Path Planning with Obstacle Avoidance Based on Normalized R-Functions
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 case of given motion parameters. Besides, the tasks like collision-checking and minimum-distance ca...
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Published in | Journal of Robotics Vol. 2018; no. 2018; pp. 1 - 10 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cairo, Egypt
Hindawi Publishing Corporation
01.01.2018
Hindawi Hindawi Limited Wiley |
Subjects | |
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Abstract | 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 case of given motion parameters. Besides, the tasks like collision-checking and minimum-distance calculating themselves are complicated and time-consuming. Rigorous mathematical analysis might be a practical way for dealing with the above-mentioned problems. An R-function is a real-valued function whose properties are fully determined by corresponding attributes of their parameters, which is usually applied to express a geometrical object. Thus, a signed distance function based on R-functions is created to represent whether two objects intervene and their level of intervention or separation. As the signed function is continuous and differentiable, the gradient information of the objective function guides a moving part to avoid its obstacles and to approach its target position rapidly. Therefore, a path planning approach with obstacle avoidance based on normalized R-functions is proposed in this paper. A discrete convex hull approach is adopted to solve the problem that R-function is inappropriate to represent a geometric object with some curves or surfaces, and pendent points and edges are generated in Boolean operations. Besides, a normalized approach ensures accuracy calculation of signed distance function. Experimental results have shown that the presented approach is a feasible way for path planning with obstacle avoidance. |
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AbstractList | 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 case of given motion parameters. Besides, the tasks like collision-checking and minimum-distance calculating themselves are complicated and time-consuming. Rigorous mathematical analysis might be a practical way for dealing with the above-mentioned problems. An R-function is a real-valued function whose properties are fully determined by corresponding attributes of their parameters, which is usually applied to express a geometrical object. Thus, a signed distance function based on R-functions is created to represent whether two objects intervene and their level of intervention or separation. As the signed function is continuous and differentiable, the gradient information of the objective function guides a moving part to avoid its obstacles and to approach its target position rapidly. Therefore, a path planning approach with obstacle avoidance based on normalized R-functions is proposed in this paper. A discrete convex hull approach is adopted to solve the problem that R-function is inappropriate to represent a geometric object with some curves or surfaces, and pendent points and edges are generated in Boolean operations. Besides, a normalized approach ensures accuracy calculation of signed distance function. Experimental results have shown that the presented approach is a feasible way for path planning with obstacle avoidance. 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 case of given motion parameters. Besides, the tasks like collision-checking and minimum-distance calculating themselves are complicated and time-consuming. Rigorous mathematical analysis might be a practical way for dealing with the above-mentioned problems. An R -function is a real-valued function whose properties are fully determined by corresponding attributes of their parameters, which is usually applied to express a geometrical object. Thus, a signed distance function based on R -functions is created to represent whether two objects intervene and their level of intervention or separation. As the signed function is continuous and differentiable, the gradient information of the objective function guides a moving part to avoid its obstacles and to approach its target position rapidly. Therefore, a path planning approach with obstacle avoidance based on normalized R -functions is proposed in this paper. A discrete convex hull approach is adopted to solve the problem that R -function is inappropriate to represent a geometric object with some curves or surfaces, and pendent points and edges are generated in Boolean operations. Besides, a normalized approach ensures accuracy calculation of signed distance function. Experimental results have shown that the presented approach is a feasible way for path planning with obstacle avoidance. |
Audience | Academic |
Author | Tan, Juan Tao, Songqiao |
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Cites_doi | 10.1177/02783640122067453 10.1016/j.mcm.2004.05.001 10.1016/j.gmod.2004.01.003 10.1007/978-3-642-39482-9_39 10.1177/0278364911406761 10.1115/1.2926574 10.1142/S0218195999000108 10.1007/s10846-012-9776-4 10.1007/s10846-011-9595-z 10.1002/rob.20014 10.1016/j.robot.2015.02.007 10.1115/1.2926575 10.1163/016918611X603855 10.1109/MRA.2008.921540 10.1163/156855306775275530 10.1002/asjc.98 10.1016/j.robot.2016.08.001 10.1109/TRO.2006.870668 10.1016/j.ast.2011.02.006 10.1109/ACCESS.2014.2302442 10.1163/156855300741960 10.1109/TRO.2014.2309836 10.1007/s13272-016-0197-0 10.1007/BF01908629 10.1177/027836498600500106 10.1016/S0096-3003(02)00832-9 |
ContentType | Journal Article |
Copyright | Copyright © 2018 Songqiao Tao and Juan Tan. COPYRIGHT 2018 Hindawi Limited Copyright © 2018 Songqiao Tao and Juan Tan. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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SubjectTerms | Analysis Boolean algebra Collision dynamics Computer simulation Continuity (mathematics) Curves Genetic algorithms Iterative methods Mathematical analysis Numerical analysis Obstacle avoidance Parameters Path planning Planning Product design Robotics Robots Unmanned aerial vehicles |
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Title | Path Planning with Obstacle Avoidance Based on Normalized R-Functions |
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