A comparative study of Dirichlet and Neumann conditions for path planning through harmonic functions

Karnik, Madhuri; DasGupta, Bhaskar; Eswaran, V.

doi:10.1016/j.future.2003.07.008

Cited by 5 publications

(1 citation statement)

References 5 publications

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“…Among heuristic approaches, many artificial potential (AP) 3-9 methods provide simple and effective motion planners for practical purpose, but they have limitations of spurious local trap and oscillation near multi-obstacles. For large scale configuration spaces, the complete algorithms [10][11][12][13][14][15] , although a bit computationally intractable is more attractive for its global optimum, especially in case of robots in supervision, i.e. the position and orientation of the robot could be determined.…”

Section: Introductionmentioning

confidence: 99%

A new strategy for robot path planning based on the finite element method

Cao

Meng

Wang

et al. 2008

Seventh International Symposium on Instrumentation and Control Technology: Sensors and Instruments, Computer Simulation, and Ar

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This paper discusses a new model that integrates the environment information for the robot path planning. This model could be regarded as a generalization of the artificial potential (AP) method. The path with the least turning angles, i.e. the smoothest, is defined as the optimal path. The finite element method is used to construct global optimum path planning strategy for a robot in a known environment for both static and dynamic cases. Simulation results show that this method is feasible for the path planning of a point robot in a complicated environment.

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Section: Introductionmentioning

confidence: 99%

A new strategy for robot path planning based on the finite element method

Cao

Meng

Wang

et al. 2008

Seventh International Symposium on Instrumentation and Control Technology: Sensors and Instruments, Computer Simulation, and Ar

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Robotic Motion Using Harmonic Functions and Finite Elements

Garrido

Moreno

Blanco

et al. 2009

J Intell Robot Syst

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The harmonic functions have proved to be a powerful technique for motion planning in a known environment. They have two important properties: given an initial point and an objective in a connected domain, a unique path exists between those points. This path is the maximum gradient path of the harmonic function that begins in the initial point and ends in the goal point. The second property is that the harmonic function cannot have local minima in the interior of the domain (the objective point is considered as a border). This paper proposes a new method to solve Laplace's equation. The harmonic function solution with mixed boundary conditions provides paths that verify the smoothness and safety considerations required for mobile robot path planning. The proposed approach uses the Finite Elements Method to solve Laplace's equation, and this allows us to deal with complicated shapes of obstacles and walls. Mixed boundary conditions are applied to the harmonic function to improve the quality of the trajectories. In this way, the trajectories are smooth, avoiding the corners of walls and obstacles, and the potential slope is not too small, avoiding the difficulty of the numerical calculus of the trajectory.Results show that this method is able to deal with moving obstacles, and even for non-holonomic vehicles. The proposed method can be generalized to 3D or more dimensions and it can be used to move robot manipulators.

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Domain Mapping for Volumetric Parameterization using Harmonic Functions

Gupta¹,

Voruganti²,

DasGupta³

2014

Computer-Aided Design and Applications

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Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the boundary of a 3D model (which is a surface). Volumetric parameterization is typically helpful in solving complicated geometric problems pertaining to shape matching, morphing, path planning of robots, and isogeometric analysis etc. A novel method is proposed in which a volume parameterization is developed by mapping a general nonconvex (genus-0) domain to its topologically equivalent convex domain. In order to achieve a continuous and bijective mapping of a domain, first we use the harmonic function to establish a potential field over the domain. The gradients of the potential values are used to track the streamlines which originate from the boundary and converge to a single point, referred to as the shape center. Each streamline approaches the shape center at a unique polar angle () and an azimuthal angle () . Once all the three parameters (potential value , polar angle , azimuthal angle ) necessary to represent any point in the given domain are available, the domain is said to be parameterized. Using our method, given a 3D non-convex domain, we can parameterize the surface as well as the interior of the domain. The proposed method is implemented and the algorithm is tested on many standard cases to demonstrate the effectiveness.

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A comparative study of Dirichlet and Neumann conditions for path planning through harmonic functions

Cited by 5 publications

References 5 publications

A new strategy for robot path planning based on the finite element method

A new strategy for robot path planning based on the finite element method

Robotic Motion Using Harmonic Functions and Finite Elements

Domain Mapping for Volumetric Parameterization using Harmonic Functions

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