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Approximate motion planning and the complexity of the boundary of the union of simple geometric figures

Helmut Alt, Rudolf Fleischer, Michael Kaufmann, Kurt Mehlhorn, Stefan Näher, Stefan Schirra, Christian Uhrig
1990 Proceedings of the sixth annual symposium on Computational geometry - SCG '90  
Similar results for the union of other simple geometric figures such as triangles and wedges are also presented.  ...  We show further that the complexity (= number of vertices) of the boundary of n bow-ties (c.f. Figure 1.1) is O(n).  ...  We also show complexity bounds for the free space defined by other simple geometric figures, e.g. wedges and triangles, which we believe to be of independent interest.  ... 
doi:10.1145/98524.98592 dblp:conf/compgeom/AltFKMNSU90 fatcat:dxuvubdzzfe2zesbxgaqotd5oq

Accurate Minkowski sum approximation of polyhedral models

Gokul Varadhan, Dinesh Manocha
2006 Graphical Models  
Our algorithm is relatively simple to implement and works well on complex models.  ...  Brake Hub Rod Brake Hub ⊕ Rod Bunny Bunny Offset Figure 1 . The images on the left show the Minkowski sum of Brake Hub and Rod models.  ...  We thank Danny Halperin for many fruitful discussions on the complexity and practical implementations of Minkowski sum.  ... 
doi:10.1016/j.gmod.2005.11.003 fatcat:cyyrkoevgba33hzinq5woaeevy

Path Planning with Obstacle Avoidance Based on Normalized R-Functions

Songqiao Tao, Juan Tan
2018 Journal of Robotics  
case of given motion parameters.  ...  Existing methods for path planning with obstacle avoidance need to check having the interference between a moving part and an obstacle at iteration and even to calculate their shortest distance in the  ...  Acknowledgments This work was supported by research team of Wuhan Technical College of Communication (no. CX2018B03).  ... 
doi:10.1155/2018/5868915 fatcat:jcmratu44bf5zbayyvgxcptozy

Topology preserving surface extraction using adaptive subdivision

Gokul Varadhan, Shankar Krishnan, TVN Sriram, Dinesh Manocha
2004 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
We use our subdivision algorithm for accurate boundary evaluation of CSG combinations of polyhedra and low degree algebraic primitives, translational motion planning, model simplification and remeshing  ...  The running time of our algorithm varies between a few seconds for simple models composed of a few thousand triangles to tens of seconds for complex polyhedral models represented using hundreds of thousands  ...  Acknowledgments We would like to thank David Applegate for providing us the QSOPT software and a modified dual LP formulation.  ... 
doi:10.1145/1057432.1057464 fatcat:7eh435u5tba6fliphbphvsng5e

Deep Neural Networks for Swept Volume Prediction Between Configurations [article]

Hao-Tien Lewis Chiang, Aleksandra Faust, Lydia Tapia
2018 arXiv   pre-print
Second, in sampling-based motion planning, SV is an ideal distance metric, because it correlates to the likelihood of success of the expensive local planning step between two sampled configurations.  ...  Results for two robots, a 6 degree of freedom (DOF) rigid body and a 7 DOF fixed-based manipulator, indicate that the network estimations are very close to the true size of SV and is more than 1500 times  ...  SV is useful in many applications such as geometric modeling [6] , robot workspace analysis [2] , collision avoidance [11] and motion planning [16] .  ... 
arXiv:1805.11597v1 fatcat:dkzjk56mlbhjnmeouaifqq32ny

Computing swept volumes

Steven Abrams, Peter K. Allen
2000 Journal of Visualization and Computer Animation  
A polyhedral approximation to the volume swept by this moving object is computed and output in a typical boundary representation.  ...  The swept volume problem is practical, dif®cult and interesting enough to have received a great deal of attention over the years, and the literature contains much discussion of methods for computing swept  ...  We would also like to thank Professor Gerd Hirzinger and Dr Max Fischer from the German Aerospace Center (DLR) for providing us with models of their robotic hand.  ... 
doi:10.1002/1099-1778(200005)11:2<69::aid-vis219>3.0.co;2-7 fatcat:5ra5q6hkfjdyjmgdmbjea6x3y4

Efficient geometrical obstacle reshaping for inevitable collision states avoidance

H. Bastani, H.M.-M. Sadeghi
2009 2008 IEEE International Conference on Robotics and Biomimetics  
Classical motion planners and most of navigation routines discard dynamics of the system and therefore fail in some special conditions.  ...  Deformed state space is then fed into the planner and navigation unit in order to move the vehicle, safely. Bounded complexity of the algorithm makes it proper to be used in realtime applications.  ...  ACKNOWLEDGMENT Authors would like to be thankful to the insights on the problem driven by Prof. Stefano Carpin, as well as constructive discussions and feedbacks of Gorkem Erinc and Dr.  ... 
doi:10.1109/robio.2009.4913072 dblp:conf/robio/BastaniS08 fatcat:ctwhbweg25a57m2ka6uuhjhf4a

