 𝑏𝑗 ∈ 𝑉 𝑞𝑖 𝑓𝑜𝑟 1 ≤ 𝑗 ≤ 𝑚 𝑎𝑛𝑑 1 ≤ 𝑖 ≤ 𝑛
𝑞𝑗, 𝑞 𝑘 𝑞 𝑘 ∈ 𝑉 𝑞𝑗 𝑓𝑜𝑟 1 ≤ 𝑗, 𝑘 ≤ 𝑛; 𝑘 ≠ 𝑗} ≡ 𝐶𝐶(𝑥)
where 𝐶𝐶(𝑥) is a connected component formed by all the vehicle-
vehicle connections.
𝑞 𝐴1 ∈ 𝑉 𝑞 𝐴2 𝑎𝑛𝑑 𝑞 𝐴2 ∈ 𝑉 𝑞 𝐴1
form a connected component

8. Problem Definition (Contd.)
• Problem 1: Communication State Validation
Given the workspace 𝑊, a set of obstacles 𝑂, a set of
configurations 𝑞1, 𝑞2, . . . , 𝑞 𝑛 for robot vehicles, and
𝑏1, 𝑏2, . . . , 𝑏 𝑚 for mobile units, determine whether a state 𝑥 ∈
𝑋 is communication-valid or not.
• Problem 2: Communication Validity Restoration
Given 𝑊 and 𝑂, the current state space 𝑥 ∈ 𝑋, and a set of
disconnected units 𝐷, select a number of vehicles to relocate
and compute their new goal region, 𝑋 𝐺, that will reconnect all
the units in 𝐷.

9. Checking Vehicle-Vehicle Connectivity
• Step1: Form a vehicle relay graph 𝐺 𝐴 𝑉𝐴, 𝐸𝐴 where
𝑉𝐴 = {𝐴1, 𝐴2, . . . , 𝐴 𝑛} 𝑎𝑛𝑑 𝐸𝐴 = {𝑒𝑖𝑗 |𝑞𝑖 ∈ 𝑉 (𝑞𝑗)}.
• Step2: Compute 𝑛 × 𝑛 Laplacian matrix, 𝐿(𝐺 𝐴) where,
i) l𝑖𝑗 = ቊ
−1 if an edge exists between i and j
0 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
ii) 𝑙𝑖𝑖 = − σ 𝑘=1,𝑘≠𝑖
𝑛
𝑙𝑖𝑘
• Step3: Check whether the second-smallest eigenvalue
𝜆2(𝐿(𝐺 𝐴)) > 0.
𝐺 𝐴 𝑉𝐴, 𝐸 𝐴 and 𝐿 𝐺 𝐴 =
1 −1
−1 1
and 𝜆2 𝐿 𝐺 𝐴 = 2

10. Checking Communication Validity
• Form a unit graph 𝐺 𝐵(𝑉𝐵, 𝐸 𝐵) where
𝑉𝐵 = {𝐴1, 𝐴2, . . . , 𝐴 𝑛, 𝐵1, 𝐵2, . . . , 𝐵 𝑚} and
𝐸 𝐵 = {𝑒𝑖𝑗 |𝑏𝑗 ∈ 𝑉 (𝑞𝑖) 𝑤ℎ𝑒𝑟𝑒 𝑛 < 𝑗 ≤ 𝑛 + 𝑚 𝑎𝑛𝑑 0 < 𝑖 ≤ 𝑛}
• Form a graph 𝐺(𝑉, 𝐸) = 𝐺 𝐴 ∪ 𝐺 𝐵.
• Compute (𝑚 + 𝑛) × (𝑚 + 𝑛) Laplacian matrix, 𝐿(𝐺) and check
whether the second-smallest eigenvalue 𝜆2(𝐿 𝐺 ) > 0.
𝐺 𝐴 𝑉𝐴, 𝐸 𝐴 𝐺 𝐵 𝑉𝐵, 𝐸 𝐵 𝐺 = 𝐺 𝐴 ∪ 𝐺 𝐵

