Recently, systems with various sensors have been constructed, and the amount of the sensor data in electric format is growing up. The combined data could be high-dimensional, and the modeling from these data may outputs poor models since it is difficult to fill the high-dimensional space, that is, the curse of dimensionality. Meanwhile, since the high-dimensional data often lies on a lower-dimensional manifold intrinsically, we can extract the low-dimensional manifold by applying the manifold learning techniques, also known as nonlinear dimensionality reduction methods. Then, we can obtain a better model avoiding the curse of dimensionality. However, considering the dimensionality reduction problem and the modeling problem separately, the task performance such as prediction or control being executed afterward with the model may be deteriorated because the required information to obtain a good model may be lacked. Thus, in this dissertation, we propose to construct new criteria into the original evaluation criteria for manifold learning, by adding constraints induced from the objective of model such as prediction or control. By introducing this criterion, we achieve both the manifold learning and the modeling simultaneously.
In this presentation, I would like to talk about this proposition and its validation through the following 2 problems.
Firstly, we consider the linear system identification method from high-dimensional input and output data. We assume that the input and output data lie on manifolds respectively, and each manifold relates dynamically. In this study, we propose the input-output manifold learning methods by introducing a new criterion to obtain the model for accurate prediction by considering the fitting error term to the linear dynamics. Using this criterion, we achieve both the dimensionality reduction of the input and output data, and the system identification. We experimentally validate the effectiveness of the proposed method through the experiment with synthetic data.
Next, a modeling method for the object recognition problem by a robot hand with tactile sensor is considered. The object recognition is achieved by estimating the inherent parameter of objects allocated in advance, by executing the exploratory action to the object. In order to achieve the recognition efficiently, we need a sensor model which represents the relationship among the sensor data, the exploratory action, and the object being touched, to measure the informativeness of the resulting sensor data of the action. The model should be smooth to make the recognition easier. Thus, we propose a modeling method to obtain a smooth model by allocating the parameter by manifold learning approach in a smooth model structure. Also, the exploratory action by the robot should be compliant to avoid breaking the object or the robot. Thus, we also propose an optimal control approach to design the controller to execute the informative and compliant action. The effectiveness of the proposed methods is validated through the numerical simulation and the experiments with the actual robot.