Geodesic trajectory generation on learnt skill manifolds

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 generate the data. This allows us to present experimental results for fast motion planning on a realistic - variable step length, width and height - walking task on a humanoid robot.