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Amplitude tuning is an important strategy in animals employing traveling wave patterns, enhancing their adaptability to unstructured environments. This paper proposes, for the first time, an amplitude tuning method that leverages the compliance of a soft corkscrew by twisting its ends. An amplitude tunable traveling wave robot (ATWBot) is developed, consisting of a soft corkscrew housed in a high DOF cage and driven by only two servos. The soft corkscrew and cage are monolithically 3D-printed. ATWBot achieves a wide range of active amplitude tuning with passive compliance adaptation, and can extend its morphology to a coiled configuration, enabling clamping and rolling. A comprehensive model is built for the twisted soft corkscrew geometry, proving that the robot's speed is decoupled from amplitude variations during twisting. A genetic algorithm is used to optimize the soft corkscrew for achieving the fastest speed while matching the cage geometry. Experiments demonstrate that the combination of active amplitude tuning and passive body compliance enables the robot to adapt to unstructured terrains including slits, steps, gaps, converging tunnels, slopes, and swimming.