Gilbert Johnson Keerthi Research Articles

A poly‐superellipsoid‐based approach on particle morphology for DEM modeling of granular media

SummaryParticle morphology plays a key role in affecting physical and mechanical behaviors of granular media. While various mathematical approaches and shape descriptors have been proposed to describe the morphological properties of granular particles, it remains a challenge to effectively incorporate them for efficient discrete modeling of granular materials. This study presents a new poly‐superellipsoid‐based approach for three‐dimensional discrete element method (DEM) modeling of non‐spherical convex particles. A uniform mathematical description of 3D poly‐superellipsoidal surface is employed to represent a realistic granular particle, which is shown to be versatile and effective in reproducing a wide range of shape features (including elongation, flatness, angularity, and asymmetry) for real particles in nature. A novel optimization approach based on hybrid Levenberg‐Marquardt (LM) and Gilbert‐Johnson‐Keerthi (GJK) algorithms is further developed for efficient and robust contact detection in DEM simulation of poly‐superellipsoidal assemblies. Simulations of granular packing and triaxial compression tests show that the proposed approach is generally robust and efficient for both dynamic and quasistatic modeling of granular media.

Collision-free path planning of cable-driven parallel robots in cluttered environments

Path planning of cable-driven parallel robots (CDPRs) is a challenging task due to cables which may cause various collisions. In this paper, three steps are suggested to perform path finding of CDPRs in cluttered environments. First, a way to visualize the cable collision of CDPRs is suggested to consider actual workspace of CDPRs. Second, a path finding algorithm based on rapidly exploring random trees (RRT) is presented to find a path free of various collisions of CDPRs including cable collisions and wrench feasible workspace. While conventional RRT algorithms are mainly focused on mazy environments, the modified RRT algorithm proposed here directly connects a sampled node and the tree to find a path faster in a non-mazy, but cluttered environment. Goal-biased sampling algorithm is also modified and employed to decrease computational cost. To deal with complicated collision detection of cables in the RRT, Gilbert–Johnson–Keerthi algorithm was employed. Finally, post-processing algorithm for any waypoint-based path is suggested to get a shorter and less winding path. A numerical study was carried out to suggest choosing proper meta parameters for the post-processing algorithm. The suggested algorithms were evaluated with 1000 times of simulations, and they were equally carried out for RRT* to compare. According to the results, the suggested algorithm found a shorter path with less computation time compared to RRT* and the post-processing algorithms made the already found path shorter.

A coupled finite volume method and Gilbert–Johnson–Keerthi distance algorithm for computational fluid dynamics modelling

We investigate a novel technique to obtain the mesh porosity (volume and area) based on the Gilbert–Johnson–Keerthi (GJK) distance algorithm for flow modelling. The GJK algorithm is used to check collisions between two convex objects. This concept is applied to check the collision between an element of the computational mesh and the geometrical model where the element of the mesh is broken recursively to obtain refined values of the porosity. The approach has demonstrated that it can handle complex geometries within feasible computational time. The porosity values obtained using this methodology are coupled in the developed Navier–Stokes. Numerical findings are compared with selected benchmarking tests. Numerical findings agree with experimental data and the main features of the fluid flow are well captured.

Grains3D, a flexible DEM approach for particles of arbitrary convex shape—Part III: extension to non-convex particles modelled as glued convex particles

Large-scale numerical simulation using the discrete element method (DEM) contributes to improving our understanding of granular flow dynamics involved in many industrial processes and geophysical flows. In industry, it leads to an enhanced design and an overall optimization of the corresponding equipment and process. Most of the DEM simulations in the literature have been performed using spherical particles. A limited number of studies dealt with non-spherical particles, even less with non-convex particles. Even convex bodies do not always represent the real shape of certain particles. In fact, more complex-shaped particles are found in many industrial applications, for example, catalytic pellets in chemical reactors or crushed glass debris in recycling processes. In Grains3D-Part I (Wachs et al. in Powder Technol 224:374–389, 2012), we addressed the problem of convex shape in granular simulations, while in Grains3D-Part II (Rakotonirina and Wachs in Powder Technol 324:18–35, 2018), we suggested a simple though efficient parallel strategy to compute systems with up to a few hundreds of millions of particles. The aim of the present study is to extend even further the modelling capabilities of Grains3D towards non-convex shapes, as a tool to examine the flow dynamics of granular media made of non-convex particles. Our strategy is based on decomposing a non-convex-shaped particle into a set of convex bodies, called elementary components. We call our method glued or clumped convex method, as an extension of the popular glued sphere method. Essentially, a non-convex particle is constructed as a cluster of convex particles, called elementary components. At the level of these elementary components of a glued convex particle, we employ the same contact detection strategy based on a Gilbert–Johnson–Keerthi algorithm and a linked-cell spatial sorting that accelerates the resolution of the contact, that we introduced in [39]. Our glued convex model is implemented as a new module of our code Grains3D and is therefore automatically fully parallel. We illustrate the new modelling capabilities of Grains3D in two test cases: (1) the filling of a container and (2) the flow dynamics in a rotating drum.

