Deformation of Angle Profiles in Forward Kinematics for Nullifying End-Point Offset While Preserving Movement Properties

Abstract

This work describes a new approach that allows an angle-domain human movement model to generate, via forward kinematics, Cartesian-space human movement representation with otherwise inevitable end-point offset nullified but much of the kinematic authenticity retained. The approach incorporates a rectification procedure that determines the minimum postural angle change at the final frame to correct the end-point offset, and a deformation procedure that deforms the angle profile accordingly to preserve maximum original kinematic authenticity. Two alternative deformation schemes, named amplitude-proportional (AP) and time-proportional (TP) schemes, are proposed and formulated. As an illustration and empirical evaluation, the proposed approach, along with two deformation schemes, was applied to a set of target-directed right-hand reaching movements that had been previously measured and modeled. The evaluation showed that both deformation schemes nullified the final frame end-point offset and significantly reduced time-averaged position errors for the end-point as well as the most distal intermediate joint while causing essentially no change in the remaining joints. A comparison between the two schemes based on time-averaged joint and end-point position errors indicated that overall the TP scheme outperformed the AP scheme. In addition, no statistically significant difference in time-averaged angle error was identified between the raw prediction and either of the deformation schemes, nor between the two schemes themselves, suggesting minimal angle-domain distortion incurred by the deformation.