Physics-based parameterized neural ordinary differential equations: prediction of laser ignition in a rocket combustor

In this work, we present a novel physics-based data-driven framework for reduced-order modeling of laser ignition in a model rocket combustor based on parameterized neural ordinary differential equations (PNODE). Deep neural networks are embedded as functions of high-dimensional parameters of laser ignition to predict various terms in a 0D flow model including the heat source function, pre-exponential factors, and activation energy. Using the governing equations of a 0D flow model, our PNODE needs only a limited number of training samples and predicts trajectories of various quantities such as temperature, pressure, and mass fractions of species while satisfying physical constraints. We validate our physics-based PNODE on solution snapshots of high-fidelity Computational Fluid Dynamics (CFD) simulations of laser-induced ignition in a prototype rocket combustor. We compare the performance of our physics-based PNODE with that of kernel ridge regression and fully connected neural networks. Our results show that our physics-based PNODE provides solutions with lower mean absolute errors of average temperature over time, thus improving the prediction of successful laser ignition with high-dimensional parameters.

Planar Robot Casting with Real2Sim2Real Self-Supervised Learning

Manipulation of deformable objects using a single parameterized dynamic action can be useful for tasks such as fly fishing, lofting a blanket, and playing shuffleboard. Such tasks take as input a desired final state and output one parameterized open-loop dynamic robot action which produces a trajectory toward the final state. This is especially challenging for long-horizon trajectories with complex dynamics involving friction. This paper explores the task of Planar Robot Casting (PRC): where one planar motion of a robot wrist holding one end of a cable causes the other end to slide across the plane toward a desired target. PRC allows the cable to reach points beyond the robot's workspace and has applications for cable management in homes, warehouses, and factories. To efficiently learn a PRC policy for a given cable, we propose Real2Sim2Real, a self-supervised framework that automatically collects physical trajectory examples to tune parameters of a dynamics simulator using Differential Evolution, generates many simulated examples, and then learns a policy using a weighted combination of simulated and physical data. We evaluate Real2Sim2Real with three simulators, Isaac Gym-segmented, Isaac Gym-hybrid, and PyBullet, two function approximators, Gaussian Processes and Neural Networks (NNs), and three cables with differing stiffness, torsion, and friction. Results on 16 held-out test targets for each cable suggest that the NN PRC policies using Isaac Gym-segmented attain median error distance (as % of cable length) ranging from 8% to 14%, outperforming baselines and policies trained on only real or only simulated examples. Code, data, and videos are available at https://tinyurl.com/robotcast.

Robots of the Lost Arc: Learning to Dynamically Manipulate Fixed-Endpoint Ropes and Cables

High-speed arm motions can dynamically manipulate ropes and cables to vault over obstacles, knock objects from pedestals, and weave between obstacles. In this paper, we propose a self-supervised learning pipeline that enables a UR5 robot to perform these three tasks. The pipeline trains a deep convolutional neural network that takes as input an image of the scene with object and target. It computes a 3D apex point for the robot arm, which, together with a task-specific trajectory function, defines an arcing motion for a manipulator arm to dynamically manipulate the cable to perform a task with varying obstacle and target locations. The trajectory function computes high-speed minimum-jerk arcing motions that are constrained to remain within joint limits and to travel through the 3D apex point by repeatedly solving quadratic programs for shorter time horizons to find the shortest and fastest feasible motion. We experiment with the proposed pipeline on 5 physical cables with different thickness and mass and compare performance with two baselines in which a human chooses the apex point. Results suggest that the robot using the learned apex point can achieve success rates of 81.7% in vaulting, 65.0% in knocking, and 60.0% in weaving, while a baseline with a fixed apex across the three tasks achieves respective success rates of 51.7%, 36.7%, and 15.0%, and a baseline with human-specified task-specific apex points achieves 66.7%, 56.7%, and 15.0% success rate respectively. Code, data, and supplementary materials are available at https: //sites.google.com/berkeley.edu/dynrope/home