By using the conceptual impedance and the elasticity of a serial chain of spring-damper system, a real-time collision-free trajectory generation algorithm is proposed. The reference points on a trajectory connected by the spring-damper system have a mechanism for self-Position adjustment to avoid a collision by the impedance, and the local adjustment of each reference point is propagated through the elasticity to a real robot at the end of the spring-damper system. As a result, the overall trajectory consisting of the reference points becomes free of collision with environmental obstacles and efficient having the shortest distance as possible. In this process, the reference points connected by the spring-damper system take role of virtual robot as global guidance for a real robot, and a cooperative optimization is carried out by the system of virtual robots. A control algorithm is proposed to implement the impedance for a car-like mobile robot.