A Comparative Study of Dirichlet and Neumann Conditions for Path Planning through Harmonic Functions

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

doi:10.1007/3-540-46080-2_46

Cited by 5 publications

(1 citation statement)

References 6 publications

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“…With such a systematic parameterization method for a 3D region in place, one can exploit it for many applications like path planning. Karnik et al [10] and Voruganti et al [25] have emphasized the utility of potential field based approaches to path planning. Hence, it can be seen that volumetric parameterization of a domain through mapping is a good approach to path planning.…”

Section: Case 2: Starfishmentioning

confidence: 99%

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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Section: Case 2: Starfishmentioning

confidence: 99%

Domain Mapping for Volumetric Parameterization using Harmonic Functions

Gupta¹,

Voruganti²,

DasGupta³

2014

Computer-Aided Design and Applications

Self Cite

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The dynamic wave expansion neural network model for robot motion planning in time-varying environments

2005

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Path Planning Simulation Using Harmonic Potential Fields Through Four Point-Edgsor Method via 9-Point Laplacian

Saudi

Sulaiman

2016

Jurnal Teknologi

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This paper presents our study on a simulation of path planning for indoor robot that relies on the use of Laplace’s equation to constrain the generation of Harmonic Potential Fields (HPF). The computation of HPF requires immense amount of computing resources, particularly when the size of environment is large. In the past, fast iterative methods that apply the use of half-sweep iteration and block technique are suggested. In this study, faster iterative method known as Four Point-Explicit Decoupled Group Successive Over relaxation via 9-Point Laplacian (4-EDGSOR-9L) is introduced. Essentially, the 4-EDGSOR-9L is actually a variant of block SOR iterative method based on four points that employs half-sweep iteration and utilizes 9-Point Laplacian discretization scheme. Once the HPF is obtained, the standard Gradient Descent Search (GDS) technique is performed for path tracing to the goal point.

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A Comparative Study of Dirichlet and Neumann Conditions for Path Planning through Harmonic Functions

Cited by 5 publications

References 6 publications

Domain Mapping for Volumetric Parameterization using Harmonic Functions

Domain Mapping for Volumetric Parameterization using Harmonic Functions

The dynamic wave expansion neural network model for robot motion planning in time-varying environments

Path Planning Simulation Using Harmonic Potential Fields Through Four Point-Edgsor Method via 9-Point Laplacian

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