Abstract— Humanoid robots are appealing due to their inherent dexterity. However, these potential benefits may only be realized if the corresponding motion synthesis procedure is suitably flexible. This paper presents a flexible trajectory generation algorithm that utilizes a geometric representation of humanoid skills (e.g., walking) - in the form of skill manifolds. These manifolds are learnt from demonstration data that may be obtained from off-line optimization algorithms (or a human expert). We demonstrate that this model may be used to produce approximately optimal motion plans as geodesics over the manifold and that this allows us to effectively generalize from a limited training set. We demonstrate the effectiveness of our approach on a simulated 3-link planar arm, and then the more challenging example of a physical 19-DoF humanoid robot. We show that our algorithm produces a close approximation of the much more computationally intensive optimization procedure used to gene...