On the Skeleton of Simple CSG Objects

1993 ◽  
Vol 115 (1) ◽  
pp. 87-94 ◽  
Author(s):  
D. Dutta ◽  
C. M. Hoffmann
Keyword(s):  
Computer Vision ◽  
Motion Planning ◽  
Mesh Generation ◽  
Minimum Distance ◽  
Medial Axis

The skeleton (medial-axis surface) of an object is the locus of all points in the object’s interior that have equal minimum distance from at least two distinct parts of the boundary. The skeleton can be used in blending, motion planning, medical tomography, computer vision, and in mesh generation. We discuss some simple but frequently encountered shape elements of the skeleton of CSG objects, and investigate properties of trimming surfaces delimiting the faces of skeletons.

scholarly journals A Geometric Investigation of the Skeleton of CSG Objects

1990 ◽  
Author(s):  
Debasish Dutta ◽  
Christoph M. Hoffmann
Keyword(s):  
Computer Vision ◽  
Motion Planning ◽  
Mesh Generation ◽  
Medial Axis ◽  
Geometric Analysis ◽  
Constructive Solid Geometry ◽  
Solid Geometry

Abstract We sketch an algorithm for computing the skeleton (medial-axis surface) of an object defined using constructive solid geometry (CSG). The skeleton can be used in blending, motion planning, medical tomography, computer vision, and in mesh generation. We also present a geometric analysis of Voronoi surfaces from which the skeleton is composed, for a large number of surface pairs arising often in practice.

Motion Planning Using Medial Axis

1992 ◽  
Vol 25 (28) ◽  
pp. 135-140 ◽  
Author(s):  
Yangsheng Xu ◽  
Raju Mattikalli ◽  
Pradeep Khosla
Keyword(s):  
Motion Planning ◽  
Medial Axis

Obstacle Avoidance Influence Coefficients for Manipulator Motion Planning

2005 ◽  
Author(s):  
Troy Harden ◽  
Chetan Kapoor ◽  
Delbert Tesar
Keyword(s):  
Motion Planning ◽  
Obstacle Avoidance ◽  
Minimum Distance ◽  
Higher Order ◽  
Second Order ◽  
Distance Functions ◽  
Cluttered Environments ◽  
Finite Difference Approximations ◽  
Planning Decisions ◽  
Influence Coefficients

Motion planning in cluttered environments is a weakness of current robotic technology. While research addressing this issue has been conducted, few efforts have attempted to use minimum distance rates of change in motion planning. Geometric influence coefficients provide extraordinary insight into the interactions between a robot and its environment. They isolate the geometry of distance functions from system inputs and make the higher-order properties of minimum distance magnitudes directly available. Knowledge of the higher order properties of minimum distance magnitudes can be used to predict the future obstacle avoidance, path planning, and/or target acquisition state of a manipulator system and aid in making intelligent motion planning decisions. Here, first and second order geometric influence coefficients for minimum distance magnitudes are rigorously developed for several simple modeling primitives. A general method for similar derivations using new primitives and an evaluation of finite difference approximations versus analytical second order coefficient calculations are presented. Two application examples demonstrate the utility of minimum distance magnitude influence coefficients in motion planning.

scholarly journals Multiquery Motion Planning in Uncertain Spaces: Incremental Adaptive Randomized Roadmaps

2019 ◽  
Vol 29 (4) ◽  
pp. 641-654
Author(s):  
Weria Khaksar ◽  
Md Zia Uddin ◽  
Jim Torresen
Keyword(s):  
Motion Planning ◽  
Minimum Distance ◽  
Planning Problem ◽  
Grid Structure ◽  
Discrete Time System ◽  
Environment Map ◽  
Sample Classification ◽  
Adjustment Strategy ◽  
Hybrid Sample ◽  
Planning Problems

Abstract Sampling-based motion planning is a powerful tool in solving the motion planning problem for a variety of different robotic platforms. As its application domains grow, more complicated planning problems arise that challenge the functionality of these planners. One of the main challenges in the implementation of a sampling-based planner is its weak performance when reacting to uncertainty in robot motion, obstacles motion, and sensing noise. In this paper, a multi-query sampling-based planner is presented based on the optimal probabilistic roadmaps algorithm that employs a hybrid sample classification and graph adjustment strategy to handle diverse types of planning uncertainty such as sensing noise, unknown static and dynamic obstacles and an inaccurate environment map in a discrete-time system. The proposed method starts by storing the collision-free generated samples in a matrix-grid structure. Using the resulting grid structure makes it computationally cheap to search and find samples in a specific region. As soon as the robot senses an obstacle during the execution of the initial plan, the occupied grid cells are detected, relevant samples are selected, and in-collision vertices are removed within the vision range of the robot. Furthermore, a second layer of nodes connected to the current direct neighbors are checked against collision, which gives the planner more time to react to uncertainty before getting too close to an obstacle. The simulation results for problems with various sources of uncertainty show a significant improvement compared with similar algorithms in terms of the failure rate, the processing time and the minimum distance from obstacles. The planner is also successfully implemented and tested on a TurtleBot in four different scenarios with uncertainty.

