LEARNING INTERPRETABLE DYNAMICS FROM IMAGES OF A FREELY ROTATING 3D RIGID BODY

Abstract

In many real-world settings, image observations of freely rotating 3D rigid bodies, such as satellites, may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation techniques to learn the dynamics and a lack of interpretability reduces the usefulness of standard deep learning methods. In this work, we present a physics-informed neural network model to estimate and predict 3D rotational dynamics from image sequences. We achieve this using a multi-stage prediction pipeline that maps individual images to a latent representation homeomorphic to SO(3), computes angular velocities from latent pairs, and predicts future latent states using the Hamiltonian equations of motion with a learned representation of the Hamiltonian. We demonstrate the efficacy of our approach on a new rotating rigid-body dataset with sequences of rotating cubes and rectangular prisms with uniform and non-uniform density.

1. INTRODUCTION

Images of 3D rigid bodies in motion are available across a range of application areas and can give insight into system dynamics. Learning dynamics from images has applications to planning, navigation, prediction, and control of robotic systems. Resident space objects (RSOs) are natural or man-made objects that orbit a planet or moon and are examples of commonly studied, free-rotating rigid bodies. When planning proximity operation missions with RSOs-collecting samples from an asteroid (Williams et al., 2018) , servicing a malfunctioning satellite (Flores-Abad et al., 2014) , or active space debris removal (Mark and Kamath, 2019)-it is critical to correctly estimate the RSO dynamics in order to avoid mission failure. Space robotic systems typically have access to onboard cameras, which makes learning dynamics from images a compelling approach for vision-based navigation and control. 2020) learn the underlying dynamics in an overparameterized black-box model. The combination of deep learning with physics-based models allows models to learn dynamics from high-dimensional data such as images (Allen-Blanchette et al., 2020; Zhong and Leonard, 2020; Toth et al., 2020) . However, as far as we know, our method is the first to use the Hamiltonian formalism to learn 3D rigid-body dynamics from images Kinematics and dynamics of 3D rigid body rotation are both fundamental to accomplishing the goals of this paper. The kinematics describe the rate of change of rigid body orientation as a function of the orientation and the angular velocity. Our method integrates the kinematic equations to compute the orientation trajectory in latent space using the latent angular velocity. The dynamics describe the rate of change of the angular velocity as a function of the angular velocity and the moment-of-inertia matrix J, which depends on the distribution of mass over the rigid body volume. J is unknown and cannot be computed from knowledge of the external geometry of the rigid body, except in the special case in which the mass is known and the mass is uniformly distributed over the rigid body volume. In our framework, we learn the dynamics from the motion of the rigid body, not from the external



Allen-Blanchette et al. (2020); Zhong and Leonard (2020); Toth et al. (2020) has made significant progress in learning dynamics from images of planar rigid bodies. Learning dynamics of 3D rigid-body motion has also been explored with a variety of types of input data Duong and Atanasov (2021); Byravan and Fox (2017); Peretroukhin et al. (2020). Duong and Atanasov (2021) uses state measurement data (i.e. rotation matrix and angular momenta), while Peretroukhin et al. (