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

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

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

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.

Dynamic obstacle avoidance for manipulators using distance calculation and discrete detection

Abstract In order to avoid dynamic obstacle timely during manufacturing tasks performed by manipulators, a novel method based on distance calculation and discrete detection is proposed. The nearest distances between the links of a manipulator and the convex hull of an arbitrarily-shaped dynamic obstacle obtained from Kinect-V2 camera in real-time are calculated by Gilbert–Johnson–Keerthi algorithm, and the minimum one is defined as the closest distance between the manipulator and the obstacle. When the closest distance is less than a safe value, whether the dynamic obstacle is located in the global path of the manipulator is determined by improved discrete collision detection, which can adjust detection step-size adaptively for accuracy and efficiency. If the obstacle will collide with the manipulator, set a local goal and re-plan a local path for the manipulator. The proposed method is implemented in Robot Operating System (ROS) using C++. The experiments indicate that the proposed method can perform safe and timely dynamic avoidance for redundant manipulators in human-robot interaction.

Grains3D, a flexible DEM approach for particles of arbitrary convex shape — Part I: Numerical model and validations

We suggest a novel variant of Discrete Element Method (DEM) to simulate the flow dynamics of granular material made of non-spherical particles. Our approach is limited to particles of convex shape but permits to consider any combination of shape and size, which makes it very versatile. The contact detection strategy relies on the use of the Gilbert–Johnson–Keerthi algorithm to compute the distance between two convex bodies. The validation of the method is based on two different test cases in three dimensions: (i) the formation of a packed pile in a cylindrical container and (ii) flow dynamics in a horizontal rotating drum. In both cases, four shapes are investigated: a sphere, a cylinder, a cube and a tetrahedron. We evidence that our numerical code, Grains3D, supplies reliable and reasonably accurate computed solutions, both for spherical and non-spherical particles. In particular, in the latter case, we show how angularity promotes the appearance of the avalanching regime at relatively high Froude number compared to the spherical counterpart.

Trajectory planning and collisions detector for robotic arms

The major contributions of this paper are as follows: (1) the Gilbert–Johnson–Keerthi (GJK) algorithm is a collisions detector algorithm, a modified Gilbert–Johnson–Keerthi algorithm is presented, the proposed GJK algorithm uses a different distance, (2) some examples of GJK algorithm are presented, in the last example, the GJK distance algorithm is used to detect the collisions of a camera with its environment inside of a warehouse, the camera cannot cross any part of the structure of the warehouse, the camera needs to go around the structure, when the camera touches the structure, the camera goes to the right or to the left, (3) the time used in a cycle of work of the transelevator robotic arm is presented, it can be extended to other kind of robotic arms, (4) some examples of the time used in a cycle of work are presented, in the least example, the algorithm is used to control the time needed for the transelevator to go from one place to other one, (5) this paper presents a new trajectory planning algorithm which divides the trajectory in n periods, when n is equal to 2, the proposed algorithm is the same as other algorithms, but for n higher than 2, the proposed algorithm gives other optional trajectories, so the proposed algorithm lets the designer to take a better trajectory than with the previous algorithms, (6) some examples of the proposed trajectories planning algorithm are presented, in the least example, the proposed trajectory planning algorithm is used to control the movements of a transelevator inside of a warehouse.

Hough transform for distance computation and collision avoidance

A new technique for collision detection based on the application of the Hough transform is presented in this paper. As a consequence of applying this technique, a method for computing the minimum translational distance (MTD) between two spherically extended polytopes is introduced. This distance algorithm is based on the Gilbert-Johnson-Keerthi (GJK) algorithm. Parameters returned by the MTD algorithm hold collision-free configurations that avoid a predicted collision.