5.3.2.5 Kinematic arm model

The presented potential field method was further applied to the kinematic arm model. Here, 150 eigenvectors were extracted (explaining 67.4% of the total variance), and the reduced set was used. The pattern association based on kernel PCA could learn the inverse one-to-many mapping (table 5.3). However, the association with kernel PCA was worse than with the mixture of local PCA (the position errors were about double). The results were averaged over three separate training cycles. In the table, only averages are shown; the variation was small (for the kernel PCA method the maximum deviation of a position error from a mean value was 2 mm, and for the mixture of local PCA 5 mm).

On this task with fewer training patterns as in section 4.5, NGPCA was restricted to 100 units (in section 4.5, 200 units were used). Increasing this number diminished the performance.

Table 5.3: Position and collision errors for an attractor network based on kernel PCA compared to one based on a mixture of local PCA (100 units, q = 6). Results are shown for two different directions of recall: forward and inverse. The inverse model takes the desired collision state as an additional input variable (third column). Position errors are averaged over 1331 test patterns, and are given with standard deviations. In the inverse case, the collision error is the percentage of trials deviating from the collision input value; in the forward case, it is the erroneous number of collision state predictions.

method	direction	input	position error (mm)	collision error (%)
kernel PCA	inverse	no collision	70 ± 33	2.1
kernel PCA	inverse	collision	75 ± 40	10.2
kernel PCA	forward	--	150 ± 64	20.5
mixture of PCA	inverse	no collision	40 ± 24	7.7
mixture of PCA	inverse	collision	38 ± 27	11.6
mixture of PCA	forward	--	66 ± 46	15.4