Masazumi KATAYAMA, Mitsuo KAWATO
Virtual Trajectory and Stiffness Ellipse
During Multi-Joint Arm Movement
Predicted by Neural Inverse Models
Abstract:Because of the long delays associated with neural feedback loops, feedforward control is essential
for relatively fast movements. Two approaches explaining the feedforward control of voluntary
movements have been proposed in computational neuroscience for motor control. One avoids
explicitly computing the inverse dynamics problem, and the other solves the problem by using
learned internal models of the motor systems. In the former approach, a virtual trajectory control
hypothesis has been intensively studied. According to this hypothesis, the brain computes the
virtual trajectory and does not need to worry about low-level control problems. If experimentally
observed roughly straight hand trajectories can be produced from such simple virtual trajectories as
the straight minimum-jerk trajectory, complicated computations associated with the inverse
dynamics problem need not be addressed. Thus, trajectory planning and control can be very simply
performed. This paper compares the computational complexity of planning the virtual trajectory
with that of solving the inverse dynamics problem. Computer simulations are performed using
stiffness values during movement measured by Bennett et al. (Bennett, 1991; Bennett, Hollerbach,
Xu, Hunter, 1992). The virtual trajectories and stiffness ellipses are predicted by neural network
models which solve the inverse dynamics problem. The shape and orientation of the stiffness
ellipses predicted during posture maintenance are similar to those measured in human experiments.
The stiffness ellipses during movements depended greatly on the orientation, amplitude, and speed
of movements. The virtual trajectories were much more complex than the actual trajectories. This
indicates that planning the virtual trajectory is as difficult as solving the inverse dynamics problem,
at least for fast movements. Finally, we propose a computational framework to integrate the virtual
trajectory control hypothesis and learning neural internal models.