Most multi-robot systems are expected to be robust in the sense that the system should maintain its functionality, possibly with degraded performance, in case a subset of the robotic agents fails, e.g., due to battery discharge. In this con- text, totally decentralized approaches benefit from enhanced fault-tolerance when compared to centralized approaches, which suffer from the single point of failure phenomenon.
Among the works surveyed, only few deal explicitly with failures during the patrol mission. One of them is [Fazli et al., 2010]. This work focused on fault- tolerance in a novel approach for multi-robot graph coverage in a known and static
Table 2.1: Overview of selected architectures analyzed [Portugal and Rocha, 2011b].
Proposed Strategy Type/Per-
ception Communication Coordi- nation Decision-Making Conscientious Reactive [Machado et al., 2003] Reactive/
Local None Emergent Local Idleness-based Conscientious Cognitive
[Machado et al., 2003]
Cognitive/
Global None Emergent
Global Idleness-based Idleness Coordinator Monitored
[Machado et al., 2003] Cognitive/ Global Coordinator Messages Centralized Idleness-based with Monitoring Heuristic Pathfinder Cognitive
Coordinated [Almeida et al., 2004]
Cognitive/ Global Coordinator Messages Centralized Heuristic (Idleness + Distance) STP [Elmaliach et al., 2007] Cognitive/ Global Coordinated
Cyclic Trajectory Centralized
Hamilton Cycle Computation Cyclic Approach [Chevaleyre, 2004] Cognitive/ Global Coordinated
Cyclic Trajectory Centralized
TSP Heuristic Calculation Partitioning Approach [Chevaleyre, 2004] Cognitive/ Global Coordinated
Cyclic Trajectory Centralized
TSP Heuristic inside each region Gray-Box Learner Agent
[Santana et al., 2004]
Reactive/
Local Flags Emergent
Reinforcement Learning (Adaptive) Bidder Agent
[Menezes et al., 2006]
Cognitive/
Global Bidding Messages Auctions
Self-Interested Idleness-based Sequential Single-Item Auctions
[Hwang et al., 2009]
Cognitive/
Global Bidding Messages Auctions
Minimize the max patrol path Heuristic Pathfinder Two-Shot
Bidder [Almeida et al., 2004]
Cognitive/
Global Bidding Messages
Two-Shot Auctions
Heuristic (Idleness + Distance) Task Propagation approach
[Semp´e and Drougoul, 2003]
Cognitive/ Global Task Propagation Messages Centralized Task strength + Idleness (Adaptive) EVAP [Chu et al., 2007] Reactive/
Local Flags Emergent Local Idleness-based CLInG
[Chu et al., 2007]
Reactive/
Local Flags Emergent
Idleness-based information diffusion TSP rank of solutions [Sak et al., 2008] Cognitive/ Global Coordinator Messages Centralized Random TSP sub-optimal solution MSP
[Portugal and Rocha, 2010]
Cognitive/ Global
Coordinated
Cyclic Trajectory Centralized
Graph-based inside each region Left-Induced Partition
[Pasqualetti et al., 2012a]
Cognitive/ Global
Coordinated
Cyclic Trajectory Centralized
Graph Partitioning with known bounds Cyclic Approximation
[Pasqualetti et al., 2012b]
Cognitive/ Global
Coordinated
Cyclic Trajectory Centralized
TSP approximation with known bounds Mixed Strategy
[Iocchi et al., 2011]
Cognitive/ Global
Coordinated
Cyclic Trajectory Centralized
Mixed Cyclic + Partitioning PatrolGRAPH* [Baglietto et al.,
2008,Cannata et al., 2011]
Reactive/
Local Flags Emergent
Uniform frequency guided visits Auction reassignment
approach[Pippin et al., 2013]
Cognitive/ Global
Coordinated
Cyclic Trajectory Centralized
Partitioning with performance-based
reassignment
2D environment represented by a graph. A series of decompositions of the graph are employed to obtain cycles, which are then assigned to covering robots. Firstly, a technique called Constrained Delaunay Triangulation (CDT) is used to extract the graph of the environment. Then, the graph is reduced to decrease the distance
2.2. Discussion and weaknesses of the literature 31
traveled by each robot and improve efficiency. Afterwards, the authors make use of an extended version of the Prim’s algorithm [Prim, 1957] that builds MSTs on weighted graphs, in order to partition the graph and form as many partial spanning trees as the number of covering robots. Finally, cycles are built on each resultant tree to form navigating areas for each agent.
