A Kangaroo Inspired Heterogeneous Swarm of Mobile Robots with Global Network Integrity for Fast Deployment and Exploration in Large Scale Structured Environments Trung Dung Ngo, Member, IEEE, Pham Duy Hung, Member, IEEE, and Minh-Trien Pham
Abstract— A heterogeneous robotic swarm for fast deployment and exploration in large scale structured environments is addressed in this paper. The swarm consists of a marsupial robot that is capable of carrying the small robots for fast deployment and loading the small robots for fast displacement. The heterogeneous robotic swarm is governed by a hierarchical distributed control including distributed node control for behavioural control and connectivity maintenance, and distributed connectivity control for network expansion and global network integrity. We illustrate systematic characteristics and potential applications of the heterogeneous robotic swarm compared to the homogeneous robotic swarm through simulation results. Keywords— Swarm Robotics, Heterogeneous Systems, Marsupial Robot, Behavioral Control, Distributed Node Control, Distributed Connectivity Control, Connectivity Maintenance, Global Network Integrity
1. I NTRODUCTION Swarm robotics has been studied with several application domains, e.g., surveillance and reconnaissance, patrolling and monitoring, area coverage, multiple target tracking. It is impractical for human operators to remotely manage each robot, instead the robots must be self-governed to maintain connectivities with their immediate neighbours to make consensus decisions for cooperative and coordinative operations. A swarm of mobile robots with capacities of deployment and exploration in large-scale structured environments is considered as a typical study case of coordinative and cooperative systems. A distributed control for connectivity (connectedness) maintenance (preservation) is the fundamental issue to guarantee swarming behaviours and collective decision makings. To ensure that collected information such as victim or poison sources, reported to human operators through peer-to-peer communication of an ad-hoc network, the mobile robots must maintain a global network integrity connecting through all the robots. Hence, a distributed control for connectivity maintenance and global network integrity is the key factor for homogeneous or heterogeneous robotic swarms with applications of exploration and rescue services. Manuscript received August 10, 2014.This research was supported in part by the University of Brunei Darrusalam (UBD/PNC2/2/RG/1(259)) and the Asia Research Centre and the Korea Foundation for Advanced Studies. Trung Dung Ngo is with the More-Than-One Robotics Laboratory (www. morelab.org), University of Brunei Darusslam, Brunei Darussalam (email:
[email protected]). Pham Duy Hung and Minh-Trien Pham are with the Faculty of Electronics and Telecommunication, University of Engineering and Technology, Hanoi, Vietnam (e-mail:
[email protected]).
Fig. 1. A heterogeneous robotic swarm consisting of the kangaroo mother robot and its juvenile robots at performance: the juvenile robots are going out from the artificial pouch to deploy into the environment [1], [2].
In this paper, we introduce a heterogeneous swarm of mobile robots that can preserve the global network integrity while performing deployment and displacement for the environmental exploration and victim identification in large-scale structured environments. The heterogeneous swarm consists of a marsupial robot and a certain number of small robots that can be loaded on and unloaded from the marsupial’s “pouch” for fast deployment and exploration. The swarm is governed by a hierarchical distributed control consisting of distributed node control that provides behavioural control for all the robots and ensures connectivity maintenance among them, and distributed connectivity control that manages connectivities for network expansion and global network integrity. 1.1 Related Works Inspired from controllability of complex networks in [3]– [5] indicating the difference between node control and connectivity control, distributed control of complex network systems can be divided into distributed node control and distributed connectivity control. Distributed node control of multi-agent networks for connectivity (connectedness) maintenance (preservation) can be roughly categorised in three mainstreams: behaviour-based control [6]–[10]; artificial potential field [11]–[21]; graph theory-based algebraic connectivity [22]–[29]. A comprehensive literature review of distributed control for multiagent coordinations can be seen in [30]. However, none of such previous works focused on preserving global network
