scholarly journals KABouM: Knowledge-Level Action and Bounding Geometry Motion Planner

2018 ◽  
Vol 61 ◽  
pp. 323-362 ◽  
Author(s):  
Andre Gaschler ◽  
Ronald P. A. Petrick ◽  
Oussama Khatib ◽  
Alois Knoll
Keyword(s):  
Information Gain ◽  
Convex Bodies ◽  
Convex Polyhedra ◽  
Knowledge Level ◽  
Convex Decomposition ◽  
Symbolic Information ◽  
Sensing Actions ◽  
Swept Volumes ◽  
Geometric Knowledge ◽  
Swept Volume

For robots to solve real world tasks, they often require the ability to reason about both symbolic and geometric knowledge. We present a framework, called KABouM, for integrating knowledge-level task planning and motion planning in a bounding geometry. By representing symbolic information at the knowledge level, we can model incomplete information, sensing actions and information gain; by representing all geometric entities--objects, robots and swept volumes of motions--by sets of convex polyhedra, we can efficiently plan manipulation actions and raise reasoning about geometric predicates, such as collisions, to the symbolic level. At the geometric level, we take advantage of our bounded convex decomposition and swept volume computation with quadratic convergence, and fast collision detection of convex bodies. We evaluate our approach on a wide set of problems using real robots, including tasks with multiple manipulators, sensing and branched plans, and mobile manipulation.

Generating Swept Volumes With Instantaneous Screw Axes

1994 ◽  
Author(s):  
Zeng-Jia Hu ◽  
Zhi-Kui Ling
Keyword(s):  
Moving Object ◽  
Ruled Surfaces ◽  
Screw Axis ◽  
Spherical Surfaces ◽  
Swept Volumes ◽  
Instantaneous Screw Axis ◽  
Swept Volume ◽  
Instantaneous Screw ◽  
Plane Polygon ◽  
Boundary Surfaces

Abstract The instantaneous screw axis is used in the generation of the swept volume of a moving object. The envelope theory is used to determine the boundary surfaces of the swept volume. Specifically, the envelope surfaces generated by a plane polygon, cylindrical and spherical surfaces are presented. Furthermore, the ruled surfaces generated by edges of the moving object are discussed.

More Problems Connected with Convexity

1968 ◽  
Vol 11 (3) ◽  
pp. 489-494 ◽  
Author(s):  
Z.A. Melzak
Keyword(s):  
Convex Sets ◽  
Infinite Sequence ◽  
Convex Bodies ◽  
Convex Polyhedra ◽  
Recent Book ◽  
Interior Points

This is a continuation of the author's article [3], and it contains further problems connected with the theory of convex sets in En. To the list of general references in [3] may be added the recent book [2] on convex polyhedra.1) Let A and B be two convex bodies in E2 and let a packing P = {B1, B2, …} be an infinite sequence of homothetic images of B sucn that:a)each Bn is a subset of A,b)no two of them share interior points,c)Area (A) = The existence of such packings is guaranteed by Vitali's Theorem. Let D(X) be the diameter of the set X and put .

Geometric Representation of Translational Swept Volumes and its Applications

1986 ◽  
Vol 108 (2) ◽  
pp. 113-119 ◽  
Author(s):  
M. C. Leu ◽  
S. H. Park ◽  
K. K. Wang
Keyword(s):  
Three Dimensional ◽  
Boundary Representation ◽  
Geometric Representation ◽  
Ray Casting ◽  
Three Dimensional Objects ◽  
Swept Volumes ◽  
Representation Method ◽  
Primitive Object ◽  
Swept Volume ◽  
Cylinders And Spheres

This paper presents a method for representing the geometries of translational swept volumes of three-dimensional objects which can be constructed by the union of three types of primitive objects: blocks, cylinders, and spheres. The representation method involves three major steps. First, the swept volume of each primitive object is modeled by a boundary representation. Second, based on ray-casting and scan-rendering methods, the boundary representation is converted into a ray in–out classification, which represents the rays entering and exiting from the primitive swept volume. Third, the ray in–out classifications for various primitive swept volumes are combined to represent the swept volume of an object constructed from the primitive objects. Examples are given to illustrate how swept-volume representations can be useful in the context of off-line NC and robot program verifications.

