Training Gaussian Process Regression Models Using Optimized Trajectories

Abstract

Quadrotor helicopters and robot manipulators are used widely for both research and industrial applications. Both quadrotors and manipulators are difficult to model. Quadrotors have complex dynamic models, especially at high speeds. Obtaining an accurate model of manipulator dynamics is often difficult, due to inaccurate values for link parameters and dynamics such as friction which are difficult to model accurately.

Supervised learning methods such as Gaussian Process Regression (GPR) have been used to learn the inverse dynamics of a system. These methods can estimate a dynamic model from experimental data without requiring the structure of the model to be known, and can be used online to update the model if the system changes over time.

This approach has been used to learn the inverse dynamics of a manipulator, but has not yet been applied to quadrotors. In addition, collecting training data for supervised learning can be difficult and time consuming, and poor or inadequate training data may result in an inaccurate model. Another problem frequently encountered when using GPR to learn the model of a system is the large computational cost of using GPR. A number of sparse approximations of GPR exist to deal with this issue, but it is not clear which sparse approximation results in the best performance, particularly when training data is being added incrementally.

This thesis proposes a method for systematically collecting training data for a GPR model. The trajectory used to collect training data is parameterized, and the parameters are optimized to maximize the GPR variance over the trajectory. This approach is tested both in simulation and experimentally for a quadrotor, and in experiments on a 4-DOF manipulator. Optimizing the training trajectories is shown to reduce the amount of training data required to learn the model of a system.

The thesis also compares three sparse approximations of GPR: the dictionary approach, Sparse Spectrum GPR (SSGP) and simple downsampling of the training data to reduce the size of the training data set. Using a dictionary is found to provide the best performance, even when the dictionary contains a very small subset of the available data.

Finally, all GPR models have hyperparameters, which have a significant impact on the prediction made by the GP model. Training these hyperparameters is important for getting accurate predictions. This thesis evaluates different methods of hyperparameter training on a 4-DOF manipulator to determine the most effective method of training the hyperparameters. For SSGP, the best hyperparameter training strategy is to reinitialize and train the hyperparameters after each trajectory. SSGP is also observed to be highly sensitive to the number of iterations of gradient descent used in hyperparameter training; too many iterations of gradient descent leads to overfitting and poor predictions. When using a dictionary, the best hyperparameter training method is to retrain the hyperparameters after each trajectory, using the previous hyperparameters as the initial starting point.