In order to control voluntary movements, the central nervous system must solve the following three computational problems at different levels: (1) the determination of a desired trajectory in visual coordinates; (2) the transformation of its coordinates into body coordinates; and (3)
the generation of motor command. Concerning these problems, relevant experimental observations obtained in the field of neuroscience are briefly reviewed. On the basis of physiological information and previous models, we propose computational theories and a neural network model which account
for these three problems. (1) A minimum torque-change model which predicts a wide range of trajectories in human multi-joint arm movements is proposed as a computational model for trajectory formation. (2) An iterative learning scheme is presented as an algorithm which solves the coordinate
transformation and the control problem simultaneously. This algorithm can be regarded as a Newton-like method in function spaces. (3) A neural network model for generation of motor command is proposed. This model contains internal neural models of the motor system and its inverse system. The
inverse-dynamics model is acquired by heterosynaptic plasticity using a feedback motor command (torque) as an error signal. The hierarchical arrangement of these neural networks and their global control are discussed. Their applications to robotics are also discussed.