M.Sc. Thesis: Othmar Gsenger on Probabilistic Models for Learning the Dynamics Model of Robots
Supervisors: Elmar Rueckert, Univ.-Prof.Dr. Wolfgang Maass
Finished: May, 2013
In this thesis I investigate three probabilistic regression models from the literature and try to use them for learning the dynamics model of robots, i.e. the function that describes the transition between two states when executing a certain action. I add regularization terms to the error function where necessary to address the problem of overfitting and numerical instability and derive the corresponding learning rules. Then I evaluate these models on four simulated robotic tasks using my MATLAB implementation of the models. A simple one-dimensional toy task is used to analyze and visualize the characteristics of the approaches. In a second and third experiment I test these models on multi-link arms and analyze their robustness to noise. Finally, in the most complex experiment I use an existing simplified model of a humanoid robot in a balancing task. The learned dynamics model is used in combination with a well-known movement planning algorithm to solve a balancing problem, where the robot gets pushed with different forces. The results demonstrate that it is possible to predict and plan movement using these models. The Hierarchical Mixtures of Experts model shows the worst performance, against the expectation to work best on high dimensional data because it has the least number of model parameters. However, this can be improved using different initialization approaches. The Gated Linear Regression with Gaussian Noise Model and Conditioned Mixture of Gaussian show good performance on small datasets. Additionally, the Conditioned Mixture of Gaussian has the advantage of training both the kinematics and inverse kinematic model at the same time, without overhead compared to the other models.