11. Communication Validity Algorithm

12. Communication Validity Checking
Experiment
𝐶𝑜𝑚𝑚𝑢𝑛𝑖𝑐𝑎𝑡𝑖𝑜𝑛 − 𝑖𝑛𝑣𝑎𝑙𝑖𝑑
𝐶𝑜𝑚𝑚𝑢𝑛𝑖𝑐𝑎𝑡𝑖𝑜𝑛 − 𝑣𝑎𝑙𝑖𝑑
𝐶𝑜𝑚𝑚𝑢𝑛𝑖𝑐𝑎𝑡𝑖𝑜𝑛 − 𝑖𝑛𝑣𝑎𝑙𝑖𝑑
𝐶𝑜𝑚𝑚𝑢𝑛𝑖𝑐𝑎𝑡𝑖𝑜𝑛 − 𝑖𝑛𝑣𝑎𝑙𝑖𝑑

13. Validity Checking Experiment
𝜆2 𝐺𝐴 = 0
𝜆2(𝐺_𝐴 ) = 1; 𝜆2 (𝐺) = 0.5024
𝜆2 𝐺𝐴 = 2; 𝜆2 𝐺 = 0

14. LoS Based Network Restoration

15. Sample Disconnections
• Two sample communication-invalid scenarios are shown below.
• The set of disconnected units is defined as 𝐷 who have no covering
vehicle.
• In first scenarios 𝑫 = {′𝑨′} and in second case, 𝑫 = {′𝑫′}
• We need to relocate a single vehicle to recover the disconnected
units.

16. Choosing Candidate Vehicles
• Set of candidate vehicles is, 𝐶 ∈ 𝑃(𝐴) that doesn’t
break the existing connectivity of graph 𝐺 𝐴, if
relocated.
𝐶 = {𝐴𝑖} 𝑠. 𝑡. 𝜆2(𝐿(𝐺 𝐴(𝑉𝐴 ∖ 𝐴𝑖, 𝐸𝐴 ∖ 𝑒𝑖))) ≤ 0
• Define 𝐻𝑖 as the set of hard constrained units 𝐴𝑖 ∈
𝐶 which are only visible from 𝐴𝑖.
• Goal polygon 𝑋 𝐺
𝑖
of a candidate vehicle 𝐴𝑖 ∈ 𝐶 must be
inside the visibility polygons of 1) the disconnected
unit 𝐵𝑗 , 2) at least one other vehicle and 3) inside the
polygon 𝑉(𝐻𝑖) of it’s hard constrained units.

17. Choosing Candidate Vehicles
Disconnected Units 𝐷 = 𝐴
CandidateVehicles 𝐶 = 1,3
𝐻1 = 𝐸
𝐻3 = 𝐵
𝐷 = 𝐷
𝐶 = 2,3
𝐻2 = 𝐵
𝐻3 = 𝐸, 𝐹

18. Goal Locations to Relocate a Vehicle
• We may get multiple goal locations for a vehicle and
select the one with largest area size:
𝑋 𝐺
𝑖
= ൞
max
𝐴 𝑘≠𝐴 𝑖,1≤𝑘≤𝑛
𝑉 𝑏𝑗 ∩ 𝑉 𝑞 𝑘 ; 𝑖𝑓 𝐻𝑖 = ∅
max
𝐴 𝑘≠𝐴 𝑖,1≤𝑘≤𝑛
𝑉 𝑏𝑗 ∩ 𝑉 𝑞 𝑘 ∩ 𝑉 𝐻𝑖 ; 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
• We select the optimal vehicle 𝐴𝑖 in terms of the
relocation cost of a vehicle from its current position
𝑥𝑖
𝑠
to the computed goal region 𝑋 𝐺
𝑖

19. Example Goal Locations Computation
𝑋 𝐺
2
𝑋 𝐺
4
𝐷 = {𝐸}
𝑅𝑅𝑇 ∗ 𝑃𝑎𝑡ℎ

20. BonnMotion Simulations (random waypoint)

21. BonnMotion Simulations (Nomadic Mobility)

22. Conclusion
• We check and repair the LoS-based
communication network on a field mission.
• Used a two-step algebraic graph theoretical
solution to verify the current status of the
visibility based network.
• Provide solution that relocates a single vehicle in
order to repair a disconnected network caused by
the mobility of the units.
• Showed illustrative examples to demonstrate the
effectiveness of the proposed model using
different mobility models.

23. Future Directions
• One immediate extension of this work is to allow
multiple vehicles to relocate.
• Remove the assumptions about the known world
and obstacles.
• A robot equipped with sensors can create a
strategy based on visibility events to explore the
unknown environment and find good LoS
locations.

24. Questions?
Thank you for coming