A control processor in a robotic system treats optically sensed locations along the path ahead of the tool, which are classified in relation to elapsed distances and identified in 3-D coordinates and 3-axes tool orientation, to apply in real time and under feedforward a control signal representing the error between anticipated tool position and anticipated sensed location on the path. In the process, the anticipated sensed location is obtained by reference to a model made ahead of time with the stored sensed locations grouped as a function of elapsed distances and having a common algebraic feature, such as the slope or the change of slope. A taught path for the robot has been recovered by the control processor also based on elapsed distances and control is related to actual tool position provided by the robot.