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This paper focuses on time-optimal path tracking, which involves planning of robot motions along prescribed geometric paths. Starting from a discretized convex reformulation of time-optimal path tracking problems, a log-barrier based batch solution method is presented which allows to rapidly obtain an approximate solution with smooth actuator torques. Based on this batch method, a recursive variant is derived for on-line path tracking. By means of an experimental test case in which the path data is generated on-line by human demonstration, the results and trade-offs in calculation time, delay and path duration are compared for the batch and recursive variant of the log-barrier method as well as for an exact solution method.