Movement Primitives (MPs) have been widely adopted for representing and learning robotic movements using Reinforcement Learning Policy Search. Probabilistic Movement Primitives (ProMPs) are a kind of MP based on a stochastic representation over sets of trajectories, able of capturing the variability allowed while executing a movement. This approach has proved effective in learning a wide range of robotic movements, but it comes with the need of dealing with a high-dimensional space of parameters. This may be a critical problem when learning tasks with two robotic manipulators, and this work proposes an approach to reduce the dimension of the parameter space based on the exploitation of symmetry. A symmetrization method for ProMPs is presented and used to represent two movements, employing a single ProMP for the first arm and a symmetry surface that maps that ProMP to the second arm. This symmetric representation is then adopted in reinforcement learning of bimanual tasks (from user-provided demonstrations), using Relative Entropy Policy Search (REPS) algorithm. The symmetry-based approach developed has been tested in an experiment of cloth manipulation, showing a speed increment in learning the task.
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