Evaluation of trajectory planning models for arm-reaching movements based on energy cost

Computational studies have suggested that many characteristics of reaching trajectories in a horizontal plane can be effectively predicted by certain models, including, the minimum end point variance model and minimum torque change model. It has also been reported that these characteristics appear to differ from those obtained by the minimum energy cost model that has been reported to explain the characteristics of locomotor patterns. Do these results imply that the human nervous system uses different strategies to resolve the redundancy problem for different tasks? In order to reexamine the optimality of reaching trajectories from a viewpoint of energy cost, we considered the corrective submovements to compensate for positional error due to signal-dependent noise in motor commands and computed the expected value of the total energy costs required to reach a target by repetition of submovements planned by each of the following models: the minimum energy cost model, minimum end point variance model, and minimum torque change model. The results revealed that when the noise is large, the total energy cost required by the minimum end point variance model and the minimum torque change model can be lower than that required by the minimum energy cost model which assumes minimizing energy cost under noise-free condition. This result indicates that the minimization of the expected value of the energy cost would be an important factor in determining the reaching trajectories.