Abstract: In the case of sequentially coating workpieces, such as motor vehicle bodies, with a program controlled painter-robot, it has hitherto been difficult or impossible to finish painting a partly coated workpiece in the event of an unscheduled breakdown. This was because the robot and the workpiece would inertially overrun their synchronized relative positions after the breakdown, thus making it difficult to resynchronize the two. According to the subject invention, based upon the synchronized relative positions of the workpiece and the painter-robot both at the time of the breakdown and after the unit has come to stop, a path of travel is determined over which the robot is returned accurately to the relative position at which the breakdown occurred. The coating operation is then resumed from this position.