Upon failure of a robot, all of the vertices of its assigned tree are released and robots in adjacent areas will expand their trees, using the same extended version of the Prim’s algorithm, to repossess the released vertices and cover the environment again. However, no hints on how failures are detected by other robots in the team are given.
As referred before, a procedure is described in [Elor and Bruckstein, 2010] for the reorganization of agents in simulations, when a member of the team fails. However, the issue of robustness to leader breakdowns was left as future work and the authors suggest the use of an election algorithm. Also, in [Pippin et al., 2013] performance of agents is monitored during the patrol mission to handle the situation when robots are not performing as expected. However, no hints are given on what happens if some of the agents fail. In fact, several authors refer how the failure problem could eventually be handled in their own framework, but there is a manifest lack of solutions implemented, especially in the real-world.
2.2.2 Scalability
Scalability of the robot team is also a very important characteristic for patrolling strategies. A good strategy should work independently of the number of agents in the team and with any environment topology. In the context of the MRPP, most works do not focus on this issue and the ones that test strategies with variable number of agents do not address the scalability issue explicitly. There have been, however, a few scalability studies presented for multi-robot systems in general.
According to economists and conclusions from previous works on mobile robo- tics [Sweeney et al., 2003], groups display increasing marginal performance only until a certain group size. Beyond this point, the groups’ productivity drops with
the addition of robots. In theory, productivity should grow during size scale-up. However, spatial limitations increase the interference between agents causing the decrease of performance. Effective coordination algorithms maintain increasing productivity. To improve the group’s performance, methods can be developed to minimize interference between robots as in [Rosenfeld et al., 2006], where the impact of scalability of homogeneous robots in the productivity of a multi-robot system applied in groups with different coordination algorithms is studied.
In order to measure the interference level with different coordination algorithms and promote comparisons, an interference variable was defined by the total time robots deal with resolving team conflicts, e.g., like re-planning due to collision avoidance. This study was first applied in the foraging domain, where robots have to locate target items from a search region and deliver them to a goal re- gion. This domain was chosen due to the wide existing research of coordination algorithms within this environment and the likeliness of arising spatial conflicts between members of the same team in a limited field of operation. The study was limited to groups of homogeneous robots without the ability to communicate, and without previous knowledge of the environment to minimize the factors involved in the experiment.
In order to check if the same results were obtained in different domains with restricted spatial resources, the authors also conducted similar experiences in a limited search domain where the main objective is to find the exit out of the room as quickly as possible.
By evaluating exhaustive simulation trials with eight different coordination algorithms in both domains, important conclusions were drawn:
• The coordination method strongly impacts the scalability of the group; • A high negative correlation between group interference and productivity was
found.
Besides the critical point in scalability where productivity starts to decrease, there is a second point where the addition of more robots ceases to negatively
2.2. Discussion and weaknesses of the literature 33
Figure 2.5: Results obtained in [Rosenfeld et al., 2006] using different coordination schemes in the foraging domain.
affect the groups’ performance. This is illustrated in Figure 2.5.
Authors conclude that the interference measure should be considered in future works to produce effective coordination methods with the ability to scale to larger team sizes and aid in the study of scalability qualities of robots.
Furthermore, in [Balch and Arkin, 1994] the speedup measure is proposed. This metric reveals how much more efficient several robots are than just one in completing a task. If Ψ(R) is the performance function for R robots7, the speedup measure is given by:
υ(R) = Ψ(R)
Ψ(1) · R. (2.1)
If the speedup measure is equal to 1.0, R robots complete the task with a performance that is exactly R times better than one robot. This is called linear improvement, i.e., performance proportional to the number of robots. Speedup values inferior to 1.0 reflect sub-linear performance and values greater than 1.0 reflect super-linear performance.
The works of [Balch and Arkin, 1994] and [Rosenfeld et al., 2006] served as
a great inspiration in this thesis to address the scalability issue in the context of multi-robot patrol, as shown later on.