Efficient Learning of Koopman Structures for Model-Based Control of Nonlinear Robotic Systems

includes bibliographical references and index

MTech (Res); 2023; Mechanical Engineering

Identification of the dynamics of a complex robotic system accurately from first principles is challenging and often infeasible. Simplifying assumptions commonly made in modeling such systems often restrict their scope and accuracy, diminishing their effectiveness for model-based control. Utilizing data-driven learning methods offers an effective substitute, as they learn models from observed data, thereby improving modeling, prediction, and control accuracy by capturing underlying dynamics faithfully. Lately, neural networks have frequently been employed as data-driven tools for system identification; nonetheless, the resulting highly nonlinear nature of such models leads to computationally demanding and less efficient control implementation. This study focuses on an efficient learning paradigm that relies on the Koopman operator to derive linear and bilinear models for complex nonlinear systems. In particular, we propose a combined Koopman-ZNN (Zeroing Neural Network) architecture for real-time control of redundant manipulators with input constraints. An autoencoder-based neural architecture is used to learn the bilinear Koopman model for manipulator dynamics in joint space. This architecture is subsequently integrated with a kinematic map obtained using a feed-forward neural network that maps the joint coordinates to end-effector Cartesian coordinates. This approach yields precise models with fewer observable states than prior studies. When coupled with a ZNN controller, it provides a computationally efficient alternative to Nonlinear Model Predictive Control (NMPC), crucial for real-time control feasibility. In addition, we propose a noble data generation algorithm for serial manipulators by defining trajectories as minimum snap rather than generated randomly. This allows the algorithm to be extended to serial robots with a 3D workspace. While this framework constitutes an important advantage over the state-of-the-art Koopman-based learning algorithm, an important limitation of this paradigm is that it lacks adaptability and excels only when training data precisely maps the actual system dynamics. Thus, any changes in the dynamics of the original system would degrade model performance, limiting its practicality for real-world applications. In addition, poor and inadequate sampling of data and suboptimal choice of hyperparameters that make up the neural network might render the learned Koopman model inaccurate. To mitigate these challenges, we propose an adaptive Koopman strategy that uses online data for continuous model adjustment. This method delivers robust, accurate, and efficient models, significantly outperforming traditional Koopman-based learning paradigms. Detailed simulation and experimental studies, including performance comparisons with leading alternative designs, are used to validate the efficacy of this approach.