Category: Rigid bodies

Fluid Directed Rigid Body Control Using Deep Reinforcement Learning

Yunsheng Tian, Pingchuan Ma, Zherong Pan, Bo Ren, and Dinesh Manocha

We present a learning-based method to control a coupled 2D system involving both fluid and rigid bodies. Our approach is used to modify the fluid/rigid simulator’s behavior by applying control forces only at the simulation domain boundaries. The rest of the domain, corresponding to the interior, is governed by the Navier-Stokes equation for fluids and Newton-Euler’s equation for the rigid bodies. We represent our controller using a general neural-net, which is trained using deep reinforcement learning. Our formulation decomposes a control task into two stages: a precomputation training stage and an online generation stage. We utilize various fluid properties, e.g., the liquid’s velocity field or the smoke’s density field, to enhance the controller’s performance. We set up our evaluation benchmark by letting controller drive fluid jets move on the domain boundary and allowing them to shoot fluids towards a rigid body to accomplish a set of challenging 2D tasks such as keeping a rigid body balanced, playing a two-player ping-pong game, and driving a rigid body to sequentially hit specified points on the wall. In practice, our approach can generate physically plausible animations.

Fluid Directed Rigid Body Control Using Deep Reinforcement Learning

Rigid Body Contact Problems using Proximal Operators

Kenny Erleben

Iterative methods are popular for solving contact force problems in rigid body dynamics. They are loved for their robustness and surrounded by mystery as to whether they converge or not. We provide a mathematical foundation for iterative (PROX) schemes based on proximal operators. This is a class of iterative Jacobi and blocked Gauss–Seidel variants that theoretically proven always converge and provides a flexible plug and play framework for exploring different friction laws. We provide a portfolio of experience for choosing r-Factor strategies for such schemes and we analyze the distribution of convergence behaviors. Our results indicate the Gauss-Seidel variant is superior in terms of delivering predictable convergence behaviour and hence should be preferred over Jacobi variants. Our results also suggest that Global r -Factor strategies are better for structured stacking scenarios and can achieve absolute convergence in more cases.

Rigid Body Contact Problems using Proximal Operators

Improving the GJK algorithm for faster and more reliable distance queries between convex objects

Mattia Montanari, Nik Petrinic, and Ettore Barbieri

This article presents a new version of the Gilbert-Johnson-Keerthi (GJK) algorithm that circumvents the shortcomings introduced by degenerate geometries. The original Johnson algorithm and Backup procedure are replaced by a distance subalgorithm that is faster and accurate to machine precision, thus guiding the GJK algorithm toward a shorter search path in less computing time. Numerical tests demonstrate that this effectively is a more robust procedure. In particular, when the objects are found in contact, the newly proposed subalgorithm runs from 15% to 30% times faster than the original one. The improved performance has a significant impact on various applications, such as real-time simulations and collision avoidance systems. Altogether, the main contributions made to the GJK algorithm are faster convergence rate and reduced computational time. These improvements may be easily added into existing implementations; furthermore, engineering applications that require solutions of distance queries to machine precision can now be tackled using the GJK algorithm.

Improving the GJK algorithm for faster and more reliable distance queries between convex objects

All’s Well That Ends Well: Guaranteed Resolution of Simultaneous Rigid Body Impact

Etienne Vouga, Breannan Smith, Danny M. Kaufman, Rasmus Tamstorf, Eitan Grinspun

Iterative algorithms are frequently used to resolve simultaneous impacts between rigid bodies in physical simulations. However, these algorithms lack formal guarantees of termination, which is sometimes viewed as potentially dangerous, so failsafes are used in practical codes to prevent infinite loops. We show such steps are unnecessary. In particular, we study the broad class of such algorithms that are conservative and satisfy a minimal set of physical correctness properties, and which encompasses recent methods like Generalized Reflections as well as pairwise schemes. We fully characterize finite termination of these algorithms. The only possible failure cases can be detected, and we describe a procedure for modifying the algorithms to provably ensure termination. We also describe modifications necessary to guarantee termination in the presence of numerical error due to the use of floating-point arithmetic. Finally, we discuss the challenges dissipation introduce for finite termination, and describe how dissipation models can be incorporated while retaining the termination guarantee.

All’s Well That Ends Well: Guaranteed Resolution of Simultaneous Rigid Body Impact

Density Maps for Improved SPH Boundary Handling

Dan Koschier, Jan Bender

In this paper, we present the novel concept of density maps for robust handling of static and rigid dynamic boundaries in fluid simulations based on Smoothed Particle Hydrodynamics (SPH). In contrast to the vast majority of existing approaches, we use an implicit discretization for a continuous extension of the density field throughout solid boundaries. Using the novel representation we enhance accuracy and efficiency of density and density gradient evaluations in boundary regions by computationally efficient lookups into our density maps. The map is generated in a preprocessing step and discretizes the density contribution in the boundary’s near-field. In consequence of the high regularity of the continuous boundary density field, we use cubic Lagrange polynomials on a narrow-band structure of a regular grid for discretization. This strategy not only removes the necessity to sample boundary surfaces with particles but also decouples the particle size from the number of sample points required to represent the boundary. Moreover, it solves the ever-present problem of particle deficiencies near the boundary. In several comparisons we show that the representation is more accurate than particle samplings, especially for smooth curved boundaries. We further demonstrate that our approach robustly handles scenarios with highly complex boundaries and even outperforms one of the most recent sampling based techniques.

