This paper proposes a decentralized navigation method with collision avoidance for a robotic swarm whose individuals possess heterogeneous abilities, such as sensing range and maximum speed. In this method, each agent distributedly constructs and maintains a local directed connection with another agent using only local information, which is relative distance. Moreover, all agents always maintain some distance from other agents to avoid collision. As a result, one leader robot can guide an entire swarm of robots to their destination, and the other robots can follow the leader while maintaining connectivity and not colliding with others. We prove the above mathematically, and we demonstrate the validity of the proposed method by numerical simulation and experimentation
