# Comparison of Gait Smoothness Metrics in Healthy Elderly and Young People
## 1 Introduction  
Human mobility is one of the fundamental skills that impact various aspects of daily life. It affects not only the quality of life but also independence and social engagement. The importance of mobility becomes particularly evident in the context of aging [1]. Among daily motor activities, gait occupies a unique status, being the fundamental and simplest form of human movement, and it is the most widely studied motor task when exploring the impact of cognitive decline [2]. Issues commonly observed in the gait in the elderly, including incorrect posture, altered postural reflexes, muscle function impairments and challenges in neuro-muscular coordination, lead to a disruption in gait smoothness [3]. Movement fluidity encompasses several features related to human movement, resulting from the combination of kinematics, dynamics and neuro-control [4]. Defined by a regular uninterrupted pattern, a'smooth' movement contrasts with an 'unsmooth' movement, which exhibits irregularities marked by peaks and results in a less uniform trend characterized by frequent accelerations and decelerations [5]. Metrics to estimate smoothnessestimation have been implemented in several fields to objectively evaluate human movement quality. In the medical context, physical impairments have been assessed through smoothness evaluation on people after stroke [6; 7; 8], Parkinson's disease individuals [9; 10] and cerebellar-ataxia-affected subjects [11]. Furthermore, it has been exploited in the sports field to improve the coordination classification protocol of para-swimmer athletes [12] and, more generally, to assess motor skills in activities of daily living (ADLs) in both open chain [13; 14] and closed chain [15]. Smoothness metrics should possess dimensionless attributes, ensuring independence from movement amplitude and duration while demonstrating a consistent response within the physiological range [13]. Several metrics have been proposed to evaluate gait smoothness, including jerk-based measures such as jerk peak infections [8], jerk root mean square (RMS) [14], log dimensionless jerk (LDL) [11; 15; 16] or the estimation of movement's frequency spectrum like the harmonic ratio (HR) [2; 3; 11; 17] and spectral arc length (SPARC) [9; 10; 18; 19]. The latter, proposed by [PERSON] et al. [13], is claimed as reliable, independent from duration and amplitude and not influenced by noise and hence able to outstand other existing metrics that were not robust enough. Several studies evaluated smoothness in balance, gait and stability, mainly in the clinical context. [PERSON] et al. quantified through the linear jerk root mean square (RMS) metric the smoothness for assessing the trunk balance control in healthy infants [14], while linear jerk inflection counting was implemented by [PERSON] et al. to determine any differences regarding motion fluidity in sit-to-stand, sit-to-walk and walking in people who had suffered a stroke [8]. Individuals in two different post-stroke phases were also evaluated in terms of body center of mass (CoM) smoothness by comparing LDLJ and SPARC on CoM velocity, finding that LDLJ is more responsive and reliable than SPARC in differentiating gait of both classes [15]. [PERSON] et al. applied SPARC to the gait velocity patterns in the three directions of post-stroke and control groups, obtaining controversial results [20]. SPARC was utilized also in two studies realized by [PERSON] et al. on trunk accelerations and angular velocities and also by [PERSON] et al. on acceleration RMS to describe walking smoothness exhibited by elderly persons with and without a history of falling, with the aim of investigating a possible fall prevention strategy, since smoothness worsening had been detected [18; 19; 21]. With regard to aging, the HR metric has been applied to trunk accelerations in three directions to assess gait smoothness, particularly focusing on stability, involving an elderly population with cognitive impairment [2], healthy children and adolescents [17], as well as healthy young and elderly subjects [3].