Generalized Multiple Correlation Coefficient as a Similarity Measurement between Trajectories Similarity distance measure between two trajectories is an essential tool to understand patterns in motion, for example, in HumanRobot Interaction or Imitation Learning. The problem has been faced in many fields, from Signal Processing, Probabilistic Theory field, Topology field or Statistics field. Anyway, up to now, none of the trajectory similarity measurement metrics are invariant to all possible linear transformation of the trajectories (rotation, scaling, reflection, shear mapping or squeeze mapping). Also not all of them are robust in front of noisy signals or fast enough for realtime trajectory classification. To overcome this limitation this paper proposes a similarity distance metric that will remain invariant in front of any possible linear transformation. Based on Pearsonxe2x80x99s Correlation Coefficient and the Coefficient of Determination, our similarity metric, the Generalized Multiple Correlation Coefficient (GMCC) is presented like the natural extension of the Multiple Correlation Coefficient. The motivation of this paper is twofold: First, to introduce a new correlation metric that presents the best properties to compute similarities between trajectories invariant to linear transformations and compare it with some state of the art similarity distances. Second, to present a natural way of integrating the similarity metric in an Imitation Learning scenario for clustering robot trajectories.

Reinforcement Learning of Trajectory Distributions: Applications in Assisted Teleoperation and Motion Planning The majority of learning from demonstration approaches do not address suboptimal demonstrations or cases when drastic changes in the environment occur after the demonstrations were made. For example, in real teleoperation tasks, the demonstrations provided by the user are often suboptimal due to interface and hardware limitations. In tasks involving comanipulation and manipulation planning, the environment often changes due to unexpected obstacles rendering previous demonstrations invalid. This paper presents a reinforcement learning algorithm that exploits the use of relevance functions to tackle such problems. This paper introduces the Pearson correlation as a measure of the relevance of policy parameters in regards to each of the components of the cost function to be optimized. The method is demonstrated in a static environment where the quality of the teleoperation is compromised by the visual interface (operating a robot in a threedimensional task by using a simple 2D monitor). Afterward, we tested the method on a dynamic environment using a real 7DoF robot arm where distributions are computed online via Gaussian Process regression.