In this paper, decentralized controllers are developed to drive a swarm of mobile agents with high-order (n>2) nonlinear dynamics in strict feedback form into a moving target region while avoiding collisions among themselves. 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 may 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 two kinds of new potential functions (target potential functions and collision avoidance potential functions), backstepping technique and Lyapunov synthesis. The presence of parametric uncertainties is handled by adaptive control techniques. The framework does not depend on a fixed ordering of agents, and is robust to individual agent failures. Therefore, flexibility and scalability are improved. Simulation results illustrate the performance of the proposed approach.