Collision-free network exploration

International audienc

Collision-Free Network Exploration

International audienceA set of mobile agents is placed at different nodes of a $n$-node network. The agents synchronously move along the network edges in a {\em collision-free} way, i.e., in no round may two agents occupy the same node. In each round, an agent may choose to stay at its currently occupied node or to move to one of its neighbors. An agent has no knowledge of the number and initial positions of other agents. We are looking for the shortest possible time required to complete the collision-free {\em network exploration}, i.e., to reach a configuration in which each agent is guaranteed to have visited all network nodes and has returned to its starting location. We first consider the scenario when each mobile agent knows the map of the network, as well as its own initial position. We establish a connection between the number of rounds required for collision-free exploration and the degree of the minimum-degree spanning tree of the graph. We provide tight (up to a constant factor) lower and upper bounds on the collision-free exploration time in general graphs, and the exact value of this parameter for trees. For our second scenario, in which the network is unknown to the agents, we propose collision-free exploration strategies running in $O(n^2)$ rounds for tree networks and in $O(n^5\log n)$ rounds for general networks

Deterministic Collision-Free Exploration of Unknown Anonymous Graphs

We consider the fundamental task of network exploration. A network is modeled as a simple connected undirected n-node graph with unlabeled nodes, and all ports at any node of degree d are arbitrarily numbered 0,.....,d-1. Each of two identical mobile agents, initially situated at distinct nodes, has to visit all nodes and stop. Agents execute the same deterministic algorithm and move in synchronous rounds: in each round, an agent can either remain at the same node or move to an adjacent node. Exploration must be collision-free: in every round at most one agent can be at any node. We assume that agents have vision of radius 2: an awake agent situated at a node v can see the subgraph induced by all nodes at a distance at most 2 from v, sees all port numbers in this subgraph, and the agents located at these nodes. Agents do not know the entire graph but they know an upper bound n on its size. The time of an exploration is the number of rounds since the wakeup of the later agent to the termination by both agents. We show a collision-free exploration algorithm working in time polynomial in n, for arbitrary graphs of size larger than 2. Moreover, we show that if agents have only vision of radius 1, then collision-free exploration is impossible, e.g., in any tree of diameter 2

Concurrent bandits and cognitive radio networks

We consider the problem of multiple users targeting the arms of a single multi-armed stochastic bandit. The motivation for this problem comes from cognitive radio networks, where selfish users need to coexist without any side communication between them, implicit cooperation or common control. Even the number of users may be unknown and can vary as users join or leave the network. We propose an algorithm that combines an $\epsilon$-greedy learning rule with a collision avoidance mechanism. We analyze its regret with respect to the system-wide optimum and show that sub-linear regret can be obtained in this setting. Experiments show dramatic improvement compared to other algorithms for this setting

The design and intelligent control of an autonomous mobile robot

This thesis presents an investigation into the problems of exploration, map building and collision free navigation for intelligent autonomous mobile robots. The project began with an extensive review of currently available literature in the field of mobile robot research, which included intelligent control techniques and their application. It became clear that there was scope for further development with regard to map building and exploration in new and unstructured environments. Animals have an innate propensity to exhibit such abilities, and so the analogous use of artificial neural networks instead of actual neural systems was examined for use as a method of robot mapping. A simulated behaviour based mobile robot was used in conjunction with a growing cell structure neural network to map out new environments. When using the direct application of this algorithm, topological irregularities were observed to be the direct result of correlations within the input data stream. A modification to this basic system was shown to correct the problem, but further developments would be required to produce a generic solution. The mapping algorithms gained through this approach, although more similar to biological systems, are computationally inefficient in comparison to the methods which were subsequently developed. A novel mapping method was proposed based on the robot creating new location vectors, or nodes, when it exceeded a distance threshold from its mapped area. Network parameters were developed to monitor the state of growth of the network and aid the robot search process. In simulation, the combination of the novel mapping and search process were shown to be able to construct maps which could be subsequently used for collision free navigation. To develop greater insights into the control problem and to validate the simulation work the control structures were ported to a prototype mobile robot. The mobile robot was of circular construction, with a synchro-drive wheel configuration, and was equipped with eight ultrasonic distance sensors and an odometric positioning system. It was self-sufficient, incorporating all its power and computational resources. The experiments observed the effects of odometric drift and demonstrated methods of re-correction which were shown to be effective. Both the novel mapping method, and a new algorithm based on an exhaustive mesh search, were shown to be able to explore different environments and subsequently achieve collision free navigation. This was shown in all cases by monitoring the estimates in the positional error which remained within fixed bounds