Page 12 - Rapid Learning in Robotics

x LIST OF FIGURES

4.10 Example node placement 3 4 2 ... ... .. ... ... . 57

5.1 [a–d] PSOM mapping example 3 3 nodes . . . . . . . . . . 64
5.2 [a–d] PSOM mapping example 2 2 nodes . . . . . . . . . . 65
5.3 Isometric projection of the 2 2 PSOM manifold . . . . . . . 65
5.4 [a–c] PSOM example mappings 2 2 2 nodes . . . . . . . . 66
5.5 [a–h] 3 3 PSOM trained with a unregularly sampled set . 67
5.6 [a–e] Different interpretations to a data set . . . . . . . . . . 69
5.7 [a–d] Topological defects . . . . . . . . . . . . . . . . . . . . 70
5.8 The map beyond the convex hull of the training data set . . 71
5.9 Non-continuous response . . . . . . . . . . . . . . . . . . . . 73

5.10 The transition from a continuous to a non-continuous re-
sponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.1 [a–b] The multistart technique . . . . . . . . . . . . . . . . . 76
6.2 [a–d] The Local-PSOM procedure . . . . . . . . . . . . . . . 79
6.3 [a–h] The Local-PSOM approach with various sub-grid sizes 80
6.4 [a–c] The Local-PSOM sub-grid selection . . . . . . . . . . . 81
6.5 [a–c] Chebyshev spacing . . . . . . . . . . . . . . . . . . . . . 84
6.6 [a–b] Mapping accuracy for various PSOM networks . . . . 85

6.7 [a–d] PSOM manifolds with a 5 5 training set . . . . . . . . 86
6.8 [a–d] Same test function approximated by LLM units .. . 87
6.9 RLC-Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.10 [a–d] RLC example: 2 D projections of one PSOM manifold 90
6.11 [a–h] RLC example: two 2 D projections of several PSOMs . 92

7.1 [a–d] Example image feature completion: the Big Dipper . . 96
7.2 [a–d] Test object in several normal orientations and depths . 98

7.3 [a–f] Reconstruced object pose examples . . . . . . . . . . . 99
7.4 Sensor fusion improves reconstruction accuracy . . . . . . . 101
7.5 [a–c] Input image and processing steps to the PSOM finger-
tip finder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.6 [a–d] Identification examples of the PSOM fingertip finder . 105
7.7 Functional dependences fingertip example . . . . . . . . . . 106

8.1 [a–d] Kinematic workspace of the TUM robot finger . . . . . 108
8.2 [a–e] Training and testing of the finger kinematics PSOM . . 110