Reinforcement Learning for Orientation on the Lie Algebra

In this paper, we propose a novel framework for Reinforcement Learning on Lie algebra and show how it applies to learning the orientation of the robot's end effector in the task space. The proposed framework is suitable for model-free Reinforcement learning algorithms. Our research is motivated by the fact that in robotics, non-Euclidean data (e.g., orientation) is common in learning manipulation skills, yet neglecting the geometric meaning of such data affects learning performance and accuracy. In particular, our innovation is to apply policy parameterization and learning on the Lie algebra, then map back the learned actions to the hemisphere manifold. The proposed framework opens the door for some model-free Reinforcement learning algorithms designed for Euclidean space to learn non-Euclidean data without change. According to the best of our knowledge, this research work is the first effort in applying a policy parameterization in the context of Reinforcement learning on the Lie algebra of the hemisphere manifold. The results of our experiments provide evidence to support our hypothesis that learning orientation on the Lie algebra is more precise and leads to a superior solution than learning through the normalization of non-Euclidean data.