Analysis of A Splitting Approach for the Parallel Solution of Linear Systems on GPU Cards

We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large; i.e., $10000 \leq N \leq 500000$. The ${\it split\ and\ parallelize}$(${\tt SaP}$) approach seeks to partition the matrix${\bf A}$into diagonal sub-blocks${\bf A}_i$,$i=1,\ldots,P$, which are independently factored in parallel. The solution may choose to consider or to ignore the matrices that couple the diagonal sub-blocks${\bf A}_i$. This approach, along with the Krylov subspace-based iterative method that it preconditions, are implemented in a solver called${\tt SaP::GPU}$, which is compared in terms of efficiency with three commonly used sparse direct solvers:${\tt PARDISO}$,${\tt SuperLU}$, and${\tt MUMPS}$.${\tt SaP::GPU}$, which runs entirely on the GPU except several stages involved in preliminary row-column permutations, is robust and compares well in terms of efficiency with the aforementioned direct solvers. In a comparison against Intel's${\tt MKL}$,${\tt SaP::GPU}$also fares well when used to solve dense banded systems that are close to being diagonally dominant.${\tt SaP::GPU}$ is publicly available and distributed as open source under a permissive BSD3 license.Comment: 38 page

On the Importance of Displacement History in Soft-Body Contact Models

Two approaches are commonly used for handling frictional contact within the framework of the discrete element method (DEM). One relies on the complementarity method (CM) to enforce a nonpenetration condition and the Coulomb dry-friction model at the interface between two bodies in mutual contact. The second approach, called the penalty method (PM), invokes an elasticity argument to produce a frictional contact force that factors in the local deformation and relative motion of the bodies in contact. We give a brief presentation of a DEM-PM contact model that includes multi-time-step tangential contact displacement history. We show that its implementation in an open-source simulation capability called Chrono is capable of accurately reproducing results from physical tests typical of the field of geomechanics, i.e., direct shear tests on a monodisperse material. Keeping track of the tangential contact displacement history emerges as a key element of the model. We show that identical simulations using contact models that include either no tangential contact displacement history or only single-time-step tangential contact displacement history are unable to accurately model the direct shear test

POLAR3D: Augmenting NASA's POLAR Dataset for Data-Driven Lunar Perception and Rover Simulation

We report on an effort that led to POLAR3D, a set of digital assets that enhance the POLAR dataset of stereo images generated by NASA to mimic lunar lighting conditions. Our contributions are twofold. First, we have annotated each photo in the POLAR dataset, providing approximately 23 000 labels for rocks and their shadows. Second, we digitized several lunar terrain scenarios available in the POLAR dataset. Specifically, by utilizing both the lunar photos and the POLAR's LiDAR point clouds, we constructed detailed obj files for all identifiable assets. POLAR3D is the set of digital assets comprising of rock/shadow labels and obj files associated with the digital twins of lunar terrain scenarios. This new dataset can be used for training perception algorithms for lunar exploration and synthesizing photorealistic images beyond the original POLAR collection. Likewise, the obj assets can be integrated into simulation environments to facilitate realistic rover operations in a digital twin of a POLAR scenario. POLAR3D is publicly available to aid perception algorithm development, camera simulation efforts, and lunar simulation exercises.POLAR3D is publicly available at https://github.com/uwsbel/POLAR-digital.Comment: 7 pages, 4 figures; this work has been submitted to the 2024 IEEE Conference on Robotics and Automation (ICRA) under revie

A performance contextualization approach to validating camera models for robot simulation

The focus of this contribution is on camera simulation as it comes into play in simulating autonomous robots for their virtual prototyping. We propose a camera model validation methodology based on the performance of a perception algorithm and the context in which the performance is measured. This approach is different than traditional validation of synthetic images, which is often done at a pixel or feature level, and tends to require matching pairs of synthetic and real images. Due to the high cost and constraints of acquiring paired images, the proposed approach is based on datasets that are not necessarily paired. Within a real and a simulated dataset, A and B, respectively, we find subsets Ac and Bc of similar content and judge, statistically, the perception algorithm's response to these similar subsets. This validation approach obtains a statistical measure of performance similarity, as well as a measure of similarity between the content of A and B. The methodology is demonstrated using images generated with Chrono::Sensor and a scaled autonomous vehicle, using an object detector as the perception algorithm. The results demonstrate the ability to quantify (i) differences between simulated and real data; (ii) the propensity of training methods to mitigate the sim-to-real gap; and (iii) the context overlap between two datasets.Comment: 12 pages, 18 figure

