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Continuum or hyper-redundant robot manipulators can exhibit behavior similar to biological trunks, tentacles, or snakes. Unlike traditional rigid-link robot manipulators, continuum robot manipulators do not have rigid joints, hence these manipulators are extremely dexterous, compliant, and are capable of dynamic adaptive manipulation in unstructured environments. However, the development of high-performance control algorithms for these manipulators is quite a challenge, due to their unique design and the high degree of uncertainty in their dynamic models. In this paper, a controller for continuum robots, which utilizes a neural network feedforward component to compensate for dynamic uncertainties is presented. Experimental results using the OCTARM, which is a soft extensible continuum manipulator, are provided to illustrate that the addition of the neural network feedforward component to the controller provides improved performance.