# Mapping of the Upper Limb Work-Space: Benchmarking Four Wrist Smoothness Metrics
## 4 Discussion  
Smoothness metrics represent the basis of many motor control tests performed in clinical environments to assess the patients' motor performance [4, 9, 23]. Upper limb gestures are typically evaluated with jerk-based indexes and associated to pathologies that involve motor impairment. It was found that smoothness is correlated with motor impairment [31] and with standard clinical measures [32, 33, 34]. Smoothness is used as a parameter for motor performance evaluation during rehabilitation in post-stroke patients [20], parkinsonian patients [35] and spinal cord injury [36]. In the previous studies, motor recovery was associated with increased smoothness. Moreover, smoothness measures can be also used for detailed evaluation of motor performance that cannot easily be assessed with clinical scales. For example, the normalized jerk was sensible enough to identify a limited motor performance of the ipsilesional limb in post-stroke patients [37]. [PERSON] et al. [38], instead, found that smoothness metrics could detect motor dysfunctions related to [PERSON]'s disease before clinical tests. However, no studies so far have investigated the sensibility of these measurements in a wide mapping of the upper limb in healthy subjects as benchmark values for clinical applications. In this paper, four smoothness metrics based on wrist motion were used to reconstruct a map of movement smoothness in the upper limb workspace in a cohort of fifteen healthy subjects. First, two upper limb movements, namely point-to-point reaching movements and multi-directional exploration tasks, were acquired from fifteen subjects in five sectors of the workspace: frontal, up, left, right and horizontal. Then, the smoothness was computed with the NJ, the SM, the SAL, and the NP. A smoothness map of each metric was reported for all the sectors, in the 3D space and with respect to the shoulder articular angles, that describe the direction of movements. Statistical tests were performed between sectors in order to investigate which sectors could be discriminated with the smoothness metrics. Finally, correlation coefficients between pairs of metrics were computed. Thus, the outcomes of this work include comprehensive smoothness maps, established in a wide variety of directions in the upper limb workspace, and a comparison between four commonly adopted metrics for movement smoothness. Smoother movements correspond to lower NJ and NP and higher SM and SAL. The NJ presented similar results between directions in each sector, except for P2P movements in the horizontal sector. In general, the left and the up sectors showed higher NJ in P2P movements and these sectors also correspond to the regions in which the plane of elevation and/or the elevation angle were higher. In EXP movements, the NJ was lower in the horizontal and frontal plane, while it was high in the left sector. The SM was always in accordance with the results of the NJ, and it shows strong discriminative sensibility between sectors. The NJ and the SM showed a very high negative correlation. The SAL presented results similar to NJ and SM, interestingly detecting lower smoothness in the up and the left sectors, probably due to the fact that the limb has less dexterous control in such sectors, that are \"at the borders\" of the upper limb workspace. The SAL could discriminate smoothness differences between the sectors in a similar way with respect to the SM, presenting a positive correlation with SM. The NP, instead, was for almost all the conditions = 1 and could discriminate only some of the directions of the up sector in EXP movements as less smooth. The NP showed no correlation with the other metrics, and it had low positive correlation with NJ in EXP movements. This index was not suitable for analyzing the smoothness of reaching movements performed by healthy subjects, since in reaching movements the number of velocity peaks is usually one. In fact, healthy persons' movements are mainly characterized by bell-shaped velocity profiles with only one velocity peak [6; 39].