skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Data-Free Learning of Reduced-Order Kinematics
Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces. This work addresses the challenge of identifying such subspaces automatically: given as input an energy function for a high-dimensional system, we produce a low-dimensional map whose image parameterizes a diverse yet low-energy submanifold of configurations. The only additional input needed is a single seed configuration for the system to initialize our procedure; no dataset of trajectories is required. We represent subspaces as neural networks that map a low-dimensional latent vector to the full configuration space, and propose a training scheme to fit network parameters to any system of interest. This formulation is effective across a very general range of physical systems; our experiments demonstrate not only nonlinear and very low-dimensional elastic body and cloth subspaces, but also more general systems like colliding rigid bodies and linkages. We briefly explore applications built on this formulation, including manipulation, latent interpolation, and sampling.  more » « less
Award ID(s):
1955697
PAR ID:
10480334
Author(s) / Creator(s):
; ; ; ; ; ;
Publisher / Repository:
ACM
Date Published:
ISBN:
9798400701597
Page Range / eLocation ID:
1 to 9
Format(s):
Medium: X
Location:
Los Angeles CA USA
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Abstract Elastic gridshell is a class of net-like structure formed by an ensemble of elastically deforming rods coupled through joints, such that the structure can cover large areas with low self-weight and allow for a variety of aesthetic configurations. Gridshells, also known as X-shells or Cosserat Nets, are a planar grid of elastic rods in its undeformed configuration. The end points of the rods are constrained and positioned on a closed curve—the final boundary—to actuate the structure into a 3D shape. Here, we report a discrete differential geometry-based numerical framework to study the geometrically nonlinear deformation of gridshell structures, accounting for non-trivial bending-twisting coupling at the joints. The form-finding problem of obtaining the undeformed planar configuration given the target convex 3D topology is then investigated. For the forward (2D to 3D) physically based simulation, we decompose the gridshell structure into multiple one-dimensional elastic rods and simulate their deformation by the well-established discrete elastic rods (DER) algorithm. A simple penalty energy between rods and linkages is used to simulate the coupling between two rods at the joints. For the inverse problem associated with form-finding (3D to 2D), we introduce a contact-based algorithm between the elastic gridshell and a rigid 3D surface, where the rigid surface describes the target shape of the gridshell upon actuation. This technique removes the need of several forward simulations associated with conventional optimization algorithms and provides a direct solution to the inverse problem. Several examples—hemispherical cap, paraboloid, and hemi-ellipsoid—are used to show the effectiveness of the inverse design process. 
    more » « less
  2. Multistable structures have widespread applications in the design of deployable aerospace systems, mechanical metamaterials, flexible electronics, and multimodal soft robotics due to their capability of shape reconfiguration between multiple stable states. Recently, the snap-folding of rings, often in the form of circles or polygons, has shown the capability of inducing diverse stable configurations. The natural curvature of the rod segment (curvature in its stress-free state) plays an important role in the elastic stability of these rings, determining the number and form of their stable configurations during folding. Here, we develop a general theoretical framework for the elastic stability analysis of segmented rings (e.g., polygons) based on an energy variational approach. Combining this framework with finite element simulations, we map out all planar stable configurations of various segmented rings and determine the natural curvature ranges of their multistable states. The theoretical and numerical results are validated through experiments, which demonstrate that a segmented ring with a rectangular cross-section can show up to six distinct planar stable states. The results also reveal that, by rationally designing the segment number and natural curvature of the segmented ring, its one- or multiloop configuration can store more strain energy than a circular ring of the same total length. We envision that the proposed strategy for achieving multistability in the current work will aid in the design of multifunctional, reconfigurable, and deployable structures. 
    more » « less
  3. Abstract This paper describes vibrational control and stability of a planar, horizontal 2-link mechanism using translational control of the base pivot. The system is a 3-DOF two-link mechanism that is subject to torsional damping, torsional stiffness, and is moving on a horizontal plane. The goal is to drive the averaged dynamics of the system to a desired configuration using a high-frequency, high-amplitude force applied at the base pivot. The desired configuration is achieved by applying an amplitude and angle of the input determined using the averaged dynamics of the system. We find the range of stable configurations that can be achieved by the system by changing the amplitude of the oscillations for a fixed input angle and oscillation frequency. The effects of varying the physical parameters on the achievable stable configurations are studied. Stability analysis of the system is performed using two methods: the averaged dynamics and averaged potential. 
    more » « less
  4. Abstract Planning and problem solving are cornerstones of higher brain function. But we do not know how the brain does that. We show that learning of a suitable cognitive map of the problem space suffices. Furthermore, this can be reduced to learning to predict the next observation through local synaptic plasticity. Importantly, the resulting cognitive map encodes relations between actions and observations, and its emergent high-dimensional geometry provides a sense of direction for reaching distant goals. This quasi-Euclidean sense of direction provides a simple heuristic for online planning that works almost as well as the best offline planning algorithms from AI. If the problem space is a physical space, this method automatically extracts structural regularities from the sequence of observations that it receives so that it can generalize to unseen parts. This speeds up learning of navigation in 2D mazes and the locomotion with complex actuator systems, such as legged bodies. The cognitive map learner that we propose does not require a teacher, similar to self-attention networks (Transformers). But in contrast to Transformers, it does not require backpropagation of errors or very large datasets for learning. Hence it provides a blue-print for future energy-efficient neuromorphic hardware that acquires advanced cognitive capabilities through autonomous on-chip learning. 
    more » « less
  5. Klann, Eric (Ed.)
    Abstract As information about the world is conveyed from the sensory periphery to central neural circuits, it mixes with complex ongoing cortical activity. How do neural populations keep track of sensory signals, separating them from noisy ongoing activity? Here, we show that sensory signals are encoded more reliably in certain low-dimensional subspaces. These coding subspaces are defined by correlations between neural activity in the primary sensory cortex and upstream sensory brain regions; the most correlated dimensions were best for decoding. We analytically show that these correlation-based coding subspaces improve, reaching optimal limits (without an ideal observer), as noise correlations between cortex and upstream regions are reduced. We show that this principle generalizes across diverse sensory stimuli in the olfactory system and the visual system of awake mice. Our results demonstrate an algorithm the cortex may use to multiplex different functions, processing sensory input in low-dimensional subspaces separate from other ongoing functions. 
    more » « less