Dispersion of mobile robots in a certain formation is prerequisite in many applications; one of the most important issues during the entire process is to maintain the interagent connections, as well as to restore them whenever they were broken. We investigate the aforementioned problem in this work by designing a holistic connectivity controller (HCC) to regulate and restore the interagent connections during the dispersion of the mobile network. HCC consists of two core structures. Firstly, to illustrate the multirobot dispersion, we adopt the distributed link removal algorithm (DLRA), which is able to remove redundant links in the multirobot network to facilitate the dispersion and only requires local information of no more than two-hop neighbors. Secondly, the proposed approach is extended to the problem of connectivity restoration with consideration of simultaneous failure of multiple agents. A connectivity restoration strategy is proposed, and then the recoverability of network connectivity is investigated. The proposed HCC has also integrated motion controller to regulate the movement of the mobile robots, so that interrobot collisions can be effectively avoided. Theoretical analysis and computer simulations have confirmed the efficiency and scalability of the proposed schemes.
The cooperative control of large groups of mobile agents (vehicles/robots) is rapidly developing because of technological advances in wireless communication and networking technologies. Mobile ad hoc network based on the IEEE 802.11 standard [
Seven mobile robots are initially deployed in a dense manner and configured to their final formation with sparse network structure and better coverage of the area.
Initial configuration (before dispersion)
Final configuration (after dispersion)
Maintaining the connectivity of MRS can be vital for achieving network-wide collaboration and the success of the entire mission, given the thought that in most scenarios mobile robots need to communicate with each other constantly to coordinate or even negotiate the execution of every task, if not just for synchronization. Due to the level of importance of interrobot communication, the
Failure of mobile robot may reduce in partition of the underlying networks.
Failure of noncritical robot
Failures of critical robots
Considering the autonomous nature of multi-agent system, to design a distributed local connectivity restoration mechanism is obligatory for dealing with such situations. Recently, closely related problems have been investigated in wireless sensor and actor networks (WSAN), and a class of connectivity restoration algorithms has been proposed to fix the network structure whenever failure of actor(s) occurs [
Aiming at bridging the gap between dispersion and connectivity restoration, we investigate the aforementioned problem in this work by designing a holistic connectivity controller (HCC) to regulate and restore the interagent connections during the dispersion of the mobile network. HCC consists of two core structures. First, to illustrate the multirobot dispersion, we adopt the distributed link removal algorithm (DLRA) [
The rest of the paper is organized as follows. Section
Consider
Furthermore, let the dynamic graph
Note that any normalized nonnegative function can be treated as a weighting function. Nevertheless, to associate with the link quality, it is rather a natural choice that
An undirected weighted dynamic graph
Now the main objectives of this paper can be described as follows.
To achieve the Objective A, we will need the DLRA algorithm [
Node
Node
For any node
Based on the aforementioned definitions, the proposed DLRA is described as follows.
Redundant link removal process in DLRA.
To provide the applicability of HCC and multirobot dispersion, we recall the following lemma.
For any subgraph
What Lemma
DLRA under stationary network scenario.
Dispersing a team of mobile agents often results in a sparse structure of the underlying network. This phenomenon represents the vulnerability of connectivity subjected to failure of mobile agent(s). Upon the failure of critical agent(s), the initially connected multi-agent network will be partitioned into disjoint segments. In such case, network-wide collaboration will not be possible and certain missions can be in jeopardy due to the fatal network disconnection. In this section, we present a connectivity restoration strategy and further design a motion controller to integrate the multirobot dispersion with restoration of the mobile networks. And most importantly, the HCC also requires only two-hop information of neighboring robots.
Denote the topology control algorithm of the connectivity restoration strategy as CRA, and the following definitions are first introduced.
Assume that node
Denote
Node
Associated with the aforementioned definitions, CRA is described in Algorithm among all the
Upon Detecting failure of node ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( Upon Finishing Connectivity Restoration at time ( ( ( ( ( ( (
When dispersing a team of mobile robots, the invariance of network topology in generated subgraph
We first utilize the combined potential function in [
A repulsive potential function is introduced in the HCC to deal with the dispersion of mobile multirobot networks between node
The design principle of repulsive potential function is to assign each mobile robot an artificial potential force; this virtue force can drive the mobile robot to move in certain direction in a way that is opposite to each other. More specifically, whenever the distance between two neighboring mobile robots in the network is small, the repulsive potential force will drive them into different direction, so that during a small time period, the distance is enlarged, and the two mobile robots are dispersed from each other. It is worthwhile to notice that the smaller the distance, the greater the repulsive force.
Similarly, to restrict all essential communication links within
The attractive potential functions work in the way that any essential communication links in
Furthermore, to integrate the restoration methods into multirobot dispersion, a distributed prey motion controller is developed as follows:
The design principle of the prey motion controller is straightforward. When a mobile robot is assigned the role of prey, it is driven by the prey controller towards the last updated location of the particular failed robot, that is, its
The proposed potential functions and controllers entitle us to assign each node
It is easy to observe from (
Denote
Given a mobile multiagent system with fixed underlying network structure
However, (
Connectivity is not restorable if the candidate prey moves away from the location of the failure robots.
