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Exploração direcionadaAlgoritmo
l Ativa e obtém as leituras dos sensores;
l Realiza a atualização local do mapa;
l Atualiza o atributo potencial das células da região visitada;
l Determina a preferência das regiões do ambiente e associa um valor de distorção às células da região.
l Calcula o vetor gradiente descendente da posição do robô;
l Desloca-se seguindo a direção definida por este gradiente;
l Repete o processo até que todo o ambiente esteja completamente explorado.
Exploração direcionadaAmbientes de Teste
Exploração direcionada
Com preferência Sem preferência
Exploração direcionada
Ambientes de Teste
Numeros de Passos Numeros de Visitas
Exploração direcionada
Com preferência Sem preferência
Exploração direcionada
Numeros de Passos Numeros de Visitas
Ambientes de Teste
Exploração direcionada
Ambiente Simulado SLAM + Exploração Gulosa
SLAM + Exploração Integrada
Exploração direcionada
Ambiente Simulado SLAM + Exploração Gulosa
SLAM + Exploração Integrada
Planejador BVP
Planejador BVP
Hierarchical BVPl Combination of BVP Path Planning and the Full Multigrid
method (FMG) [9].
l FMG solves PDE through a combination of solutions at several resolution levels.
Hierarchical BVP
(1)
(2)
Considering the error of approximation
Ae = �Ap̃and using eq. (2), we obtain
where r is the residual and defined by
The error is relaxed
and used to correct the potential
Assuming the operator , eq. 1 becomes
Hierarchical BVP
Hierarchical BVP
Hierarchical BVPOperators:
Restriction (R) Prolongation (P)
Full weighting restriction Bilinear interpolation
Hierarchical BVP
Level 0
33 x 33
Hierarchical BVP
Level 0
33 x 33 Solves the coarsest level
Hierarchical BVP
Level 0
33 x 33
The robot starts the navigation in this level
Hierarchical BVP
prolongs the potential
Level 0 Level 1
33 x 33 65 x 65
Hierarchical BVP
Level 0 Level 1
33 x 33 65 x 65
restricts the residual
Hierarchical BVP
Level 0 Level 1
33 x 33 65 x 65
restricts the residual
Compute the error approximation
Hierarchical BVP
prolongs the error and updates the potential
Level 0 Level 1
33 x 33 65 x 65
restricts the residual
Hierarchical BVP
prolongs the error and updates the potential
Level 0 Level 1
33 x 33 65 x 65
restricts the residual
The robot can navigate using the potential field at
this level
Hierarchical BVP
prolongation prolongs the potential
Level 0 Level 1 Level 2
33 x 33 65 x 65 129 x 129
Hierarchical BVP
Level 0 Level 1 Level 2
33 x 33 65 x 65 129 x 129
restricts the residual
Hierarchical BVP
Level 0 Level 1 Level 2
33 x 33 65 x 65 129 x 129
restricts the residual restricts the residual
Hierarchical BVP
Level 0 Level 1 Level 2
33 x 33 65 x 65 129 x 129
restricts the residual restricts the residual
Compute the error approximation
Hierarchical BVP
Level 0 Level 1 Level 2
33 x 33 65 x 65 129 x 129
restricts the residual restricts the residual
prolongs and update the error
Hierarchical BVP
Level 0 Level 1 Level 2
33 x 33 65 x 65 129 x 129
restricts the residual restricts the residual
prolongs and update the error prolongs and update the error
Hierarchical BVP
Level 0 Level 1 Level 2
33 x 33 65 x 65 129 x 129
Update de potential. The robot can use the highest resolution grid to navigate
Hierarchical BVP
prolongation prolongation
Level 0 Level 1 Level 2
33 x 33 65 x 65 129 x 129
restriction
restriction restriction
Hierarchical BVP
Hierarchical BVP
17x17
129 x129 Navigation switching the grids
Hierarchical BVP
17x17
129 x129 Navigation switching the grids
Hierarchical BVP
17x17
129 x129 Navigation switching the grids
Hierarchical BVP
Resolution Time (seconds)Time (seconds)Time (seconds)Time (seconds)Resolution
HBVP PP BVP PP (SOR) BVP PP (GS) A*
9 x 9 2.29 x 10-5 2.04 x 10-3 2.01x10-3 6.58 x 10-5
17 x 17 2.37 x 10-4 2.10 x 10-3 3.61 x 10-3 2.10 x 10-4
33 x 33 1.24 x 10-3 5.52 x 10-3 3.11 x 10-2 5.57 x 10-4
65 x 65 1.51 x 10-2 3.53 x 10-2 4.88 x 10-1 1.70 x 10-3
129 x 129 2.64 x 10 -2 2.90 x 10-1 7.94 5.36 x10-3
257 x 257 2.39 x 10-1 2.56 130.32 1.95 x 10-2
BIBLIOGRAFIAl [7] Prestes, E., Idiart, M. Sculpting Potential Fields in the BVP Path Planner. IEEE
International Conference on Robotics and Biomimetics, 2009.l [8] Prestes, E. Idiart, M. Computing Navigational Routes in Inhomogeneous
Environments using BVP Path Planner. IEEE/RSJ International Conference on Robotics and Systems, 2010.
l [9] Silveira, R. , Prestes, E. Nedel, L. Fast Path Planning using Multi-Resolution Boundary Value Problems. IEEE/RSJ International Conference on Robotics and Systems, 2010.
l [10] Prestes, E. Engel, P. Exploration driven by Local Potential Distortions. Submetido ao IEEE/RSJ International Conference on Robotics and Systems, 2011.
l [11] Stachniss, C., Grisetti, G., Burgard, W. Information Gain-based Exploration using Rao-Blackwellized Particle Filters. Proc. of Robotics: Science and Systems (RSS), 2005.
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