Data-Driven Spectral Submanifold Reduction for Nonlinear Optimal Control of High-Dimensional Robots

Modeling and control of high-dimensional, nonlinear robotic systems remains a challenging task. While various model- and learning-based approaches have been proposed to address these challenges, they broadly lack generalizability to different control tasks and rarely preserve the structure of the dynamics. In this work, we propose a new, data-driven approach for extracting low-dimensional models from data using Spectral Submanifold Reduction (SSMR). In contrast to other data-driven methods which fit dynamical models to training trajectories, we identify the dynamics on generic, low-dimensional attractors embedded in the full phase space of the robotic system. This allows us to obtain computationally-tractable models for control which preserve the system's dominant dynamics and better track trajectories radically different from the training data. We demonstrate the superior performance and generalizability of SSMR in dynamic trajectory tracking tasks vis-a-vis the state of the art, including Koopman operator-based approaches.Comment: 9 pages, 4 figures, 1 table, Submission to International Conference for Robotics and Automation 202

Automated synthesis of low-rank stochastic dynamical systems using the tensor-train decomposition

Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2016.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 79-83).Cyber-physical systems are increasingly becoming integrated in various fields such as medicine, finance, robotics, and energy. In these systems and their applications, safety and correctness of operation is of primary concern, sparking a large amount of interest in the development of ways to verify system behavior. The tight coupling of physical constraints and computation that typically characterize cyber-physical systems make them extremely complex, resulting in unexpected failure modes. Furthermore, disturbances in the environment and uncertainties in the physical model require these systems to be robust. These are difficult constraints, requiring cyberphysical systems to be able to reason about their behavior and respond to events in real-time. Thus, the goal of automated synthesis is to construct a controller that provably implements a range of behaviors given by a specification of how the system should operate. Unfortunately, many approaches to automated synthesis are ad hoc and are limited to simple systems that admit specific structure (e.g. linear, affine systems). Not only that, but they are also designed without taking into account uncertainty. In order to tackle more general problems, several computational frameworks that allow for more general dynamics and uncertainty to be investigated. Furthermore, all of the existing computational algorithms suffer from the curse of dimensionality, the run time scales exponentially with increasing dimensionality of the state space. As a result, existing algorithms apply to systems with only a few degrees of freedom. In this thesis, we consider a stochastic optimal control problem with a special class of linear temporal logic specifications and propose a novel algorithm based on the tensor-train decomposition. We prove that the run time of the proposed algorithm scales linearly with the dimensionality of the state space and polynomially with the rank of the optimal cost-to-go function.by John Irvin P. Alora.S.M

Practical Deployment of Spectral Submanifold Reduction for Optimal Control of High-Dimensional Systems

Real-time optimal control of high-dimensional, nonlinear systems remains a challenging task due to the computational intractability of their models. While several model-reduction and learning-based approaches for constructing low-dimensional surrogates of the original system have been proposed in the literature, these approaches suffer from fundamental issues which limit their application in real-world scenarios. Namely, they typically lack generalizability to different control tasks, ability to trade dimensionality for accuracy, and ability to preserve the structure of the dynamics. Recently, we proposed to extract low-dimensional dynamics on Spectral Submanifolds (SSMs) to overcome these issues and validated our approach in a highly accurate simulation environment. In this manuscript, we extend our framework to a real-world setting by employing time-delay embeddings to embed SSMs in an observable space of appropriate dimension. This allows us to learn highly accurate, low-dimensional dynamics purely from observational data. We show that these innovations extend Spectral Submanifold Reduction (SSMR) to real-world applications and showcase the effectiveness of SSMR on a soft robotic system.ISSN:2405-896

Robust Nonlinear Reduced-Order Model Predictive Control

ISSN:0743-154