In this paper, behavior of a group of autonomous mobile agents under cyclic pursuit is studied. Cyclic pursuit is a simple distributed control law, in which the agent $i$ pursues agent $i+1modn$. The equations of motion are linear, with no kinematic constraints on motion. Behaviorally, they are identical but may have different controller gains. We generalize existing results in the literature, which consider only homogenous gains, to the case where controller gains are heterogenous. We show that, by selecting suitable controller gains, collective behavior of agents can be controlled significantly to obtain not only point convergence but also directed motion. In particular, we obtain analytical results that relate the controller gains to the direction of movement of the agents when the system is unstable. Invariance results with respect to the pursuit sequence are also proved. Finally, we also obtain some results that show some aspects of system behavior that is invariant with respect to finite switching of connections. Simulation experiments are given in support of the analytical results.

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