Derivation of simple rules for complex flow vector fields on the lower part of the human face for robot face design

It is quite difficult for android robots to replicate the numerous and various types of human facial expressions owing to limitations in terms of space, mechanisms, and materials. This situation could be improved with greater knowledge regarding these expressions and their deformation rules, i.e. by using the biomimetic approach. In a previous study, we investigated 16 facial deformation patterns and found that each facial point moves almost only in its own principal direction and different deformation patterns are created with different combinations of moving lengths. However, the replication errors caused by moving each control point of a face in only their principal direction were not evaluated for each deformation pattern at that time. Therefore, we calculated the replication errors in this study using the second principal component scores of the 16 sets of flow vectors at each point on the face. More than 60% of the errors were within 1 mm, and approximately 90% of them were within 3 mm. The average error was 1.1 mm. These results indicate that robots can replicate the 16 investigated facial expressions with errors within 3 mm and 1 mm for about 90% and 60% of the vectors, respectively, even if each point on the robot face moves in only its own principal direction. This finding seems promising for the development of robots capable of showing various facial expressions because significantly fewer types of movements than previously predicted are necessary.