integrity for network utilisation, i.e., inter-agent communication, cooperative sensing. Distributed connectivity control emphasises on capability of link addition and deletion [22]–[29]. We even found a fewer related works of distributed multi-agent coordination with global connectivity preservation [26], [31]. However, such works are not either integrated with distributed node control for the overall network management or associated with specific applications such as deployment, exploration, or rescue services. Cooperative deployment, exploration and coverage [12], [13], [32]–[40] are closely relative research. However, such works were not dedicated for fast deployment and exploration and their performance efficiency is not statistically measured for system validation. To our best of knowledge, our work presented in this paper is unique because we have not found any previous works of heterogeneous robotic systems that has dealt with the networking constraints while none of existing distributed controls of robotic systems are capable of performing fast deployment and exploration, and intelligently dealing with global network integrity enhancing online information flow for emergency and rescue services. 1.2 Statement of Contributions To overcome shortcomings of the existing methods, we propose a new approach of a heterogeneous robotic swarm to exploration and rescue services in large-scale structured environments. The heterogeneous robotic swarm is governed by a hierarchical distributed control that is originally built up by behavioural control but upgraded the distributed node control for connectivity maintenance and distributed connectivity control for network expansion and global network integrity. Thanks to the hierarchical distributed control and the marsupial robot, the heterogeneous swarm of mobile robots is capable of performing fast deployment, displacement and exploration while preserving the global network integrity. Specifically, • Fast deployment, displacement, and exploration: the marsupial robot can fast deliver the small robots to office like rooms without making efforts on dealing with complex constraints of network connectivities. • Global network integrity: the hierarchical distributed control intelligently minimises connectivities for network expansion required for exploration and coverage while preserving the global network integrity for online information flows to report victim identifications and their locations to the human operators. 1.3 Paper Outline The rest of this paper is organised as follows: Fundamental knowledge of the graph theoretic network model and local connectivity topologies used to develop the distributed control are illustrated in section 2. The hierarchical distributed control is described in detail in section 3. Experiment setups, simulation results, and discussions are elaborated in section 4.
2. G RAPH - REPRESENTED N ETWORK M ODEL A large-scale network of N mobile robots (a mother and N − 1 children) and E connectivities made among them is described as an undirected graph G(N, E). A connectivity between two mobile robots, i and j, is represented by an edge of the connectivity graph, ei j ∈ E. A mobile robot i can perceive and communicate with its neighbouring robots Ni , if the relative distance between them is within the diskbased sensing and communication range rc . That is, the connectivity ei j between the robots i and j exists if e ji ≤ rc : j ∈ Ni . This rule is applied for both relationship between the mother and children, and the children only as shown in Figure 2(b) and 2(c) . Connectivity graph can be described by the mean of the adjacency matrix A ∈ RN∗N Each element ei j of the adjacency matrix A is defined as the weight of the edge between the robot i and the robot j, which is a positive value if j ∈ Ni , or zero otherwise. In the undirected graph, A is a symmetric matrix with each element ei j represented below: ( 1 ei j = e ji = 0
