Improvement of the real-time performance of tracking control is increasingly desirable. It is a routine for most conventional algorithms that the control input at current time instant is to track the current desired output. However, lagging errors resulting from computational time and the fluctuation of the desired output exist for the tracking control. Different from conventional algorithms, a look-ahead scheme of zeroing dynamics (ZD) is established in this paper to achieve the real-time tracking control of both serial and parallel manipulators. With the exploitation of data at current time and that in history, the control inputs generated by the proposed ZD algorithms never lead to lagging errors with the source from the inevitable computational time. To tackle prediction errors for ZD algorithms, a new high-precision discretization formula, as an essential part of ZD algorithms, is presented to confine the prediction error in an ignorable range in comparison with lagging errors.