scholarly journals A Grid-Based Motion Planning Approach for Coherent Groups

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yue-wen Fu ◽  
Meng Li ◽  
Jia-hong Liang ◽  
Xiao-qian Hu
Keyword(s):  
Motion Planning ◽  
Medial Axis ◽  
Evaluation Function ◽  
Degree Relative ◽  
Deformation Degree ◽  
Probabilistic Roadmap ◽  
Planning Approach ◽  
Constant Area ◽  
Grid Based

This paper presents a novel motion planning approach for coherent groups with constant area, and it integrates C-L method into the probabilistic roadmap algorithm with sampling on the medial axis (MAPRM). In the preprocessing phase, the group is discretized into a grid-set which represents the configuration of the group. Then, a number of samples are generated on workspace by medial axis technique. These samples are extended into group’s configuration nodes of the roadmap using an extending strategy. Also, the group's deformation degree relative to the desired shape is introduced to improve the evaluation function. It gives users more flexibility to determine the respective weights of the group’s deformation degree and its distance to the goal in the query phase. After that, a novel local planner is constructed to connect any two neighbor configurations by using C-L method and the improved evaluation function. Experiments show that our approach is able to find paths for the coherent group efficiently and keep its area invariant when moving toward the goal.

Collision-free motion planning for two articulated robot arms using minimum distance functions

Robotica ◽  
1990 ◽  
Vol 8 (2) ◽  
pp. 137-144 ◽  
Author(s):  
C. Chang ◽  
M. J. Chung ◽  
Z. Bien
Keyword(s):  
Motion Planning ◽  
Minimum Distance ◽  
Three Dimensional ◽  
Distance Functions ◽  
Free Motion ◽  
Planning Problem ◽  
Robot Arm ◽  
Robot Arms ◽  
Nonlinear Minimization ◽  
Articulated Robot

SummaryThis paper presents a collision-free motion planning method of two articulated robot arms in a three dimensional common work space. Each link of a robot arm is modeled by a cylinder ended by two hemispheres, and the remaining wrist and hand is modeled by a sphere. To describe the danger of collision between two modeled objects, minimum distance functions, which are defined by the Euclidean norm, are used. These minimum distance functions are used to describe the constraints that guarantee no collision between two robot arms. The collision-free motion planning problem is formulated as a pointwise constrained nonlinear minimization problem, and solved by a conjugate gradient method with barrier functions. To improve the minimization process, a simple grid technique is incorporated. Finally, a simulation study is presented to show the significance of the proposed method.

A family of skeletons for motion planning and geometric reasoning applications

2011 ◽  
Vol 25 (4) ◽  
pp. 375-392
Author(s):  
Ata A. Eftekharian ◽  
Horea T. Ilieş
Keyword(s):  
Motion Planning ◽  
Medial Axis ◽  
A Priori ◽  
Three Dimensional ◽  
Geometric Reasoning ◽  
Spatial Configurations ◽  
Planning Algorithm ◽  
Logic Operations ◽  
Path Planning Algorithm ◽  
Special Case

AbstractThe task of planning a path between two spatial configurations of an artifact moving among obstacles is an important problem in practically all geometrically intensive applications. Despite the ubiquity of the problem, the existing approaches make specific limiting assumptions about the geometry and mobility of the obstacles, or those of the environment in which the motion of the artifact takes place. We present a strategy to construct a family of paths, or roadmaps, for two- and three-dimensional solids moving in an evolving environment that can undergo drastic topological changes. Our approach is based on a potent paradigm for constructing geometric skeletons that relies on constructive representations of shapes with R-functions that operate on real-valued half-spaces as logic operations. We describe a family of skeletons that have the same homotopy as that of the environment and contains the medial axis as a special case. Of importance, our skeletons can be designed so that they are “attracted to” or “repulsed by” prescribed spatial sites of the environment. Moreover, the R-function formulation suggests the new concept of a medial zone, which can be thought of as a “thick” skeleton with significant applications for motion planning and other geometric reasoning applications. Our approach can handle problems in which the environment is not fully known a priori, and intrinsically supports local and parallel skeleton computations for domains with rigid or evolving boundaries. Furthermore, our path planning algorithm can be implemented in any commercial geometric kernel, and has attractive computational properties. The capability of the proposed technique are explored through several examples designed to simulate highly dynamic environments.

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