Polygonal boundary approximation for a 2D general sweep based on envelope and boolean operations

Joo-Haeng Lee, Sung Je Hong, Myung-Soo Kim
2000 The Visual Computer  
The authors wish to acknowledge the financial support of the Korea Research Foundation in the program year of 1998.  ...  For a simple approximation of the swept volume, a sequence of unions may be applied to densely sampled instances of a moving object along its motion trajectory.  ...  When we make a union of two alternative approximations of a Minkowski sum, we get a smoother boundary of the Minkowski sum. Figures 26 and 27 illustrate how this approach works.  ... 
doi:10.1007/s003710050209 fatcat:6pnvemsubjcl5atnkfhga7qlqe

A comparison of sampling strategies for computing general sweeps

Hüseyin Erdim, Horea T. Ilieş
2010 Computer-Aided Design  
of features in terms of performance and accuracy for the boundary evaluation of general sweeps.  ...  Sweeping moving objects has become one of the basic geometric operations used in engineering design, analysis and physical simulation.  ...  The accuracy of the octree-based sampling as a function of the number of tested points in each octree cell.  ... 
doi:10.1016/j.cad.2009.06.002 fatcat:eo5hprvsbjctze5s7rpgqj6faa

Reliable sweeps

Xinyu Zhang, Young J. Kim, Dinesh Manocha
2009 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling on - SPM '09  
We highlight the performance of our algorithm on many complex benchmarks that arise in geometric and solid modeling, motion planning and CNC milling applications.  ...  Abstract We present a simple algorithm to generate a topology-preserving, error-bounded approximation of the outer boundary of the volume swept by a polyhedron along a parametric trajectory.  ...  Acknowledgements This research work was supported in part by the KRF Grant funded by the Korean Government (KRF-2007-331-D00400) and the IT R&D program of MKE/MCST/KOCCA (2008-F-033-02, Development of  ... 
doi:10.1145/1629255.1629306 dblp:conf/sma/ZhangKM09 fatcat:x2dbvujikvd3jl6fs7uyxyfg4m

Page 6327 of Mathematical Reviews Vol. , Issue 93k [page]

1993 Mathematical Reviews  
boundary of the union of simple geometric figures.  ...  68097 68U05 52B55 68Q25 Alt, Helmut (D-FUB); Fleischer, Rudolf; Kaufmann, Michael; Mehlhorn, Kurt; Naher, Stefan; Schirra, Stefan; Uhrig, Christian Approximate motion planning and the complexity of the  ... 

Algorithms for planar geometric models [chapter]

Chanderjit Bajaj, Myung-Soo Kim
1988 Lecture Notes in Computer Science  
We consider planar geometric models given by an explicit boundary of 0 en) algebraic curve segments of maximum degree d.  ...  Both operations, besides being solutions to interesting computational geometry problems, prove useful in motion planning with planar geometric models. ...  ...  For gross motion planning, one may compute the C-Space obstacles for the convex hull of the original planar models.  ... 
doi:10.1007/3-540-19488-6_107 fatcat:s7pmuaedtjh7lizfrdrxnxzdeu

KABouM: Knowledge-Level Action and Bounding Geometry Motion Planner

Andre Gaschler, Ronald P. A. Petrick, Oussama Khatib, Alois Knoll
2018 The Journal of Artificial Intelligence Research  
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.  ...  Acknowledgements The authors would like to thank Torsten Kröger, Svetlana Nogina, Quirin Fischer, and Sören Jentzsch for their help with the implementation and evaluation, and Markus Rickert for his comments  ... 
doi:10.1613/jair.5560 fatcat:c7sga7fdffg4rl3k5vypntq5he

Achieving Dextrous Grasping by Integrating Planning and Vision-Based Sensing

Christian Bard, Christian Laugier, Christine Milési-Bellier, Jocelyne Troccaz, Bill Triggs, Gianni Vercelli
1995 The international journal of robotics research  
determination of appropriate grasping con gurations from computed'preshapes' of the hand, and the automatic generation and execution of hand/arm motions using a hybrid geometric path planner and a hybrid  ...  E ective grasping requires a combination of sensing and planning capabilities: sensing to construct a well-adapted model of the situation and to guide the execution of the task, and planning to determine  ...  We would like to thank the`Region Rhône-Alpes' for allowing LIFIA to acquire the Salisbury hand, and Enrico Grosso from DIST for his help in the reconstruction of voxmaps.  ... 
doi:10.1177/027836499501400504 fatcat:ibpmj2cea5fbfjrrseqifrlncm

Page 2967 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
The computational complexity of a number of algorithms in com- puter graphics and motion planning depends on the combinatorial complexity of the union of simple geometric figures.  ...  The main result of this paper is that the union of n triangles whose angles are at least 6 has O(n) holes and its boundary is of  ... 
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