Exploração direcionada Algoritmo 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 l valor de distorção às células da região. 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 l completamente explorado.
Exploração direcionada Ambientes de Teste
Exploração direcionada Com preferência Sem preferência
Exploração direcionada Numeros de Passos Numeros de Visitas Ambientes de Teste
Exploração direcionada Com preferência Sem preferência
Exploração direcionada Numeros de Passos Numeros de Visitas Ambientes de Teste
Exploração direcionada Ambiente Simulado SLAM + Exploração SLAM + Exploração Gulosa Integrada
Exploração direcionada Ambiente Simulado SLAM + Exploração SLAM + Exploração Gulosa Integrada
Planejador BVP
Planejador BVP
Hierarchical BVP l 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) Assuming the operator , eq. 1 becomes (2) Considering the error of approximation A e = − A ˜ and using eq. (2), we obtain p where r is the residual and defined by The error is relaxed and used to correct the potential
Hierarchical BVP
Hierarchical BVP
Hierarchical BVP Operators: Restriction (R) Prolongation (P) Full weighting restriction Bilinear interpolation
Hierarchical BVP 33 x 33 Level 0
Hierarchical BVP 33 x 33 Solves the coarsest level Level 0
Hierarchical BVP 33 x 33 The robot starts the navigation in this level Level 0
Hierarchical BVP prolongs the potential 33 x 33 65 x 65 Level 0 Level 1
Hierarchical BVP 33 x 33 65 x 65 Level 0 Level 1 restricts the residual
Hierarchical BVP Compute the error approximation 33 x 33 65 x 65 Level 0 Level 1 restricts the residual
Hierarchical BVP prolongs the error and updates the potential 33 x 33 65 x 65 Level 0 Level 1 restricts the residual
Hierarchical BVP prolongs the error and updates the potential 33 x 33 65 x 65 The robot can navigate using the potential field at this level Level 0 Level 1 restricts the residual
Hierarchical BVP prolongation prolongs the potential 33 x 33 65 x 65 129 x 129 Level 0 Level 1 Level 2
Hierarchical BVP 33 x 33 65 x 65 129 x 129 Level 0 Level 1 Level 2 restricts the residual
Hierarchical BVP 33 x 33 65 x 65 129 x 129 Level 0 Level 1 Level 2 restricts the residual restricts the residual
Hierarchical BVP Compute the error approximation 33 x 33 65 x 65 129 x 129 Level 0 Level 1 Level 2 restricts the residual restricts the residual
Hierarchical BVP prolongs and update the error 33 x 33 65 x 65 129 x 129 Level 0 Level 1 Level 2 restricts the residual restricts the residual
Hierarchical BVP prolongs and update the error prolongs and update the error 33 x 33 65 x 65 129 x 129 Level 0 Level 1 Level 2 restricts the residual restricts the residual
Hierarchical BVP 33 x 33 65 x 65 129 x 129 Level 0 Level 1 Level 2 Update de potential. The robot can use the highest resolution grid to navigate
Hierarchical BVP prolongation prolongation 33 x 33 65 x 65 129 x 129 Level 0 Level 1 Level 2 restriction restriction restriction
Hierarchical BVP
Hierarchical BVP 17x17 129 x129 Navigation switching the grids
Hierarchical BVP 17x17 Navigation switching the grids 129 x129
Hierarchical BVP 17x17 129 x129 Navigation switching the grids
Hierarchical BVP Resolution Time (seco me (seconds) HBVP PP BVP PP (SOR) BVP PP (GS) A* 2.29 x 10-5 2.04 x 10-3 2.01x10-3 6.58 x 10-5 9 x 9 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
BIBLIOGRAFIA [7] Prestes, E., Idiart, M. Sculpting Potential Fields in the BVP Path Planner. IEEE l International Conference on Robotics and Biomimetics, 2009. [8] Prestes, E. Idiart, M. Computing Navigational Routes in Inhomogeneous l Environments using BVP Path Planner. IEEE/RSJ International Conference on Robotics and Systems, 2010. [9] Silveira, R. , Prestes, E. Nedel, L. Fast Path Planning using Multi-Resolution l Boundary Value Problems. IEEE/RSJ International Conference on Robotics and Systems, 2010. [10] Prestes, E. Engel, P. Exploration driven by Local Potential Distortions. l Submetido ao IEEE/RSJ International Conference on Robotics and Systems, 2011. [11] Stachniss, C., Grisetti, G., Burgard, W. Information Gain-based Exploration l using Rao-Blackwellized Particle Filters. Proc. of Robotics: Science and Systems (RSS), 2005.
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