VN-Transformer: Rotation-Equivariant Attention for Vector Neurons

Rotation equivariance is a desirable property in many practical applications such as motion forecasting and 3D perception, where it can offer benefits like sample efficiency, better generalization, and robustness to input perturbations. Vector Neurons (VN) is a recently developed framework offering a simple yet effective approach for deriving rotation-equivariant analogs of standard machine learning operations by extending one-dimensional scalar neurons to three-dimensional "vector neurons." We introduce a novel "VN-Transformer" architecture to address several shortcomings of the current VN models. Our contributions are: $(i)$ we derive a rotation-equivariant attention mechanism which eliminates the need for the heavy feature preprocessing required by the original Vector Neurons models; $(ii)$ we extend the VN framework to support non-spatial attributes, expanding the applicability of these models to real-world datasets; $(iii)$ we derive a rotation-equivariant mechanism for multi-scale reduction of point-cloud resolution, greatly speeding up inference and training; $(iv)$ we show that small tradeoffs in equivariance ($\epsilon$-approximate equivariance) can be used to obtain large improvements in numerical stability and training robustness on accelerated hardware, and we bound the propagation of equivariance violations in our models. Finally, we apply our VN-Transformer to 3D shape classification and motion forecasting with compelling results.Comment: Published in Transactions on Machine Learning Research (TMLR), 2023; Previous version appeared in Workshop on Machine Learning for Autonomous Driving, Conference on Neural Information Processing Systems (NeurIPS), 202

MotionLM: Multi-Agent Motion Forecasting as Language Modeling

Reliable forecasting of the future behavior of road agents is a critical component to safe planning in autonomous vehicles. Here, we represent continuous trajectories as sequences of discrete motion tokens and cast multi-agent motion prediction as a language modeling task over this domain. Our model, MotionLM, provides several advantages: First, it does not require anchors or explicit latent variable optimization to learn multimodal distributions. Instead, we leverage a single standard language modeling objective, maximizing the average log probability over sequence tokens. Second, our approach bypasses post-hoc interaction heuristics where individual agent trajectory generation is conducted prior to interactive scoring. Instead, MotionLM produces joint distributions over interactive agent futures in a single autoregressive decoding process. In addition, the model's sequential factorization enables temporally causal conditional rollouts. The proposed approach establishes new state-of-the-art performance for multi-agent motion prediction on the Waymo Open Motion Dataset, ranking 1st on the interactive challenge leaderboard.Comment: To appear at the International Conference on Computer Vision (ICCV) 202

Folded polygonal unit cells for deployable metamaterials and mechanisms

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2016.Cataloged from PDF version of thesis.Includes bibliographical references (pages 83-85).Deployable and transformable structures are of broad interest for applications including satellites and space exploration, temporary shelters, packaging, transportation, robotics and medical devices. One emerging approach to scalable fabrication of such structures involves the general concept of Origami-inspired design along with cutting, folding, and fastening of sheet materials. However, contrasting the classical approach of modeling Origami structures as having perfect hinges and rigid panels, consideration of the finite bending and rotational stiffness of these elements is essential to understand their constituent mechanics. Moreover, meta-materials and functional structures having fundamentally new mechanical properties can be designed this way. We present the design, fabrication and mechanics of a novel, deployable cellular material, which we call Flexigami. The unit cell takes the form of two parallel regular polygons, connected by a circuit of diagonally creased panels. Upon compression, individual unit cells transform either gently or abruptly between two stable equilibrium states depending on the interplay between hinge and panel properties. The mechanical behavior of each unit cell can be deterministically designed via geometry, dimensions and topology of the panels and hinges. Individual unit cells can collapsed reversible to less than 10% of their deployed volume. Within this transition regime, the force-displacement curve of each cell can be tuned to exhibit a smooth compression behavior or an instability followed by a self-reinforcing response. We use finite-element models complemented by analytical and computational analysis of the results to understand the importance of different mechanical properties of constituent hinges and panels and also demonstrate the fabrication of flexigami cells and mechanisms in various structural materials. Finally we present different mechanisms and their subsequent applications.by Nigamaa Nayakanti.S.M

Twist-coupled Kirigami cells and mechanisms

Manipulation of thin sheets by folding and cutting offers opportunity to engineer structures with novel mechanical properties, and to prescribe complex force–displacement relationships via material elasticity in combination with the trajectory imposed by the fold pattern. Here we study the mechanics of a cellular Kirigami that rotates and buckles upon compression, presenting an example of a design strategy that we call ”flexigami”. The addition of diagonal cuts to an equivalent closed cell permits the cell to collapse reversibly without incurring significant tensile strains in its panels. Using finite-element modeling and experiments we show how the mechanical behavior of the cell is governed by the coupled rigidity of the panels and hinges and we design cells to achieve reversible force response ranging from smooth mono-stability to sharp bi-stability. We then demonstrate the cell-based construction of laminates with multi-stable behavior and a rotary-linear boom actuator, as well as self-deploying cells with shape memory alloy hinges. Advanced digital fabrication methods can enable the realization of this and other so-called flexigami designs that derive their overall mechanics from fold and panel elasticity, for applications including deployable structures, soft robotics and medical devices.National Science Foundation (Grant EFRI-1240264)U. S. Army Research Office (Contract W911NF-13-D-0001

Soft nanocomposite electroadhesives for digital micro- and nanotransfer printing

Automated handling of microscale objects is essential for manufacturing of next-generation electronic systems. Yet, mechanical pick-and-place technologies cannot manipulate smaller objects whose surface forces dominate over gravity, and emerging microtransfer printing methods require multidirectional motion, heating, and/or chemical bonding to switch adhesion. We introduce soft nanocomposite electroadhesives (SNEs), comprising sparse forests of dielectric-coated carbon nanotubes (CNTs), which have electrostatically switchable dry adhesion. SNEs exhibit 40-fold lower nominal dry adhesion than typical solids, yet their adhesion is increased >100-fold by applying 30 V to the CNTs. We characterize the scaling of adhesion with surface morphology, dielectric thickness, and applied voltage and demonstrate digital transfer printing of films of Ag nanowires, polymer and metal microparticles, and unpackaged light-emitting diodes.National Science Foundation (U.S.) (CMMI-1463181)Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (contract W911NF-13-D-0001