Ensuring Network Connectivity During Formation Control Using A Decentralized Navigation Function Z. Kan, A. P. Dani, J. M. Shea, and W. E. Dixon Abstract— In many applications of formation control, agents coordinate and communicate to make appropriate decisions. Connectivity of the network is paramount in such applications. The goal in this paper is to drive a group of agents with limited sensing capabilities to a desired configuration while ensuring the connectivity of the wireless communication network among the agents. Based on a navigation function formalism, a decentralized cooperative controller is proposed where agent only uses information within its sensing zone to guarantee connectivity maintenance of the network and achieve the desired formation with collision avoidance between themselves and with obstacles in the environment. I. I NTRODUCTION In multi-agent cooperative control, agents coordinate and communicate to achieve a collective goal (e.g., flocking, consensus, or pattern formation). As agents move to perform some mission objective, ensuring the group remains close enough to maintain radio communication (i.e., the group does not partition) can be challenging in a decentralized control system. The use of an artificial potential field is one method that has been widely used for formation control. The potential func- tion produces a repulsive potential field around a workspace boundary and obstacles, and an attractive potential field is produced at the goal configuration. A common problem with artificial potential field-based formation control algorithms is the existence of local minima when attractive and repulsive force are combined [1]. In the seminal work in [2] and [3], a navigation function approach is developed for a single point- mass agent moving in an environment with spherical obstacles. The navigation function proposed is a real valued function which is designed such that the negated gradient field does not have any local minima. This closed-loop approach guarantees the convergence to a desired destination, as well as collision avoidance. In [4], the navigation function framework is extended to multi-agent system. In [5], a centralized navigation function control strategy is proposed to steer a group of mobile agents 1 This research is supported by National Science Foundation grant number CNS-0626863. 2 Z. Kan, A. P. Dani and W. E. Dixon are with the Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611- 6250, USA. W. E. Dixon is also with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611-6250, USA. Email: {kanzhen0322, ashwin31, wdixon}@ufl.edu 3 J.M. Shea is with the Department of Electrial and Computer Engi- neering, University of Florida, Gainesville, FL 32611-6250, USA. Email: jshea@ece.ufl.edu to achieve a particular formation while avoiding collisions be- tween the agents, and obstacles in the environment. A limited sensing region of agents is assumed in [5] for obstacle avoid- ance assuming that the agents are connected. The problem of connectivity maintenance is addressed using a centralized navigation function in [6] and [7] by modeling the sensing region of the base station as a workspace and assuming that agents are always connected to the base station as long as they stay within the workspace. In [8], a decentralized navigation function is developed to achieve obstacle avoidance assuming that the agents are connected. A decentralized navigation function is also used in [9] for motion control of agents with global knowledge of the position of other agents. For agents with limited sensing capabilities, a decentralized navigation function approach is presented in [10] with the assumption that total number of agents in the system is apriori known. In [11], a navigation function based path planning algorithm is developed for multiple UAVs with finite sensing capabilities in a combat area. A review of literature indicates that most formation control efforts simply assume that agents within the network are able to communicate, such as [5] and [8]. The assumption of a connected graph is restrictive in the case of a mobile network, where communication between a pair of agents depends (in part) on the distance between agents. In practical applications, each agent has limited communication and sensing capability to determine relative position and velocity information that would be required by the agent’s control system. Thus, connec- tivity maintenance is a key requirement for formation control. For multi-agent systems (especially for a large number of agents), a centralized control approach has a higher cost to implement than a decentralized approach because of the increased computation load and the decreased robustness [12]. However, since the motion by any agent in the network may partition the underlying network graph (i.e., connectivity is a global graph property [13]), maintaining connectivity of a formation is challenging for a decentralized control scheme that only relies on locally available information. In a related work [14], a potential field is designed for a group of mobile agents to form a desired configuration while maintain network connectivity. However, the mission maybe fail because of the existence of local minima. The contribution of this paper is the development of a decentralized control scheme for each agent that ensures network connectivity and achieves a desired formation using only local information. Specifically, by using a navigation function formulation, the developed decentralized The 2010 Military Communications Conference - Unclassified Program - Networking Protocols and Performance Track 978-1-4244-8179-8/10/$26.00 ©2010 IEEE 954