ri j ≤ rc
ri j > rc
(1)
Connectivity property of the mobile robots is identified through the second smallest eigenvalue λ2 of the Laplacian matrix A - so called algebraic connectivity. The mobile robots are considered as being connected if λ2 > 0. Connectivity strength is proportional to the value of λ2 - the higher value, the stronger connectivity graph. We release the following definitions used to develop the distributed node control and distributed connectivity control. Definition 1: (Sub Adjacency Matrix) The robot i has a set of neighbours Ni . We define Sub Adjacency Matrix, subA, of the robot i as the adjacency matrix of Ni . The sensing and communication range of each mobile robot is divided into three areas: obstacle avoidance area Sa with radii range r1 ; free area Sf inside annulus circle between two radii r2 and r1 , and critical area Sc inside annulus circle between two radii rc and r2 - so-called as critical error ε as in Figure 2(a). Definition 2: (Candidates as Critical Neighbours) The robot j becomes a candidate of critical neighbours of the robot i if it is within the robot i’s critical area Sci and no obstacle exists within intersection of critical area and free area of the robots i and j, Oi j = (Sfi ∪ Sc j ) ∩ (Sfi ∪ Sc j ). Once obstacles k appear within Oi j , the robot j becomes a candidate of critical neighbours of the robot i if it is within the robot i’s critical area and free area Sci ∪ Sfi . ( Ci =
j ∈ Sci j ∈ Sci ∪ Sfi
@k∈ Oi j ∃k∈ Oi j
(2)
Compared to our previous work in [41], Ci is expanded to Sci ∪ Sfi where obstacles exist in order to guarantee
k rc
rb
r2 i
r1
Avoid area Sai
Si i1 i Sci
Sfi Sfj
Sfi
jSaj
Sai i
Free area Sfi Critical area Sci
(a) Connectivity range
Sj j1j
rc
Sfj
Sfj
Saj
Scj
Scj SaM
m
SfM
Sci Scj
ScM
(b) Critical robots
(c) Mother and child robot
Fig. 2. Connectivity range and critical robots: (a) the robot j freely move within the S fi , move away from Sai , and is considered as a candidate of critical robots for the robot i if the robot j is within Sci ; (b) the robot i has critical robots j, k, m; the robot j has critical robots i and k; the robot i is not the critical robot of the robot j;(c) The Mother robot M with radius of body rb and sensing range rc . Sensing range area square of mother robot is more than child robot 2πrb rc .
that connectivity between i and j is consistently preserved without intervention of obstacles. Definition 3: (Critical Neighbours and Critical Connectivities) The robot j is a candidate of critical robots of the robot i, j ∈ Ci . The robot i becomes a critical robot of the robot j, and the connectivity between the robot i and the robot j is considered as the critical connectivity, and vice versa if there does not exist any other robots inside the intersection area between their free areas Sf j ∩ Sfi .
n13
n10 n11 n9 n12 n6
T2
Sf6
Sc6
Sc2 Sf2 n4
Sc1 n1 n2
Sf1 T1
n5 Sf8 n8 n3
Sc8 n7
Sf3 Sf7 Sc3 Sc7
Cni = { j ∈ Ci , : Sf j ∩ Sfi = 0} /
(3)
Note that the mother robot M will be not considered as a critical neighbour of other robots in any circumstance. However, child robots can be critical neighbours of the mother robot M with all the above mentioned definitions. 2.1 Local Connectivity Topologies In general, we have to take all the neighbours of the robot i into consideration to design its distributed control. However, the robot i’s critical neighbours act like ”anchors” preventing of the robot i moving out of the relative range to further explore unknown areas. We have to deal with three connectivity topologies established by the robot i and its critical neighbours Cni to allow the robot i the possibility of moving towards an assigned destination while preserving the global network integrity: Triangle topology: There exists two critical neighbours j and k connected together in Cni , i.e., checked by subAi = 1. Both the critical connectivities, ei j and eik , cause the robot i impossible to reach a destination out of the coverage by the neighbours j and k. As illustrated in Figure 3(a), the triangle topology of three robots n1 , n2 , n3 prevents the robot n1 to reach the target T1 . K-connected topology: A robot i has two critical neighbours j and k that are not connected in Cni , i.e., subAi = 0. If the robots j, k have the neighbouring robots in N ∩ Ni connected directly or indirectly through groups of intermediate robots, denoted R j and Rk , and the intersection of the two groups is not a empty set, R j ∩ Rk 6= 0, / the robots i, j,
