3D human arm reaching movement planning with principal patterns in successive phases.

There are observations indicating that the central nervous system (CNS) decomposes a movement into several successive sub-movements as an effective strategy to control the motor task. In this study, we propose an algorithm in which, Arm Reaching Movement (ARM) in 3D space is decomposed into several successive phases using zero joint angle jerk features of the arm kinematic data. The presented decomposition algorithm for 3D motions is, in fact, an improved and generalized version of the decomposition method proposed earlier by Emadi and Bahrami in 2012 for 2D movements. They assumed that the motion is coordinated by minimum jerk characteristics in joint angles space in each phase. However, at the first glance, it seems that in 3D ARM joint angles are not coordinated based on the minimum jerk features. Therefore, we defined a resultant variable in the joint space and showed that one can use its jerk properties together with those of the elbow joint in movement decomposition. We showed that phase borders determined with the proposed algorithm in 3D ARM, are defined with jerk characteristics of ARM's performance variable. We observed the same results in the Sit-to-Stand (STS) movement, too. Thus, based on our results, we suggested that any 3D motion can be decomposed into several phases, such that in each phase a set of principal patterns (PPs) extracted by Principal Component Analysis (PCA) method are linearly recruited to regenerate angle trajectories of each joint. Our results also suggest that the CNS, as the primary policy, may simplify the control of the ARMs by reducing the dimension of the control space. This dimension reduction might be accomplished by decomposing the movement into successive phases in which the movement satisfies the minimum joint angle jerk constraint. Then, in each phase, a set of PPs are recruited in the joint space to regenerate angle trajectory of each joint. Then, the dimension of the control space will be the number of the recruitment coefficients.