Mitsuo Kawato
Unidirectional versus Bi-directional Theory for Trajectory Planning and Control
Abstract:Three computational problems to be solved for visually guided reaching movements, trajectory formation, coordinate transformation, and calculation of motor commands, are all ill-posed in redundant biological motor control systems. Two different theories, unidirectional and bi-directional, have been developed to account for how the brain solves them. In the unidirectional theory, the three problems are solved sequentially and step by step. In each calculation, the higher-level in the hierarchy resolves ill-posedness at that level without reference to what happens at the lower-level in the hierarchy. The representative models developed in the unidirectional theory framework are minimum-jerk model and virtual trajectory control hypothesis. The bi-directional theory retains the same hierarchical structure, but the three computational problems are solved simultaneously rather than sequentially while using both upward and downward information flows between different levels in the hierarchy. The upward and downward information flows are achieved by the internal forward and inverse models of the controlled object and the environment, respectively. The representative models developed in the bi-directional-theory framework are minimum-torque-change model and feedforward control using an inverse dynamics model. The two theories disagree on many points, some of which can be tested by a combination of carefully controlled experiments and computer simulations. This paper first summarizes comparisons between the two theories and introduces recent experimental and simulation data which address their differences.