Fig. 3. Connectivity topologies: a) A triangle topology of the robot n1 red triangle - consists of two critical robots n2 and n3 making two critical connectivities e12 and e13 within Sc1 , and the connectivity e23 ≤ rc . b) A k-connect topology (quadrangle topology) of the robot n8 - green polygon consists of three critical robots {n5 , n6 , n7 } in which the intersection of two groups of the robots n6 and n7 is non-empty, i.e. R6 = {n5 }, R7 = {n5 }, R6 ∩R7 = {n5 } 6= 0. / c) A k-connected topology vs. a one-connected topology: any robot in the group {n4 , n5 , n6 , n9 , n10 , n11 , n12 } consists of either oneconnected topology or k-connected topology with its neighbours, depending the neighbourhood level ` ( ` ≥ 3 for k-connected topology, e.g., R5 = {n6 , n7 , n8 , n9 , n10 }, R4 = {n1 , n2 , n3 , n10 , n11 , n12 , n13 }, R5 ∩ R4 = {n10 } = 6 0/ and ` < 3 for one-connected topology, e.g., e.g., R5 = {n6 , n7 , n8 , n9 , n9 }, R4 = {n1 , n2 , n3 , n11 , n12 , n13 }, R5 ∩ R4 = 0). / d) If neighbourhood level ` ≤ 2, an one-connected topology of the robot n5 - blue line - between the robot n5 and the robot n4 is the critical connectivity e45 , i.e. R5 = {n6 , n7 , n8 , n9 }, R4 = {n1 , n2 , n3 , n11 , n12 , n13 }, R5 ∩ R.4 = 0. /
k establish a k-connected topology (a type of k-connected graph, where k = 2, in the graph theory). Specifically, kconnected topology can be in the form of four edges, so-called as quadrangle topology; five edges, so-called as pentagon topology; six edges, so-called as hexagon topology, and so forth. Both the critical connectivities ei j and eik cause the robot i impossible to reach destinations out of the coverage area of the robot j and the robot k. As illustrated in Figure 3(b), the k-connected topology with four robots n5 , n6 , n7 and n8 become anchors preventing the node n8 to reach to the target T2 . One-connected topology: A robot i has only one critical neighbour j, and vice versa the robot j has only one critical neighbour i. If the robots i and j have the neighbouring
robots in N ∩ Ni connected directly or indirectly through intermediate robots, denoted Ri , R j , and the intersection of the two groups is a empty set, Ri ∩ R j = 0, / the robots i and j make a one-connected topology. The connectivity between the robot i and the robot j must be preserved for the network integrity. If Ri ∩ R j 6= 0, / the critical connectivity ei j causes the robot i impossible to reach its destination as illustrated in Figure 3(c). 3. H IERARCHICAL D ISTRIBUTED C ONTROL FOR C ONNECTIVITY M AINTENANCE , N ETWORK E XPANSION , AND G LOBAL N ETWORK I NTEGRITY We assume that all the mobile robots are equipped with sensing and communication capacity. That is, a robot is capable of identifying and measuring relative distance to its nearest neighbours within the radii range rc . They can peerto-peer communicate each other within the radii range rc . This section is dedicated to designing the hierarchical distributed control for the heterogeneous robotic system. Note that the hierarchical distributed control is only applied for the children robots that need to maintain connectivity with their mother or their peers. The mother is not considered as critical neighbour of the children robots so it will be treated differently in terms of functionalities, which will be explained next section. 3.1 Distributed Node Control Level 1 - Behavioural Control: Inspired from behavioural control in [6] [7], velocity vector of the robot i, vti , is synthesised by cohesion vci , separation vsi , and alignment vai velocity vectors. vi = αvci + β vsi + γvai
a robot has critical robots and critical connectivities. The distributed node control is synthesised by the current velocity of the robot and its critical robots’ relative positioning as in (5):
vit+1
vijt v it
vpt _ ij t vo_ik
Fig. 4.