When integrating the control law (
Specification design of the holistic connectivity controller (HCC).
Furthermore, to understand the efficiency and capability of the HCC, in the next section, we present theoretical analysis about the restorability of the mobile MRS with HCC.
As is described in Section
To understand how HCC works in the case of single robot failure, we first have the following lemma.
The disconnection of
The proof is straightforward and is omitted in this paper. With the aid of Lemma
Assume a mobile multi-agent network
The result is obvious for the case that
To understand the connectivity restorability of mobile multirobot networks with respect to the case of multiple simultaneous agent failures, we provide the following illustrative analysis.
First, we denote the
With a loop circuit structure, the network disconnection induced by concurrent multiple failures of agents is unrecoverable.
With the aforementioned notions, we conclude the following.
With respect to the simultaneous failure of multiple robots in MRS system, the connectivity of the network is not restorable by HCC if
Refer to Figure
To evaluate the performance of the proposed HCC for multirobot dispersion with respect to failure of mobile nodes, a variety of simulations have been conducted, and the results are presented in this section. The simulations are categorized into three subcategories: (1) multirobot dispersion without failure of mobile robot, (2) multirobot dispersion with the failure of a single robot, and (3) multirobot dispersion with respect to simultaneous failure of multiple mobile robots. General parameters are set as in Table
Simulation parameters.
Symbol | Quantity | Value |
---|---|---|
|
Execution time slot | 0.01 s |
|
Interval of consecutive switches | 0.1 s |
|
Minimum sensing capability of normalized RSSI | 10% |
|
Optimized sensing value of normalized RSSI | 40% |
|
Restricted radium (reference distance) | 2 m |
|
Path loss (outdoor, 802.11b) | 0.02 |
|
Exponential gain | 0.7 |
|
Repulsive potential gain | 2500 |
|
Attractive potential gain | 200 |
|
Restoration potential gain | 10 |
|
Maximum agent velocity | 5 m/s−1 |
In case no mobile robot failed during dispersion, the HCC will not trigger CRA, and the motion controller law (
We simulate the dispersion of 20 mobile robots initially located within 100 m × 100 m
The evolution trajectory of a mobile MRS under the HCC. (a)
We further conducted simulations to evaluate the effectiveness and the stability of the HCC in multirobot dispersion without robot failures. It can be seen from Figure
Average communication links and robots’ velocities during dispersion.
Average communication links
Robots’ velocity in
Robots’ velocity in
To evaluate the HCC in case of single robot failure, we further conduct an experimental simulation with a networked MRS scenario with 11 mobile robots. At a certain point during dispersion, one of the mobile robots failed, and the network is partitioned into two connected subgraphs. The results can be found in Figure
Restoration process with respect to the failure of single mobile robot during dispersion. (a)
In Figure
A scenario of 18 mobile robots is then evaluated with the control of HCC, as shown in Figure
Restoration process with respect to the simultaneous failures of multiple mobile robots during dispersion. (a)
As is argued in Section
As is shown in Figure
Unrecoverable network with respect to the simultaneous failures of multiple mobile robots during dispersion. (a)
In most mobile multirobot applications, dispersion of mobile robots in a certain formation is often required. However, due to the complex and extreme environments in deploying robot team, single or multiple concurrent failures of mobile robot are inevitable. One of the most important problems induced by the failure of mobile robot is the disconnection in the underlying network. In this paper, we investigated and solved the aforementioned problem by designing a holistic connectivity controller (HCC). The proposed HCC can regulate and restore the interagent connections during the dispersion of the mobile multirobot network. Two main components are included in the HCC. Firstly, to illustrate the multirobot dispersion, we adopt the distributed link removal algorithm (DLRA), which is able to remove redundant links in the multirobot network to facilitate the dispersion. Secondly, the proposed approach is extended to the problem of connectivity restoration with consideration of concurrent failure of multiple agents. A connectivity restoration strategy is proposed, and then the recoverability of network connectivity is provided to unfold the capability of HCC with respect to simultaneous failure of multiple robots. The proposed HCC has also integrated motion controller to regulate the movement of the mobile robots, so that interrobot collisions can be effectively avoided. It is worthwhile to mention that the HCC only relies on local information of no more than two-hop neighbors, so the message complexity can be minimized. Finally, theoretical analysis and computer simulations are also provided to confirm the efficiency and scalability of the proposed schemes.
This work was supported by the National Science Foundation of China (Grants nos. 61272432, 61202508), China Postdoctoral Science Foundation (Grant no. 2011M500243), and Fundamental Research Funds for the Central Universities (FRF-TP-12-082A).