Our newly developed event-based planning and control theory is applied to robotic systems. It introduces a suitable action or motion reference variable other than time, but directly related to the desired and measurable system output, called event. Here the event is the length of the path tracked by a robot. It enables the construction of an integrated planning and control system where planning becomes a real-time closed-loop process. The path-based integration planning and control scheme is exemplified by a single-arm tracking problem. Time and energy optimal motion plans combined with nonlinear feedback control are derived in closed form. To the best of our knowledge, this closed-form solution was not obtained before. The equivalence of path-based and time-based representations of nonlinear feedback control is shown, and an overall system stability criterion has also been obtained. The application of event-based integrated planning and control provides the robotic systems the capability to cope with unexpected and uncertain events in real time, without the need for replanning. The theoretical results are illustrated and verified by experiments.