Distributed node control for connectivity maintenance
vt+1 = i
∑
(vti + vtp i j ) +
j∈Cni
(5)
k∈Oi j
where vti is the current velocity of the robot i, vtp i j is the projection of vti on the edge, ei j , of the robots i and the robot j, and vto ik is aligned with the opposite direction of existing obstacle k. At an instance, the modified velocity of the robot i for maintaining connectivity with the critical neighbour j rc −krti j k must satisfy the condition: kvt+1 i k < min 2∆t , where ri j j∈Cni
is the relative distance between the robot i and the neighbour rc −krti j k j, and ∆t is time step. If kvt+1 i k ≥ min 2∆t , the velocity j∈Cni
(4)
where α, β , γ are factors to adjust cohesion, separation, and alignment for the overall behaviour. Cohesion vci is the vector driving the robot i towards its neighbouring robots satisfying j ∈ S fi ∪ Sci . Separation vsi is the vectors that drives the the robot i away from its neighbours satisfying j ∈ Sai . Alignment vai is the vector guiding the robot i towards the unexplored areas. Alignment vai becomes the vector for the robot i towards its assigned destination when the mother robot recognised the door and make a decision of sensing the small robots. The factors α, β , γ are normalised (all the robots are assigned with the same α and γ) in order to guarantee the smooth movement of the whole network of mobile robots for exploration and search services. Note that all the robots operate with this behavioural control if they have no critical neighbours. To guarantee that the robot i is not disconnected with the robot j when the robot i is within the free area of the robot j, i ∈ S f j , we adjust the velocity vi = ε if vi > ε. Level 2 - Connectivity Maintenance: The distributed node control for connectivity maintenance aims at keeping all the robots connected in the network for data intercommunication - no robot is disconnected from the network at any time. This distributed node control is only activated when
vto ik
∑
min (
is normalised by a factor ξ < vt+1 i
j∈Cni
rc − rtij 2∆t )
k ∑ (vti +vtp i j )k
to ensure
j∈Cni
that the robot i cannot disconnect with the robot j, ri j ≤ rc . Since then, the velocity of the robot i is recalculated by the numerical factor ξ : vt+1 = i
∑
j∈Cni
ξ (vti + vtp i j ) +
∑
vto ik
(6)
k∈Oi j
3.2 Distributed Connectivity Control The distributed node control guarantees all the robots well connected in the network. However, connectivity maintenance plays the role of constraints that prevent the mobile robots to move towards their assigned destination. The fact is that only one interconnectivity - so called global network integrity - is needed to be maintained for intercommunication through all the robots while there might exist more than one interconnectivity in the network. If the “redundant” connectivities are identified by the robots, they can negotiate through information exchange in order to remove such connectivities, allowing the mobile robots to expand explored areas spatially. The distributed connectivity control is trigged only if a robot has at least two critical neighbours, which fall into one of two cases triangle topologies and k-connected topologies.
If so, the mobile robot is still working with the connectivity maintenance but intelligently removing redundant connectivities to accelerate the process of exploration and search. Level 3 - Connectivity Minimisation of Triangle Topologies: A robot i has two critical neighbours j and k connected together in Cni . Both the critical connectivities, ei j and eik , cause the robot i impossible to reach a destination out of the sensing and communicating area of the neighbours j and k. If so, the distributed connectivity control can decide to remove the longer connectivity between ei j and eik because the neighbour on this connectivity tends to escape from the network preservation. If all triangle topologies have been properly minimised, all existing connectivity topologies on a robot i has only either k-connected topologies or one-connected topologies. Level 4 - Connectivity Minimisation of K-connected Topologies: A robot i has two critical neighbours j and k that are not connected in Cni . If the robots j, k have the neighbouring robots in N ∩ Ni connected directly or indirectly through groups of intermediate robots, denoted R j and Rk , and the intersection of the two groups is not a empty set, R j ∩ Rk 6= 0, / the robots i, j, k establish a kconnected topology. The critical connectivities ei j and eik cause the robot i impossible to reach a destination out of the sensing and communicating area of the robot j and k. If so, the distributed connectivity control can decide to remove the longer connectivity between ei j and eik . Note that the robots in the two groups R j and Rk need to communicate each other to check whether there are common neighbours. To remain the distributivity of this SoS in this paper, every robot is set to only peer-to-peer communicate with its nearest neighbours, thus R j and Rk might have common neighbours where the neighbourhood level ` > 1 will not be considered as kconnected topologies instead of one-connected topologies only. Once triangle topologies and k-connected topologies is minimised, the inter-connectivity among the robots becomes one-connected topologies, which must be preserved for the global network integrity that is useful for information exchange among the robots. 3.3 Hierarchical Distributed Control for Connectivity Maintenance, Network Expansion, and Global Network Integrity The hierarchical distributed control for all mobile robots synthesised by distributed node control and distributed connectivity control is event-based trigged. Level 1 - Behavioural Control: governing the fundamental behaviours of the robots, e.g., navigation and exploration. Level 2 - Connectivity Maintenance: added on the top of the Level 1 - Behavioural Control to keep all the robots connected robustly through the network. This control is only trigged when the robots tend to escape from the network connectivities. Level 3 - Connectivity Minimisation of Triangle Topologies:: added on the top of the Level 2 - Connectivity Maintenance allowing the robots to expand their possible
