Abstract. In this paper a new method based on Orthogonal basis Functions and Template Matching (OFTM) for learning trajectory by imitation is intro- duced.
ICSR2013, 067, v1: ’Learning Comple...’
Learning Complex Trajectories by Imitation using Orthogonal basis Functions and Template Matching Mohsen Falahi1, Mohammad Mashhadian1, Mohsen Tamiz1 1
Neural and Cognitive Sciences Laboratory, Amirkabir University of Technology, Tehran, Iran {mfalahi13, m-mashhadian, mohsen_tamiz}@aut.ac.ir Abstract. In this paper a new method based on Orthogonal basis Functions and Template Matching (OFTM) for learning trajectory by imitation is introduced. In this method, the robot uses primitive movements including template and orthogonal basis trajectories, which are learnt by using Gaussian Mixture Model (GMM), to construct new given trajectories. To obtain this goal, the robot calculates the dissimilarity between the new trajectory and arbitrary templates, then the similar parts will be replaced by the template, and the rest of the new trajectory will be constructed by using the orthogonal learnt trajectories. The results show that our method is more accurate and requires less computation in comparison with learning the whole trajectory by GMM. Keywords: Learning by imitation, template matching, orthogonal basis functions, primitive movements
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Introduction
As the importance of social robots increases, the focus on learning methods, especially learning by imitation as a natural and safe approach [1] has increased. There are several methods for learning a trajectory as the fundamental component in imitation learning systems [2] such as GMM [3] and HMM [4]. In this paper a new method based on OFTM is introduced to address this issue.
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Proposed Method for Learning Trajectories by Imitation
In our algorithm, firstly, the demonstrator shows some arbitrary trajectories to the robot, and the robot learns them via GMM. These trajectories are learned as templates. Then, we demonstrate sine and cosine trajectories as the orthogonal basis functions to the robot. Now the robot’s learning steps are completed. Hereinafter, when a new trajectory is given to the robot, it calculates the dissimilarity between templates and the given trajectory as a criterion of similarity by ∑
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Where is the start point of the template which varies from zero to the length of ) and the given trajectory, denotes dissimilarity, ) are the values of the given trajectory and the template at the time , respectively. In cases that is less than μ, the defined threshold, those parts will be eliminated from the trajectory and replaced by the corresponding templates. It is notable that dissimilarities are calculat-
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ICSR2013, 067, v1: ’Learning Comple...’
ed with various periods ( ) and scales of the learned templates. Since sine and cosine functions are learnt as orthogonal functions, the robot applies Fourier transform to construct rest of the given trajectory. As Fourier transform is not able to reconstruct functions with high frequency changes, because of Gibbs phenomenon, and considering robot’s frequency limitation in its movements, it is recommended to teach these kinds of trajectories by template. The results of our tests show that OFTM is more accurate than GMM and needs less computation. As an example of our tests, in which a new trajectory is given to both methods, the accuracy of OFTM with μ=0.05 is more than GMM/GMR in reconstructing it (see Fig. 2). Moreover, the average time it takes to produce the result for OFTM and GMM/GMR is 0.84 and 13.09 seconds respectively, on a same computer.
(a) (b) (c) Fig. 1. (a) and (b) are two templates and (c) is a new given trajectory which the robot should learn.
Fig. 2. (a) Using GMM to learn the new trajectory.
Fig. 2. (b) Using OFTM to learn the new trajectory.
References 1. Bandera, J. P., Rodriguez, J. A., Molina-Tanco, L., and Bandera A.: A Survey of VisionBased Architecture for Robot Learning by Imitation. Int. Journal of Humanoid Robotics, Vol. 9, No. 1 (2012). 2. Aleotti, J., Caselli, S.: Robust Trajectory Learning and Approximation for Robot Programming by Demonstration. Int. Journal of Robotics and Autonomous Systems, 54, (2006), pp. 409-413. 3. Sumin Cho, Sungho Jo: Kinesthetic Learning of Behaviors in a Humanoid Robot. 11 th Int. Conf. on Control, Automation and Systems, Gyeonggi-do, Korea. 4. Calinon, S., Sauser, E. L., Billard, A. G., Caldwell, D. G.: Evaluation of a Probabilistic approach to Learn and Reproduce Gestures by Imitation. 2010 IEEE Int. Conf. on Robotics and Automation, Anchorage, Alaska, USA.