Distance Calculations in Motion Planning Problems With Interference Situations

1990 ◽  
Author(s):  
C. Y. Liu ◽  
R. W. Mayne
Keyword(s):  
Quadratic Form ◽  
Convex Polyhedron ◽  
Linear Inequality ◽  
Convex Bodies ◽  
Three Dimensional ◽  
Robot Path Planning ◽  
Contact Distance ◽  
Swept Volume ◽  
Planning Problems ◽  
Robot Path

Abstract This paper discusses distance calculations for three dimensional polyhedra with the assumption of convex bodies. An n-surface convex polyhedron is viewed as the intersection of n half-spaces and is represented by n linear inequality equations while the square of the distance between two points is of a quadratic form in terms of two sets of x-y-z coordinates. The static distance-to-contact between two non-interfering convex polyhedral shapes is then directly solvable by quadratic programming. Based on the concept of distance-past-contact, distance calculations for situations with interference are presented and tested in optimization based robot path planning examples. The distance evaluation is further investigated for the dynamic situations by a swept volume computation strategy. The approach is illustrated in examples with a moving robot link and a fixed obstacle.

Linear Octree Represented Tool Swept Volume Modeling on Complex Surface Machining

2012 ◽  
Vol 190-191 ◽  
pp. 699-704
Author(s):  
Xu Bing Chen ◽  
Chen Yu Shan ◽  
You Lun Xiong
Keyword(s):  
Storage Capacity ◽  
Local Coordinate System ◽  
Complex Surface ◽  
Minkowski Sum ◽  
Surface Machining ◽  
Novel Approach ◽  
Swept Volumes ◽  
Volume Modeling ◽  
Linear Octree ◽  
Swept Volume

In this paper, a novel approach of linear octree is employed to represent discrete tools and build their swept volumes along machining trajectories. Firstly, a data structure of linear octree is defined as the base of geometrical transformations. The linear octree can be extended into leaf nodes in the deepest level for simplifying homogeneous transformations, and all leaf nodes in the deepest level can also be concentrated into a linear octree for saving storage capacity inversely. Secondly, tool trajectories are interpolated as short lines, and swept volumes between neighbor interpolation points are defined as the Minkowski sum of their cell sets at both locations. Thirdly, equations of the rotation matrix for local coordinate system, roll, pitch and yaw angles of tool orientations are established to define the global rotation motions. Finally, a case of discrete sphere tool and its swept volume modeling are studied to validate the proposed approach.

scholarly journals Closed-Form Swept Volume of Implicit Surfaces

2000 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Jingzhou Yang ◽  
Denis Blackmore
Keyword(s):  
Closed Form ◽  
Implicit Surfaces ◽  
Parametric Surfaces ◽  
Rank Deficiency ◽  
Complex Shapes ◽  
Swept Volumes ◽  
Recent Developments ◽  
Swept Volume

Abstract Recent developments in formulations for generating swept volumes have made a significant impact on the efficiency of employing such algorithms and on the extent to which formulations can be used in representing complex shapes. In this paper, we outline a method for employing the representation of implicit surfaces using the Jacobian rank deficiency condition presented earlier for the sweep of parametric surfaces. A numerical and broadly applicable analytic formulation is developed that yields the exact swept volume.

Five-Axis Swept Volumes for Graphic NC Simulation and Verification

1989 ◽  
Author(s):  
K. Sambandan ◽  
K. K. Wang
Keyword(s):  
Nc Machining ◽  
Image Space ◽  
Numerical Control ◽  
Mathematical Basis ◽  
Nc Simulation ◽  
Swept Volumes ◽  
Nc Milling ◽  
Depth Buffer ◽  
Swept Volume ◽  
Five Axis

Abstract This paper explains in detail a simulator that has been developed for graphic verification of five-axis Numerical Control (NC) machining. Exact parametric representations for the surfaces generated by common NC milling cutters during five-axis motions have been derived using the theory of envelopes as the mathematical basis. Parts of these surfaces form the boundary of the total swept volume generated. For each cutting motion, the swept volume of the cutter is determined and then subtracted from the stock. The Boolean subtraction is done in the image space at the pixel level, using a modified depth-buffer algorithm. A shaded image of the “as machined” part at the end of each cutting motion is then displayed for verification.

Motion Planning With Convex Swept Volume Segments

1996 ◽  
Author(s):  
Chiusheng Wu ◽  
Roger W. Mayne
Keyword(s):  
Motion Planning ◽  
Moving Objects ◽  
Planning Process ◽  
Optimization Methods ◽  
Three Dimensions ◽  
Robot Motion ◽  
Optimization Strategy ◽  
Swept Volumes ◽  
Volume Strategy ◽  
Swept Volume

Abstract This paper presents a swept volume approach for distance-to-contact computation in motion planning. The approach is based on approximating the swept volumes of moving objects with convex segments formulated for the use of quadratic programming in distance-to-contact calculations. This swept volume strategy is designed to conservatively estimate the distance-to-contact between moving and static objects and is well suited for the planning of motions using optimization methods. It has been adapted to obtain convenient distance-to-contact gradient information which is an important factor in the application of efficient optimization algorithms to the motion planning process. The paper describes the generation of the swept volume segments and applies the process to examples of robot motion planning in three dimensions using an SQP optimization strategy.