exploration area through intelligently removing redundant connectivities of the network integrity. This control is only trigged if a robot has more than two critical neighbours. Level 4 - Connectivity Minimisation of K-Connected Topologies:: added on the top of the Level 3 - Connectivity Minimisation of Triangle Topologies to optimally minimise redundant connectivities of the global network integrity for exploration expansion area through intelligently removing redundant connectivities of the network integrity. This control is only trigged if a robot has more than two critical neighbours obtaining at least a common neighbour not including itself. 4. S IMULATIONS AND D ISCUSSIONS A. Scenario Generation To examine performances of the heterogeneous robotic swarm with the developed hierarchical distributed control, we generated structured building as shown in Figure 5(a). The scenario consists of office rooms along the main corridor with only one main entrance. These rooms are designed with different sizes and shapes for random exploration process. We assume that a number of victims are trapped in the building due to natural disasters, e.g, earthquake. The victims are randomly allocated in different offices and they can not find a way to escape due to environmental conditions, e.g. no entrance direction due to dark smoke, injuries. With the generated scenario, we expect that the heterogeneous robotic swarm is sent into the structured building to explore and identify trapped victims and their locations. Once victims are found and identified, a life path of mobile robots is online built up to help victims to escape through the main entrance. This life path is also used by fire fighters to approach the victim for rescue services if the victim is not capable of going out by themselves. B. Parameter Setting We set rc = 1, ε = 0.1rc , time step ∆ = 1.0. The factors is automatically α, β , γ can be arbitrarily chosen because vt+1 i normalised to ensure the connectedness as seen in 6. Here, we set α = 2.5, β = 5.0, γ = 2.5 for experiments in this paper. The size of the building 25 x 12 m2 is divided into 11 office rooms. The total of 80 joey robots are used: 32 joey robots are used to explore all the office rooms and 48 joey robots to make the backbone to maintain the global network integrity. Note that, with the marsupial robot, 48 joey robots used to build the backbone can be replaced by static wireless beacons. 4.1 Simulations The kangaroo mother-like marsupial robot containing a number of joey-like small robots on her “pouch” is sent into the structured building for exploration and victim identification. Like other large scale robotic platforms, this marsupial platform is equipped with high resolution sensors such as laser range finders, 2D and 3D cameras with software framework for sensor fusion and data association, and highly capable mobility allowing the robots to autonomously navigate and explore at the high speed in the main corridor.
(a) Structured scenario
(b) Initial state
(c) Explore the first room
(d) Complete exploration of the right wing
(e) Explore the left wing
(f) Complete exploration and coverage
Deployment, displacement, and exploration of the heterogeneous robotic swarm over time
The marsupial robot can recognise office doors, but can not go through the door due to its large body size so that the marsupial robot unloads the small robots on her “pouch” into the office rooms to cooperatively explore and identify victims, call them back on the “pouch” when the room is completely explored and covered, then displace to the next room for new routine of environmental exploration and victim identification. Note that, an office room is completely covered when this room is fully covered by incorporated sensing coverage of joey robots. To guarantee that the global network integrity connecting all mobile robots is maintained over time, the marsupial robot sequently lays out the small robots in the constraint of its sensing and communication range along the corridor. The small robots laid down along the trait of the marsupial robot act as wireless routers of an ad-hoc network for information exchange between the robots and the human operators standing out of the main entrance. Such small robots also play the role as the life path for the victim to escape out of the building, or for the fire fighters to follow the the marsupial robot explored trait for rescue services. 4.2 Results and Discussions A. Self-Deployment and Self-Displacement The overall performance of deployment, displacement for environmental exploration and victim identification by the heterogeneous swarm of mobile robots in the large-scale structured building can be seen in the Figure 5. Less number of the robots: thanks to the highly capable mobility of the marsupial robot, her loading and unloading capacity, and cooperative exploration of the small robots, the victims trapped in the large-scale building can be explored very fast. Instead of deploying a lot of mobile robots to cover the large-scale building like in [12], we use the technique of self-deployment to send the robots into each room, and selfdisplacement to shift over the small robots to other rooms so that only a certain number of the small robots, which is
Total deployment time between rooms 35 Mother and children Only children 30
25
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Fig. 5.