Density Maps for Improved SPH Boundary Handling

Long Range Constraints for Rigid Body Simulations

Matthias Müller, Nuttapong Chentanez, Miles Macklin, Stefan Jeschke

The two main constraints used in rigid body simulations are contacts and joints. Both constrain the motion of a small number of bodies in close proximity. However, it is often the case that a series of constraints restrict the motion of objects over longer distances such as the contacts in a large pile or the joints in a chain of rigid bodies. When only short range constraints are considered, a large number of solver iterations is typically needed for long range effects to emerge because information has to be propagated through individual joints and contacts. Our basic idea to signicantly speed up this process is to analyze the contact or joint graphs and automatically derive long range constraints such as upper and lower distance bounds between bodies that can potentially be far apart both spatially and topologically. The long range constraints are either generated or updated at every time step in case of contacts or whenever their topology changes within a joint graph. The signicant increase of the convergence rate due to the use of long range constraints allows us to simulate scenarios that cannot be handled by traditional solvers with a number of solver iterations that allow real time simulation.

Long Range Constraints for Rigid Body Simulations

Geometric Stiffness for Real-time Constrained Multibody Dynamics

Sheldon Andrews, Marek Teichmann, Paul Kry

This paper focuses on the stable and efficient simulation of articulated rigid body systems for real-time applications. Specifically, we focus on the use of geometric stiffness, which can dramatically increase simulation stability. We examine several numerical problems with the inclusion of geometric stiffness in the equations of motion, as proposed by previous work, and address these issues by introducing a novel method for efficiently building the linear system. This offers improved tractability and numerical efficiency. Furthermore, geometric stiffness tends to significantly dissipate kinetic energy. We propose an adaptive damping scheme, inspired by the geometric stiffness, that uses a stability criterion based on the numerical integrator to determine the amount of non-constitutive damping required to stabilize the simulation. With this approach, not only is the dynamical behavior better preserved, but the simulation remains stable for mass ratios of 1,000,000-to-1 at time steps up to 0.1 s. We present a number of challenging scenarios to demonstrate that our method improves efficiency, and that it increases stability by orders of magnitude compared to previous work.

Geometric Stiffness for Real-time Constrained Multibody Dynamics

Bounce Maps: An Improved Restitution Model for Real-Time Rigid-Body Impact

Jui-Hsien Wang, Rajsekhar Setaluri, Dinesh K Pai, Doug L James

We present a novel method to enrich standard rigid-body impact models with a spatially varying coefficient of restitution map, or Bounce Map. Even state-of-the art methods in computer graphics assume that for a single rigid body, post- and pre-impact dynamics are related with a single global, constant, namely the coefficient of restitution. We first demonstrate that this assumption is highly inaccurate, even for simple objects. We then present a technique to efficiently and automatically generate a function which maps locations on the object’s surface along with impact normals, to a scalar coefficient of restitution value. Furthermore, we propose a method for two-body restitution analysis, and, based on numerical experiments, estimate a practical model for combining one-body Bounce Map values to approximate the two-body coefficient of restitution. We show that our method not only improves accuracy, but also enables visually richer rigid-body simulations

Bounce Maps: An Improved Restitution Model for Real-Time Rigid-Body Impact

Example-Based Expressive Animation of 2D Rigid Bodies

Marek Dvorožňák, Pierre Bénard, Pascal Barla, Oliver Wang, Daniel Sýkora

We present a novel approach to facilitate the creation of stylized 2D rigid body animations. Our approach can handle multiple rigid objects following complex physically-simulated trajectories with collisions, while retaining a unique artistic style directly specified by the user. Starting with an existing target animation (e.g., produced by a physical simulation engine) an artist interactively draws over a sparse set of frames, and the desired appearance and motion stylization is automatically propagated to the rest of the sequence. The stylization process may also be performed in an off-line batch process from a small set of drawn sequences. To achieve these goals, we combine parametric deformation synthesis that generalizes and reuses hand-drawn exemplars, with non-parametric techniques that enhance the hand-drawn appearance of the synthesized sequence. We demonstrate the potential of our method on various complex rigid body animations which are created with an expressive hand-drawn look using notably less manual interventions as compared to traditional techniques.

Example-Based Expressive Animation of 2D Rigid Bodies

Real-time Interactive Tree Animation

We present a novel method for posing and animating botanical tree models interactively in real time. Unlike other state of the art methods which tend to produce trees that are overly flexible, bending and deforming as if they were underwater plants, our approach allows for arbitrarily high stiffness while still maintaining real-time frame rates without spurious artifacts, even on quite large trees with over ten thousand branches. This is accomplished by using an articulated rigid body model with as-stiff-as-desired rotational springs in conjunction with our newly proposed simulation technique, which is motivated both by position based dynamics and the typical O(N) algorithms for articulated rigid bodies. The efficiency of our algorithm allows us to pose and animate trees with millions of branches or alternatively simulate a small forest comprised of many highly detailed trees. Even using only a single CPU core, we can simulate ten thousand branches in real time while still maintaining quite crisp user interactivity. This has allowed us to incorporate our framework into a commodity game engine to run interactively even on a low-budget tablet. We show that our method is amenable to the incorporation of a large variety of desirable effects such as wind, leaves, fictitious forces, collisions, fracture, etc.

Real-time Interactive Tree Animation