Swept-Volume Computation for Virtual Reality Application of Machining Simulation

1999 ◽  
Author(s):  
Bilal Y. Maiteh ◽  
Ming C. Leu ◽  
Denis Blackmore ◽  
Guangyu Liu ◽  
Layek Abdel-Malek
Keyword(s):  
Virtual Reality ◽  
Nc Machining ◽  
Virtual Manufacturing ◽  
Virtual Space ◽  
Path Generation ◽  
Efficient Computation ◽  
Machining Simulation ◽  
Swept Volumes ◽  
Swept Volume ◽  
Cutter Path Generation

Abstract Growing interest in Virtual Reality (VR) over the past few years has led to the development of VR techniques for applications such as virtual manufacturing, virtual assembly, virtual training, etc. Most of these applications involve the moving of objects and interaction of them with the environment in virtual space. One foreseeable important application of virtual manufacturing is Numerically Controlled (NC) machining path generation and verification in a VR environment. In this application the efficient computation and accurate representation of swept volumes of the machining cutters is an important issue. This paper describes a fast and accurate method for generating the swept volume of a moving object undergoing an arbitrary translational and rotational motion, with application to NC machining simulation in a VR setting. The Sweep Differential Equation (SDE) method, which we initially developed for representing and computing the swept volumes of rigid moving objects and subsequently extended to objects that may deform during the course of motion, forms the basis for the VR application of NC cutter path generation and verification. An example is provided to demonstrate the effectiveness of the SDE method for simulation of multi-axis NC machining.

scholarly journals Collisions of Small Drops in a Turbulent Flow. Part III: Relative Droplet Fluxes and Swept Volumes

2006 ◽  
Vol 63 (8) ◽  
pp. 2123-2139 ◽  
Author(s):  
M. B. Pinsky ◽  
A. P. Khain ◽  
B. Grits ◽  
M. Shapiro
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Dissipation Rate ◽  
Reynolds Numbers ◽  
Distribution Functions ◽  
Cumulus Clouds ◽  
Droplet Motion ◽  
Sharp Maximum ◽  
Swept Volumes ◽  
Swept Volume

Abstract Swept volumes of cloud droplets with radii below 20 μm are calculated under conditions typical of atmospheric cloud turbulence characterized by enormous values of Reynolds numbers, high turbulent intermittency, and characteristic values of the dissipation rate. To perform the calculations, the motion equation for small droplets proposed by Maxey is generalized for Stokes numbers St > 0.1, which allows one to simulate relative droplet motion even for very high turbulence intensities typical of deep cumulus clouds. Analytical considerations show that droplet motion is fully determined by turbulent shears and the Lagrangian accelerations. A new statistical representation of a turbulent flow has been proposed based on the results of the scale analysis of turbulence characteristics and those related to the droplet motion. According to the method proposed, statistical properties of turbulent flow are represented by a set of noncorrelated samples of turbulent shears and Lagrangian accelerations. Each sample can be assigned to a certain point of the turbulent flow. Each such point can be surrounded by a small “elementary” volume with linear length scales of the Kolmogorov length scale, in which the Lagrangian acceleration and turbulent shears can be considered as uniform in space and invariable in time. This present study (Part III) investigates the droplet collisions in a turbulent flow when hydrodynamic droplet interaction (HDI) is disregarded. Using a statistical model, long series of turbulent shears and accelerations were generated, reproducing probability distribution functions (PDF) at high Reynolds numbers, as they were obtained in recent laboratory and theoretical studies. Swept volumes of droplets are calculated for each sample of an acceleration–shear pair, and the PDF of swept volumes is calculated for turbulent parameters typical of cloud turbulence. The effect of turbulent flow intermittency manifests itself in two aspects: 1) an increase of swept volume variance with increasing Reynolds number, and 2) formation of the swept volume PDF that has a sharp maximum and an elongated tail. In spite of the fact that the magnitude of the mean swept volume increases significantly with Reynolds number and the dissipation rate, this increase does not exceed ∼60% of pure gravity values even under turbulent conditions typical of strong cumulus clouds. A comparison with the classical results of Saffman and Turner is presented and discussed.

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