Solving some optimal path planning problems using an approach based on measure theory

Borzabadi, Akbar Hashemi; Kamyad, Ali Vahidian; Farahi, Mohammad Hadi; Mehne, Hamed Hashemi

doi:10.1016/j.amc.2005.01.035

Cited by 10 publications

(11 citation statements)

References 8 publications

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“…There are many methods for solving ONP (2),(3) and (5) [1][2][3]. For example Borzabadi [3] defines the artificial control function u( t ) as…”

Section: The Solution Of Onp'smentioning

confidence: 99%

“…In reference [2] two novel approaches, constrained optimization and semi-infinite constrained optimization, for unmanned under water vehicle are considered. In reference [3] is presented a new approach based on measure theory for finding approximation optimal path planning problem in the present of obstacles. In all of above references the distance between rigid object and obstacles are assumed crisp values.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fuzzy Path Planning In A Plane With Stationary Obstacles

Zamirian¹,

Kamyad²

2011

J. Math. Computer Sci.

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In this paper a new approach for finding optimal path planning in a plane with stationary obstacles is discussed. At first, we consider a movable rigid object in a plane with stationary obstacles. The goal is to find the shortest path planning which brings rigid object from a given initial point to a given final point such that the length of path be minimized and distance between object and obstacles be maximized. By considering the length of path and the distance between rigid object with obstacles as objective functions, we obtain a multi-objective problem. Because of the imprecise nature of decision maker's judgment, these multiple objectives are viewed as fuzzy variables. Then we determine intervals for the value of objective functions such that these intervals for the distance between rigid object and obstacles are given by decision maker, and for the length of path is achieved by solving two optimal nonlinear problems (ONP). Now, we define a decreasing or increasing membership function for any objective functions on achieved intervals. Then the optimal __________________________________________

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“…There are many methods for solving ONP (2),(3) and (5) [1][2][3]. For example Borzabadi [3] defines the artificial control function u( t ) as…”

Section: The Solution Of Onp'smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fuzzy Path Planning In A Plane With Stationary Obstacles

Zamirian¹,

Kamyad²

2011

J. Math. Computer Sci.

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“…Finding an optimal path planning is one of the most applicable problems, especially in the robot industry, the military and recently in surgery planning [1]. Latombe [11] has gathered novel methods for path planning in the presence of obstacles.…”

Section: Introductionmentioning

confidence: 99%

“…Wang et al [28] have considered two novel approaches: constrained optimization and semi-infinite constrained optimization for unmanned underwater vehicle path planning. Borzabadi et al [1] have presented a new approach based on measure theory for finding the approximate optimal path in the presence of obstacles. Zamirian et al [29] have proposed an applicable method for solving the shortest path problem.…”

Section: Introductionmentioning

confidence: 99%

A Wavelet Collocation Scheme for Solving Some Optimal Path Planning Problems

Mortezaee

Nazemi

2016

ANZIAM J.

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We consider an approximation scheme using Haar wavelets for solving optimal path planning problems. The problem is first expressed as an optimal control problem. A computational method based on Haar wavelets in the time domain is then proposed for solving the obtained optimal control problem. A Haar wavelets integral operational matrix and a direct collocation method are used to find an approximate optimal trajectory of the original problem. Numerical results are also presented for several examples to demonstrate the applicability and efficiency of the proposed method.

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“…To find an safe path in a dangerous environment for a mobile robot is an essential requirement for the success of any such mobile robot project. When an optimal path planning problem is formulated as an optimization problem, solving the problem is also of great importance in theoretical and computational investigations [1] The main goal of the robot path planning is to search a safe path for a mobile robot, to make the robot move from the start point to the destination point without collision with obstacles. Also, the path is often required to be optimal in order to reduce energy consumption and communication delay.…”

Section: Introductionmentioning

confidence: 99%