High-Performance Modeling and Simulation of Anchoring in Granular Media for NEO Applications

NASA is interested in designing a spacecraft capable of visiting a near-Earth object (NEO), performing experiments, and then returning safely. Certain periods of this mission would require the spacecraft to remain stationary relative to the NEO, in an environment characterized by very low gravity levels; such situations require an anchoring mechanism that is compact, easy to deploy, and upon mission completion, easy to remove. The design philosophy used in this task relies on the simulation capability of a high-performance multibody dynamics physics engine. On Earth, it is difficult to create low-gravity conditions, and testing in low-gravity environments, whether artificial or in space, can be costly and very difficult to achieve. Through simulation, the effect of gravity can be controlled with great accuracy, making it ideally suited to analyze the problem at hand. Using Chrono::Engine, a simulation pack age capable of utilizing massively parallel Graphic Processing Unit (GPU) hardware, several validation experiments were performed. Modeling of the regolith interaction has been carried out, after which the anchor penetration tests were performed and analyzed. The regolith was modeled by a granular medium composed of very large numbers of convex three-dimensional rigid bodies, subject to microgravity levels and interacting with each other with contact, friction, and cohesional forces. The multibody dynamics simulation approach used for simulating anchors penetrating a soil uses a differential variational inequality (DVI) methodology to solve the contact problem posed as a linear complementarity method (LCP). Implemented within a GPU processing environment, collision detection is greatly accelerated compared to traditional CPU (central processing unit)- based collision detection. Hence, systems of millions of particles interacting with complex dynamic systems can be efficiently analyzed, and design recommendations can be made in a much shorter time. The figure shows an example of this capability where the Brazil Nut problem is simulated: as the container full of granular material is vibrated, the large ball slowly moves upwards. This capability was expanded to account for anchors of different shapes and penetration velocities, interacting with granular soils

A discussion of low order numerical integration formulas for rigid and flexible multibody dynamics

ABSTRACT The premise of this work is that real-life mechanical systems limit the use of high order integration formulas due to the presence in the associated models of friction and contact/impact elements. In such cases producing a numerical solution necessarily relies on low order integration formulas. The resulting algorithms are generally robust and expeditious; their major drawback remains that they typically require small integration stepsizes in order to meet a user prescribed accuracy. This paper looks at three low order numerical integration formulas: Newmark, HHT, and BDF of order two. These formulas are used in two contexts. A first set of three methods is obtained by considering a direct index-3 discretization approach that solves for the equations of motion and imposes the position kinematic constraints. The second batch of three additional methods draws on the HHT and BDF integration formulas and considers in addition to the equations of motion both the position and velocity kinematic constraint equations. The first objective of this paper is to review the theoretical results available in the literature regarding the stability and convergence properties of these low order methods when applied in the context of multibody dynamics simulation. When no theoretical results are available, numeri- * Address all correspondence to this author. cal experiments are carried out to gauge order behavior. The second objective is to perform a set of numerical experiments to compare these six methods in terms of several metrics: (a) efficiency, (b) velocity constraint drift, and (c) energy preservation. A set of simple mechanical systems is used for this purpose: a double pendulum, a slider crank with rigid bodies, and a slider crank with a flexible body represented in the floating frame of reference formulation. INTRODUCTION A multitude of phenomena, processes, and applications are described in terms of mixed systems of differential equations combined with linear and nonlinear algebraic equations, most often corresponding to models coming from engineering, physics, and chemistry. Differential equations relate certain quantities to their derivatives with respect to time and/or space variables. Algebraic equations usually model conservation laws and the constraints present in the system. When there are derivatives with respect to only one independent variable (usually time) the equations are called differential-algebraic equations (DAEs). DAEs are basically differential equations defined on submanifolds of R n . The constrained equations of motion can be expressed in th