Coding proprioceptive information to control movement to a target: Simulation with a simple neural network

When the stick insect walks, the middle and rear legs step to positions immediately behind the tarsus of the adjacent rostral leg. Previous reports have described this movement to a target as a relationship between the tarsus positions of the two legs in a Cartesian coordinate system. However, leg proprioceptors measure the position of the target leg in terms of joint angles and leg muscles bring the tarsus of the moving leg to the proper end-point by establishing appropriate angles at the joints. Representation of this task in Cartesian coordinates requires non-linear coordinate transformations; realizing such a transformation in the nervous system appears to require many neurons. The present simulation using the back-propagation algorithm shows that a simple network of only nine units — 3 sensory input units, 3 motor output units, and 3 hidden units — suffices. The simulation also shows that an analytic coordinate transformation can be replaced by a direct association of joint configurations in the moving leg with those in the target leg.