In this paper, decentralized controllers are developed to drive a swarm of mobile agents with high-order (m > 2) nonlinear dynamics in strict feedback form into a moving target region while avoiding collisions among themselves. At the same time, the connectivity of the communication graph remains for all time. It is important to consider coordination of multiple high-order agent dynamics which generalize the existing simple single-integrator/double-integrator ones because, in practice, we need to incorporate actuator dynamics into the vehicle dynamics in order to achieve better performance, thus increasing the order of the system dynamics. The control design is based on a fusion of potential functions, backstepping technique and Lyapunov synthesis. The presence of parametric uncertainties is handled by adaptive control techniques. Simulation studies have been carried out to verify the effectiveness of the proposed approach.