The classical n-bugs problem has attracted considerable attention from researchers. This problem stems from the study of movement of a group of animals. In the context of multi- agent systems the problem has been modelled as cyclic pursuit. Under this paradigm, every agent, indexed i, chases its unique leader, agent i + 1 (modulo n), with n being the total number of agents. In the existing literature, cyclic pursuit has been studied for homogeneous agents where each agent’s velocity is proportional to the distance separating it from its leader and is directed along the line joining it to its leader. The constant of proportionality, initially chosen to be the same for all the agents, resulted in consensus in position, without the need for any centralized controller. Later, the constant of proportionality, alternately called the gain, was allowed to be heterogeneous and positional consensus was still achieved. Moreover, it was shown that the point of convergence, where the agents rendezvous, could be chosen at will, except for some diagnostic cases. In this thesis, besides admitting heterogeneous gains, the agents are assumed to pursue their respective leaders with an angle of deviation from the line joining them to their corresponding leaders. This expands the reachability set (set of points where the agents can rendezvous) for the system of agents to include points that were hitherto unreachable. Sufficient conditions for stability of such systems have been derived in this thesis. Detailed analysis of the reachability set has also been carried out. Some researchers have also investigated hierarchical cyclic pursuit, where there are multiple levels of pursuit. For instance, in the two level hierarchical pursuit, the agents are divided into m groups of n agents each, where each agent in a group chases its leader within the group as well as a similarly indexed agent in its leading group. Thus, groups of agents are also in cyclic pursuit. So far, only homogeneous gains were considered under this paradigm. The present thesis admits heterogeneous gains and establishes necessary and sufficient conditions for the stability of heterogeneous hierarchical cyclic pursuit, that generalize existing results. Reachable sets are also derived for this case. It is proved that the existing results can be derived as special cases of the ones considered in this thesis. As an extension to a realistic application, the importance of expansion in reachable set vis-a`-vis capturing a moving target is highlighted in this thesis. It has been shown that if the target’s initial position is reachable, then using a control law proposed in the thesis, the target can be captured. This control law is essentially an augmented cyclic pursuit law with the target’s velocity information fed to each agent in addition to the conventional cyclic pursuit command. Analysis has been carried out for agents with double integrator dynamics as well. A control law in conjunction with an algorithm is proposed that helps ensure global reachability of agents, with double integrator dynamics, in cyclic pursuit. Another application, in which cyclic pursuit and a closely related topology called platooning have been coupled together to track the boundaries of unknown regions and constantly monitor them, is addressed in this thesis. This problem is especially important in monitoring forest fire, marine contamination, volcanic ash eruptions, etc., and can protect human life by cordoning off unsafe regions using multiple autonomous agents. Lastly, discrete time cyclic pursuit laws are analyzed to obtain results similar to the continuous time counterparts that exist in the literature. Moreover, heterogeneous gains and deviations are admitted similar to the continuous time version considered in this thesis. Gershgorin’s theorem is used extensively to arrive at sufficient conditions for the stability of such discrete time deviated cyclic pursuit systems. Reachability sets are also derived. In case of discrete time systems, loss of synchronization due to no common clock for autonomous agents is a very realistic scenario. This thesis obtains some results on the stability of such asynchronous cyclic pursuit systems and indicates that special precautions are needed for dealing with heterogeneous cyclic pursuit systems even when one gain is negative, since the system may not converge, depending on the initial positions of the agents and the sequence of updates.

One of the main focus of research on multi-agent systems is that of coordination in a group of agents to solve problems that are beyond the capability of a single agent. Each agent in the multi-agent system has limited capacity and/or knowledge which makes coordination a challenging task. Applications of multi-agent systems in space and ocean exploration, military surveillance and rescue missions, require the agents to achieve some consensus in their motion. The consensus has to be achieved and maintained without a centralized controller. Multi-agent system research borrows ideas from the biological world where such motion consensus strategies can be found in the flocking of birds, schooling of fishes, and colony of ants. One such classes of strategies are the cyclic pursuit strategies which mimic the behavior of dogs, birds, ants, or beetles, where one agent pursues another in a cyclic manner, and are commonly referred to as the `bugs' problem, In the literature, cyclic pursuit laws have been applied to a swarm of homogenous agents, where there exists a predefined cyclic connection between agents and each agent follows its predecessor. At equilibrium, the agents reach consensus in relative positions. Equilibrium formation, convergence, rate of convergence, and stability are some of the aspects that have been studied under cyclic pursuit. In this thesis, the notion of cyclic pursuit has been generalized. In cyclic pursuit, usually agents are homogenous in the sense of having identical speeds and controller gains where an agent has an unique predecessor whom it follows. This is defined as the basic cyclic pursuit (BCP) and the sequence of connection among the agents is defined as the Pursuit sequence (PS). We first generalize this system by assuming heterogeneous speed and controller gains. Then, we consider a strategy where an agent can follow a weighted centroid of a group of other agents instead of a single agent. This is called centroidal cyclic pursuit (CCP). In CCP, the set of weights used by the agents are assumed to be the same. We generalize this further by considering the set of weights adopted by each agent to be different. This defines a generalized centroidal cyclic pursuit (GCCP). The behavior of the agents under BCP, CCP and GCCP are studied in this thesis. We show that a group of holonomic agents, under the cyclic pursuit laws ¡ BCP, CCP and GCCP ¡ can be represented as a linear system. The stability of this system is shown to depend on the gains of the agents. A stable system leads to a rendezvous of the agents. The point of rendezvous, also called the reachable point, is a function of the gains. In this thesis, the conditions for stability of the heterogeneous system of agents in cyclic pursuit are obtained. Also, the reachable point is obtained as a function of the controller gains. The reachable set, which is a region in space where rendezvous can occur, given the initial positions of the agents, are determined and a procedure is proposed for calculating the gains of the agents for rendezvous to occur at any desired point within the reachable set. Invariance properties of stability, reachable point and reachable set, with respect to the pursuit sequence and the weights are shown to exist for these linear cyclic pursuit laws. When the linear system is unstable, the agents are shown to exhibit directed motion. We obtain the conditions under which such directed motion is possible. The straight line asymptote to which the agents converge is characterized by the gains and the pursuit sequence of the agents. The straight lines asymptote always passes through a point, called the asymptote point, for given initial positions and gains of the agents. This invariance property of the asymptote point with respect to the pursuit sequence and the weights are proved. For non-homonymic agents, cyclic pursuit strategies give rise to a system of nonlinear state equations. It is shown that the system at equilibrium converges to a rigid polygonal formation that rotates in space. The agents move in concentric circles at equilibrium. The formation at equilibrium and the conditions for equilibrium are obtained for heterogeneous speeds and controller gains. The application of cyclic pursuit strategies to autonomous vehicles requires the satisfaction of some realistic restrictions like maximum speed limits, maximum latex limits, etc. The performances of the strategies with these limitations are discussed. It is also observed that the cyclic pursuit strategies can also be used to model some behavior of biological organisms such as schools of fishes.