The real challenge in development of the Internet-based robotic system is to develop a new planning and control method which is capable of coupling with the random communication time delay and independent of a human operator. The technical difficulties include that there does not exist a realistic mathematical model for the Internet time-delay which can be used to design a controller; the probabilistic type of analysis based on a stochastic model is usually not acceptable for some applications such as telemedicine. It is even more difficult to study the common nature of the role of human operators beyond the individual mechanical character. This paper explores a new method for planning and control of Internet-based telerobotic system. The significance of the method is that it can effectively deal with the random time-delay existing in the Internet. In addition, the system stability and dynamic performance is independent of human operator. First, a novel non-time referenced action control scheme will be introduced. Instead of using time as an action reference, a new sensor-based action reference will be developed. As a result, the communication delay will have little impact on the operations, in particular the stability of the system. Furthermore the stability of the system is not dependent on the model of the human operator in the system. All these will lead to the development of the theoretical foundation on the stability of Internet-based telerobotic systems. The implementations and experimental outcomes presented herein will verify the theoretical results.