This thesis proposes a method that plans trajectories for autonomous agents to enable them to fulfil different tasks while ensuring the collision-free movement. The agents are locally controlled and connected over an unreliable communication network that may induce packet losses and transmission delays. Further sensors e.g. for a distance measurement are not used and communication should only be invoked if it is necessary to avoid a collision. The basic problem occurs for two agents. The first agent can change its trajectory at any time without regard to the second agent, which has to ensure the collision avoidance. To this aim it adapts its trajectory based only on local data and communicated information about the current and future movement of the first agent. A control unit for the second agent is introduced that has to execute four tasks to ensure the control aims: 1. Estimation of the current network properties. 2. Prediction of the movement of the stand-on agent. 3. Invocation of communication whenever the local data becomes too uncertain. 4. Planning of collision avoiding trajectories. The main result of the thesis is a novel control method for mobile agents that solves the four tasks leading to a proven collision avoidance. The method consists of a delay estimator, a prediction unit, an event generator and a trajectory planning unit. The method can be used for different types of agents (e.g. UAVs or cars) with only slight modifications. The proposed method is tested and evaluated through simulations and experiments with both, two quadrotors and two nonholonomic robots.