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Fig. 6. Comparative time consuming between the heterogeneous robotic swarm and the homogeneous robotic swarm: 1,2,3,...,11 indicate the time consuming for deployment and exploration in the room; 1-2, 2-3, 3-4,..., 10-11 implies the time consuming for displacement from the current room to the next room
sufficient to cover the largest room, is required to explore the whole large scale building. Easer to control and manage the network: like complex network systems discussed in [3]–[5], the more nodes used, the more connectivities created. If the number of connectivities and nodes are dramatically increased, we encounter the difficulty of controlling the robots and managing their connectivities to guarantee the global network integrity for information flow through all the robots and human operators. The self-deployment and self-displacement help to reduce the number of the robots used while accelerating the process of exploration and victim identification as explained in [41], [42]. Faster deployment, displacement and exploration: the idea of using the marsupial robot carrying the small robots
0 16
Connectivity properties of the system with mother and children 12.65 29.61 54.12 77.23
100.23
0
Time(s)
Mobile Network Integrity Global Network Integrity
20.79
Connectivity properties of the system with children only 40.97 59.73 77.71 94.46 110.56 125.19
Mobile Network Integrity Global Network Integrity
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(a) Marsupial and joeys Fig. 7.
0.0026 0 0
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Status of the global network integrity through the second smallest value of the adjacency matrix
results in faster deployment and displacement for exploration of large-scale structured environments. As illustrated in the Figure 6, we compare the time consuming for exploration between the heterogeneous robotic swarm (with the marsupial robot) and the homogeneous robot swarm (only the small robots) with the same hierarchical distributed control applied. The time consuming of the heterogeneous robotic swarm is sufficiently less than the one of the homogeneous robot swarm in both deployment for exploration in the office rooms and displacement to the next room in the corridor. As a result, the total time consuming of the heterogeneous robotic swarm is less than the one of the homogeneous robotic swarm (100s vs. 140s) as shown in the Figure 7. B. Global Network Integrity The key issue of search and rescue services in the largescale structured environment is that information about victim identifications and their locations must be online reported during progress of exploration, search and rescue. Therefore, the global network integrity connecting all the robots as an wireless ad-hoc network for information exchange is necessarily essential. As depicted in the Figure 7(a), the hierarchical distributed control including the distributed node control and distributed connectivity control guarantees that the global network integrity is consistently preserved (λ2 = 0.003) while the heterogeneous robotic swarm is deployed to explore the whole structured building. To compare complexity of the network integrity, we measured λ2 of the mobile network integrity and the global network integrity in both the heterogeneous and homogeneous robotic swarms, resulted in the Figure 7. It is expected that λ2 is as small as possible so that the robotic swarm has higher flexibility in terms of deployment and exploration. Indeed, λ2 of the mobile heterogeneous network (maximum λ2 ≈ 16.5) is smaller than the one of the mobile homogeneous network (maximum λ2 ≈ 26). With the marsupial robot, the mobile network integrity (blue curve) sometimes reaches the global network integrity (red curve) because all the small robots are on the “pouch” of the marsupial for faster displacement, which can not happen with the homogeneous robotic swarm.
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