Tom Z. Jiahao

Tom Z. Jiahao, Kong Yao Chee, M. Ani Hsieh

In this work, we consider the task of improving the accuracy of dynamic models for model predictive control (MPC) in an online setting. Although prediction models can be learned and applied to model-based controllers, these models are often learned offline. In this offline setting, training data is first collected and a prediction model is learned through an elaborated training procedure. However, since the model is learned offline, it does not adapt to disturbances or model errors observed during deployment. To improve the adaptiveness of the model and the controller, we propose an online dynamics learning framework that continually improves the accuracy of the dynamic model during deployment. We adopt knowledge-based neural ordinary differential equations (KNODE) as the dynamic models, and use techniques inspired by transfer learning to continually improve the model accuracy. We demonstrate the efficacy of our framework with a quadrotor, and verify the framework in both simulations and physical experiments. Results show that our approach can account for disturbances that are possibly time-varying, while maintaining good trajectory tracking performance.

Sandeep Manjanna, Tom Z. Jiahao, M. Ani Hsieh

Persistent monitoring of a spatiotemporal fluid process requires data sampling and predictive modeling of the process being monitored. In this paper we present PASST algorithm: Predictive-model based Adaptive Sampling of a Spatio-Temporal process. PASST is an adaptive robotic sampling algorithm that leverages predictive models to efficiently and persistently monitor a fluid process in a given region of interest. Our algorithm makes use of the predictions from a learned prediction model to plan a path for an autonomous vehicle to adaptively and efficiently survey the region of interest. In turn, the sampled data is used to obtain better predictions by giving an updated initial state to the predictive model. For predictive model, we use Knowledged-based Neural Ordinary Differential Equations to train models of fluid processes. These models are orders of magnitude smaller in size and run much faster than fluid data obtained from direct numerical simulations of the partial differential equations that describe the fluid processes or other comparable computational fluids models. For path planning, we use reinforcement learning based planning algorithms that use the field predictions as reward functions. We evaluate our adaptive sampling path planning algorithm on both numerically simulated fluid data and real-world nowcast ocean flow data to show that we can sample the spatiotemporal field in the given region of interest for long time horizons. We also evaluate PASST algorithm's generalization ability to sample from fluid processes that are not in the training repertoire of the learned models.

Tom Z. Jiahao, Ryan Adolf, Cynthia Sung et al.

Soft robots have many advantages over rigid robots thanks to their compliant and passive nature. However, it is generally challenging to model the dynamics of soft robots due to their high spatial dimensionality, making it difficult to use model-based methods to accurately control soft robots. It often requires direct numerical simulation of partial differential equations to simulate soft robots. This not only requires an accurate numerical model, but also makes soft robot modeling slow and expensive. Deep learning algorithms have shown promises in data-driven modeling of soft robots. However, these algorithms usually require a large amount of data, which are difficult to obtain in either simulation or real-world experiments of soft robots. In this work, we propose KNODE-Cosserat, a framework that combines first-principle physics models and neural ordinary differential equations. We leverage the best from both worlds -- the generalization ability of physics-based models and the fast speed of deep learning methods. We validate our framework in both simulation and real-world experiments. In both cases, we show that the robot model significantly improves over the baseline models under different metrics.

Tom Z. Jiahao, Lishuo Pan, M. Ani Hsieh

Understanding decentralized dynamics from collective behaviors in swarms is crucial for informing robot controller designs in artificial swarms and multiagent robotic systems. However, the complexity in agent-to-agent interactions and the decentralized nature of most swarms pose a significant challenge to the extraction of single-robot control laws from global behavior. In this work, we consider the important task of learning decentralized single-robot controllers based solely on the state observations of a swarm's trajectory. We present a general framework by adopting knowledge-based neural ordinary differential equations (KNODE) -- a hybrid machine learning method capable of combining artificial neural networks with known agent dynamics. Our approach distinguishes itself from most prior works in that we do not require action data for learning. We apply our framework to two different flocking swarms in 2D and 3D respectively, and demonstrate efficient training by leveraging the graphical structure of the swarms' information network. We further show that the learnt single-robot controllers can not only reproduce flocking behavior in the original swarm but also scale to swarms with more robots.

Kong Yao Chee, Tom Z. Jiahao, M. Ani Hsieh

In this work, we consider the problem of deriving and incorporating accurate dynamic models for model predictive control (MPC) with an application to quadrotor control. MPC relies on precise dynamic models to achieve the desired closed-loop performance. However, the presence of uncertainties in complex systems and the environments they operate in poses a challenge in obtaining sufficiently accurate representations of the system dynamics. In this work, we make use of a deep learning tool, knowledge-based neural ordinary differential equations (KNODE), to augment a model obtained from first principles. The resulting hybrid model encompasses both a nominal first-principle model and a neural network learnt from simulated or real-world experimental data. Using a quadrotor, we benchmark our hybrid model against a state-of-the-art Gaussian Process (GP) model and show that the hybrid model provides more accurate predictions of the quadrotor dynamics and is able to generalize beyond the training data. To improve closed-loop performance, the hybrid model is integrated into a novel MPC framework, known as KNODE-MPC. Results show that the integrated framework achieves 60.2% improvement in simulations and more than 21% in physical experiments, in terms of trajectory tracking performance.

Yifan Wu, Tom Z. Jiahao, Jiancong Wang et al.

Deformable image registration (DIR), aiming to find spatial correspondence between images, is one of the most critical problems in the domain of medical image analysis. In this paper, we present a novel, generic, and accurate diffeomorphic image registration framework that utilizes neural ordinary differential equations (NODEs). We model each voxel as a moving particle and consider the set of all voxels in a 3D image as a high-dimensional dynamical system whose trajectory determines the targeted deformation field. Our method leverages deep neural networks for their expressive power in modeling dynamical systems, and simultaneously optimizes for a dynamical system between the image pairs and the corresponding transformation. Our formulation allows various constraints to be imposed along the transformation to maintain desired regularities. Our experiment results show that our method outperforms the benchmarks under various metrics. Additionally, we demonstrate the feasibility to expand our framework to register multiple image sets using a unified form of transformation,which could possibly serve a wider range of applications.

Tom Z. Jiahao, M. Ani Hsieh, Eric Forgoston

Extracting predictive models from nonlinear systems is a central task in scientific machine learning. One key problem is the reconciliation between modern data-driven approaches and first principles. Despite rapid advances in machine learning techniques, embedding domain knowledge into data-driven models remains a challenge. In this work, we present a universal learning framework for extracting predictive models from nonlinear systems based on observations. Our framework can readily incorporate first principle knowledge because it naturally models nonlinear systems as continuous-time systems. This both improves the extracted models' extrapolation power and reduces the amount of data needed for training. In addition, our framework has the advantages of robustness to observational noise and applicability to irregularly sampled data. We demonstrate the effectiveness of our scheme by learning predictive models for a wide variety of systems including a stiff Van der Pol oscillator, the Lorenz system, and the Kuramoto-Sivashinsky equation. For the Lorenz system, different types of domain knowledge are incorporated to demonstrate the strength of knowledge embedding in data-driven system identification.