This paper addresses the problem of compactly encoding a continuous family of trajectories corresponding to a robotic skill, and using this representation for the purpose of constrained trajectory generation in an environment with many (possibly dynamic) obstacles. With a skill manifold that is learnt from data, we show that constraints can be naturally handled within an iterative process of minimizing the total geodesic path length and curvature over the manifold. We demonstrate the utility of this process with two examples. Firstly, a three-link arm whose joint space and corresponding skill manifold can be explicitly visualized. Then, we demonstrate how this procedure can be used to generate constrained walking motions in a humanoid robot.
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