Many everyday tasks performed by people, such as reaching, pointing or drawing, resolve redundant degrees of freedom in the arm in a similar way. In this paper we present a novel method for learning the strategy used to resolve redundancy by exploiting the variability in multiple observations of different tasks. We demonstrate the effectiveness of this method on three simulated plants: a toy example, a three link planar arm, and the KUKA lightweight arm.

The least squares approach works efficiently in value function approximation, given appropriate basis functions. Because of its smoothness, the Gaussian kernel is a popular and useful choice as a basis function. However, it does not allow for discontinuity which typically arises in real-world reinforcement learning tasks. In this paper, we propose a new basis function based on geodesic Gaussian kernels, which exploits the non-linear manifold structure induced by the Markov decision processes. The usefulness of the proposed method is successfully demonstrated in a simulated robot arm control and Khepera robot navigation.