ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor

X-CAD: Optimizing CAD Models with Extended Finite Elements

We propose a novel generic shape optimization method for CAD models based on the eXtended Finite Element Method (XFEM). Our method works directly on the intersection between the model and a regular simulation grid, without the need to mesh or remesh, thus removing a bottleneck of classical shape optimization strategies. This is made possible by a novel hierarchical integration scheme that accurately integrates finite element quantities with sub-element precision. For optimization, we efficiently compute analytical shape derivatives of the entire framework, from model intersection to integration rule generation and XFEM simulation. Moreover, we describe a differentiable projection of shape parameters onto a constraint manifold spanned by user-specified shape preservation, consistency, and manufacturability constraints. We demonstrate the utility of our approach by optimizing mass distribution, strength-to-weight ratio, and inverse elastic shape design objectives directly on parameterized 3D CAD models

Capture and Modeling of Non-Linear Heterogeneous Soft Tissue

This paper introduces a data-driven representation and modeling technique for simulating non-linear heterogeneous soft tissue. It simplifies the construction of convincing deformable models by avoiding complex selection and tuning of physical material parameters, yet retaining the richness of non-linear heterogeneous behavior. We acquire a set of example deformations of a real object, and represent each of them as a spatially varying stress-strain relationship in a finite-element model. We then model the material by non-linear interpolation of these stress-strain relationships in strain-space. Our method relies on a simple-to-build capture system and an efficient run-time simulation algorithm based on incremental loading, making it suitable for interactive computer graphics applications. We present the results of our approach for several non-linear materials and biological soft tissue, with accurate agreement of our model to the measured data.Engineering and Applied Science

Design and fabrication of materials with desired deformation behavior

Figure 1: Two examples of real and replicated objects. Thanks to our data-driven process, we are able to measure, simulate, and obtain material combinations of non-linear base materials that match a desired deformation behavior. We can then print those objects with multi-material 3D printers using two materials (blue and black) with varying internal microstructure. This paper introduces a data-driven process for designing and fab-ricating materials with desired deformation behavior. Our process starts with measuring deformation properties of base materials. For each base material we acquire a set of example deformations, and we represent the material as a non-linear stress-strain relationship in a finite-element model. We have validated our material measure-ment process by comparing simulations of arbitrary stacks of base materials with measured deformations of fabricated material stacks. After material measurement, our process continues with designing stacked layers of base materials. We introduce an optimization pro-cess that finds the best combination of stacked layers that meets a user’s criteria specified by example deformations. Our algorithm employs a number of strategies to prune poor solutions from the combinatorial search space. We demonstrate the complete process by designing and fabricating objects with complex heterogeneous materials using modern multi-material 3D printers

Active Learning for Interactive Audio-Animatronic Performance Design

We present a practical neural computational approach for interactive design of Audio-Animatronic® facial performances. An offline quasi-static reference simulation, driven by a coupled mechanical assembly, accurately predicts hyperelastic skin deformations. To achieve interactive digital pose design, we train a shallow, fully connected neural network (KSNN) on input motor activations to solve the simulated mesh vertex positions. Our fully automatic synthetic training algorithm enables a first-of-its-kind learning active learning framework (GEN-LAL) for generative modeling of facial pose simulations. With adaptive selection, we significantly reduce training time to within half that of the unmodified training approach for each new Audio-Animatronic® figure

Volume MLS ray casting

The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and well-understood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework for ray casting of scalar data stored over regular as well as irregular grids. We use the MLS reconstruction to render smooth isosurfaces and to compute accurate derivatives for high-quality shading effects. We also present a novel, adaptive preintegration scheme to improve the efficiency of the ray casting algorithm by reducing the overall number of function evaluations, and an efficient implementation of our framework exploiting modern graphics hardware. The resulting system enables high-quality volume integration and shaded isosurface rendering for regular and irregular volume data

Optimal Design of Flexible-Link Mechanisms With Desired Load-Displacement Profiles

Robot mechanisms that exploit compliance can perform complex tasks under uncertainty using simple control strategies, but it remains difficult to design mechanisms with a desired embodied intelligence. In this paper, we propose an automated design technique that optimizes the desired load-displacement behavior of planar flexible-link mechanisms. To do so, we replace a subset of rigid with flexible links in an existing mechanism, and optimize their rest shape. We demonstrate the efficacy of our approach on a set of examples, including two fabricated prototypes, illustrating applications for grasping and locomotion tasks.ISSN:2377-376