# Heterogeneous Cooperative Networks

### Network topology based characterization of heterogeneity

Heterogeneity has emerged as an important aspect of multiagent systems, in which agents with different capabilities and resources interact with each other to perform various complex tasks. In this work, we aim to provide a framework for a network topology based characterization of heterogeneity in multiagent and cooperative networks that also incorporates distinctions among agents of various types. Coordination and interactions among agents are modeled using constructs from graph theory. A graph coloring problem is then formulated to examine an inter-relationship between the network topology and distribution of agents with assorted capabilities in heterogeneous networks. As a result, we will be able to answer how agents with different resources can be distributed within a network to maximally exploit the available resources through local interactions.

**Energy Efficient Heterogeneous Wireless Sensor and Actor Networks**

Wireless sensor and actor networks (WSANs) provide an effective solution to the distributed sensing and response related problems. In such networks, information gathered by the sensing nodes is made available to the actor nodes through a wireless medium that utilize this information to make decisions and act upon the environment.

In this work, we address the issue of energy-efficient information gathering in heterogeneous WSANs. A scheme is proposed in which actors utilize coordination among themselves, and heterogeneity among sensors to deactivate a large portion of originally deployed sensors of various types to preserve sensors’ power resources. Under the initial deployment of sensors, if an actor *v* receives a particular type of data either directly from a sensor, or by interacting with a neighbor actor, then as a result of our scheme,* v* continues to receive same data but with only a small subset of activated sensors. We formulate this problem in graph-theoretic terms, thereby providing solutions using graph-coloring and graph-domination related concepts.

**Efficient Complete Coverage Through Heterogeneous Disks**

Complete coverage problems constitute an important class of problems in the domain of multiagent and multirobot systems. The primary objective is to deploy and distribute agents with sensing capabilities to completely monitor a domain under consideration while satisfying certain constraints and criteria. Coverage problem can find its roots in computational geometry. One of the primary problems there is related to circle covering; what is the most *efficient* way to place circular disks of same radii to completely cover a region? The solution is known and states that the most efficient way (minimizing the overlap) among disks is to place disks in an equilateral triangle lattice. In multiagent and sensor networks, circular disks correspond to the sensing footprints of sensing nodes and minimizing overlap means that power is consumed efficiently for the sensing operation. We examine if efficiency of the circle coverings can be further increased by using heterogeneous circular disks, i.e., disks with different radii. In fact, it is shown that for complete coverage, configurations of heterogeneous disks exhibit better efficiency as compared to the homogeneous case. We also analyze coordination frameworks required to ensure that formations of agents in a particular configurations are maintained when agents exhibit movements.

#### Investigators

#### Publications

- Waseem Abbas and Magnus B. Egerstedt. Distribution of Agents in Heterogeneous multiagent systems.
*IEEE Conference on Decision and Control*, Orlando, Florida, December 2011. - Waseem Abbas and Magnus B. Egerstedt. Distribution of Agents with Multiple Capabilities in Heterogeneous multiagent systems.
*IEEE Conference on Decision and Control*, Maui, Hawaii, December 2012. - Waseem Abbas, Hassan Jaleel, and Magnus B. Egerstedt. Energy-efficient Data Collection in Heterogeneous Wireless Sensor and Actor Networks.
*IEEE Conference on Decision and Control*, Florence, Italy, December 2013 - Waseem Abbas, Magnus B. Egerstedt, Chun-Hung Liu, Robin Thomas, and Peter Whalen. Deploying Robots with Two Sensors in K_{1,6}-free Graphs. Available at: http://arxiv.org/abs/1308.5450
- Waseem Abbas and Magnus B. Egerstedt. On the Value of Heterogeneity for Efficient Complete Coverage.
*In preparation*