Abstract: A unified representation of the actuation signals of earthworm-like locomotion robots based on travelling-wave functions is proposed. Firstly, the expression of the actuation signals based on travelling-wave functions is derived for the continuum earthworm-like locomotion robots, and a method is presented to construct the waveform generation functions of the actuation signals. Secondly, the expression of the actuation signals based on travelling-wave functions is reformulated for the multi-segment earthworm-like locomotion robots, which can be transformed into that of the continuum robots in the following mathematical proof. Next, the actuation signal expressions are briefly introduced when there are actuation signals with different wave speeds and when there are different waveform generation functions of actuation signals on different parts of the robot. Finally, the representation proposed is applied to a continuum earthworm-like locomotion robot and two multi-segment earthworm-like locomotion robots. Both the original actuation signal expressions and the new ones get the same results, showing the great applicability of the proposed representations.