Abstract
Mobile robots, especially unmanned aerial vehicles (UAVs), are of increasing interest for surveillance and disaster response scenarios. We consider the problem of multi-robot persistent surveillance with connectivity constraints where robots have to visit sensing locations periodically and maintain a multi-hop connection to a base station. We formally define several problem instances closely related to multi-robot persistent surveillance with connectivity constraints, i.e., connectivity-constrained multi-robot persistent surveillance (CMPS), connectivity-constrained multi-robot reachability (CMR), and connectivity-constrained multi-robot reachability with relay dropping (CMRD), and show that they are all NP-hard on general graph. We introduce three heuristics with different planning horizons for convex grid graphs and combine these with a tree traversal approach which can be applied to a partitioning of non-convex grid graphs (CMPS with tree traversal, CMPSTT). In simulation studies we show that a short horizon greedy approach, which requires parameters to be optimized beforehand, can outperform a full horizon approach, which requires a tour through all sensing locations, if the number of robots is larger than the minimum number of robots required to reach all sensing locations. The minimum number required is the number of robots necessary for building a chain to the farthest sensing location from the base station. Furthermore, we show that partitioning the area and applying the tree traversal approach can achieve a performance similar to the unpartitioned case up to a certain number of robots but requires less optimization time.
Highlights
Mobile robots, especially unmanned aerial vehicles (UAVs), are of increasing interest in various application domains including surveillance
Determining the optimal relay positions such that a goal can be reached with a predefined number of robots on a predefined path to the goal is NP-hard, which we show with a transformation from 3SAT to d-constrained multi-robot reachability with relay dropping (CMRD) defined in Definition 6 (d-CMRD): The problem d-CMRD is described by a set of tuples of the form (P, EC, r) where P := (b, v1, . . . , vn) is a sequence of vertices that describe a movement path, EC denotes the connectivity edges between the vertices, and r is the number of robots
In this simple scenario short horizon cooperative (SHC) shows the optimal behavior resulting in the best possible WI of 60: One robot acts as relay for the other two and visits s4, while another robot is commuting between s1 and s2 and the third robot between s2 and s3
Summary
Especially unmanned aerial vehicles (UAVs), are of increasing interest in various application domains including surveillance. We define the decision problem d-CMR to show that the problem of determining the minimum number of robots necessary to reach a particular vertex (as well as determining the minimum number of time steps to do so), when all robots start at the base station, is NP-hard (NP-complete). Determining the optimal relay positions such that a goal can be reached with a predefined number of robots on a predefined path to the goal is NP-hard, which we show with a transformation from 3SAT to d-CMRD (see Proposition 7 and Figure 4) defined in Definition 6 (d-CMRD): The problem d-CMRD is described by a set of tuples of the form (P, EC , r) where P := If a robot can reach cβ , the vertices x1, . . . , xα, c1, . . . , cβ are connected to the base station, which is only possible if a relay is placed at each zi such that the 3SAT instance is satisfied
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