Non-Smooth Newton Methods for Deformable Multi-Body Dynamics MILES MACKLIN, NVIDIA and University of Copenhagen KENNY ERLEBEN, University of Copenhagen MATTHIAS MÜLLER, NVIDIA NUTTAPONG CHENTANEZ, NVIDIA STEFAN JESCHKE, NVIDIA VIKTOR MAKOVIYCHUK, NVIDIA Fig. 1. The Fetch robot picking up and transferring a tomato to a mechanical scale. The tomato is modeled using tetrahedral FEM, while the robot and working mechanical scale are modeled as rigid bodies connected by revolute and prismatic joints. Our method provides full two-way coupling that allows for stable grasping and force sensing on the gripper. The robot is controlled by a human operator in real-time. Model provided courtesy of Fetch Robotics, Inc. We present a framework for the simulation of rigid and deformable bodies in the presence of contact and friction. Our method is based on a non-smooth Newton iteration that solves the underlying nonlinear complementarity problems (NCPs) directly. This approach allows us to support nonlinear dynamics models, including hyperelastic deformable bodies and articulated rigid mechanisms, coupled through a smooth isotropic friction model. The fxed-point nature of our method means it requires only the solution of a symmetric linear system as a building block. We propose a new complemen- tarity preconditioner for NCP functions that improves convergence, and we develop an efcient GPU-based solver based on the conjugate residual (CR) method that is suitable for interactive simulations. We show how to improve robustness using a new geometric stifness approximation and evaluate our method’s performance on a number of robotics simulation sce- narios, including dexterous manipulation and training using reinforcement learning. CCS Concepts: · Computing methodologies → Simulation by anima- tion; Interactive simulation; · Computer systems organization → Robot- ics. Authors’ addresses: Miles Macklin, NVIDIA, University of Copenhagen, mmacklin@nvidia.com; Kenny Erleben, University of Copenhagen, kenny@di.ku.dk; Matthias Müller, NVIDIA, matthiasm@nvidia.com; Nuttapong Chentanez, NVIDIA, nchentanez@nvidia.com; Stefan Jeschke, NVIDIA, sjeschke@nvidia.com; Viktor Makoviychuk, NVIDIA, vmakoviychuk@nvidia.com. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proft or commercial advantage and that copies bear this notice and the full citation on the frst page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specifc permission and/or a fee. Request permissions from permissions@acm.org. © 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. 0730-0301/2019/6-ART20 $15.00 https://doi.org/10.1145/3338695 Additional Key Words and Phrases: numerical optimization, friction, contact, multi-body dynamics, robotics ACM Reference Format: Miles Macklin, Kenny Erleben, Matthias Müller, Nuttapong Chentanez, Ste- fan Jeschke, and Viktor Makoviychuk. 2019. Non-Smooth Newton Methods for Deformable Multi-Body Dynamics. ACM Trans. Graph. 38, 5, Article 20 (June 2019), 20 pages. https://doi.org/10.1145/3338695 1 INTRODUCTION Enabling the next-generation of robots that can, for example, en- ter a kitchen and prepare dinner, requires new control algorithms capable of navigating complex environments and performing dex- terous manipulation of real-world objects, as illustrated in Figure 1. Machine-learning based approaches hold the promise of unlocking this capability, but require large amounts of data to work efectively [Levine et al. 2018]. For many tasks, gathering this data from the real-world may be inefcient, or impractical due to safety concerns. In contrast, simulation is relatively inexpensive, safe, and has been used to learn and transfer behaviors such as walking and jump- ing to real robots [Tan et al. 2018][Sadeghi et al. 2017]. Extending transfer learning beyond locomotion to a wider range of behaviors requires the robust and efcient simulation of richer environments incorporating multiple physical models [Heess et al. 2017]. We believe the computer graphics community is uniquely placed to address the simulation needs of robotics. One area that computer graphics has studied extensively is two-way coupled simulation of rigid and deformable objects. Such algorithms are necessary to simulate tasks involving dexterous manipulation of soft objects, or even soft robots themselves. An example of the latter is found in ACM Trans. Graph., Vol. 38, No. 5, Article 20. Publication date: June 2019. arXiv:1907.04587v1 [cs.RO] 10 Jul 2019