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This paper presents a front-unit-following control method for a snake-like robot using screw drive mechanism. The operators are required to command only one unit in the head, then commands for the rest of the units are automatically calculated to track the path of the preceding units. The proposed method estimates the tracking error expressed in the Frenet frame using past velocity commands in order to determine the control inputs. Since the past velocity commands stored at discrete points are used for estimation of the tracking error, we also propose a method to dynamically change the data storage interval for reducing the amount of data stored, without losing the accuracy of estimation. Effectiveness of the proposed method is demonstrated by computer simulations and laboratory experiments.