# A Parametric Identification Method of Human Gait Differences and its Application in Rehabilitation
## 1 Introduction  
Gait is the external behavior characteristics of human walking based on the structure and function of the human body and nervous system. When walking naturally, the gait of lower limbs shows strong periodic regularity [1]. Many studies have proved that people in good condition have similar gait characteristics while some people with disorders show obvious differences compared to them, so the analysis of gait characteristics has gained increasing attention at present [2; 3; 4; 5]. Gait analysis, one of the most commonly used methods to explore gait characteristics, plays a vital role in clinical practice [6]. It mainly divides gait properties into four categories, which are temporal and spatial data (time and distance variables), kinematics (joint motions), kinetics (joint moments, ground reaction forces, etc. ), and bioelectrical data (muscle forces and electromyography signals), providing an objective measuring instrument of the subject's functional level. There are many related works for gait analysis, including computer simulation of normal human gait, gait modelling and simulation based on anatomy, simulation based on neural networks, and automatic gait recognition, etc. [7; 8; 9; 10; 11]. In the methods of summarizing gait kinematics data, the most widely used approach is applying statistics to conduct a comprehensive gait analysis by using a motion capture system. In current studies, different ages, genders, walking speeds, etc. are the factors influencing the variety of gait parameters. So, some researchers have summarized the'reference ranges' of gait parameters of healthy individuals under a certain condition by statistics, such as for stride time, joint range of motion, jointso on [12; 13; 14; 15]. Several reporters focused on the differences of gait parameters between normal people and patients (e.g., cerebral palsy, knee osteoarthritis, etc.) as a valid basis for distinguishing different types of diseases [16; 17; 18; 19; 20]. An increasing number of investigations have begun to choose a particular type of patient, conducting more comprehensive assessment through all kinds of gait parameters [21; 22; 23]. As a result, the gait characteristics of patients have been constantly improved and enriched in academic research; the pathological features of diseases are also well understood and have been mastered in medical care in a data-orienting way, thus providing a more complete basis for diagnosis, gait training [24], and prosthesis design. However, gait analysis principally tries to reflect the overall regularity of a large number of sample statistics while reducing the characteristics of individual differences, which is one inevitable limitation. Besides, there are too many evaluation indexes of gait parameters for characteristics description, and parameters that are more simple and concise for estimation are always required in medical research [25]. In addition, people's living system has stepped into an in-depth development stage. It has significant values not only for understanding the laws of human motion but also for researching the mathematical model of gait in this information age [26]. There has been a growing awareness that the shape of gait curves during walking can greatly give expressions of the characteristics and structure of gait data. Although various people present very similar situations to the whole curve shape for the same kind of gait feature, differences still exist between them. Therefore, gait curves also contain important information, such as the so-called generality and individuality of the characteristics. On this basis, the study of gait parameter characteristics can be transformed into the study of curve shape characteristics, namely, the parameterization of the gait curve shape. Bezier and NURBS (Non-Uniform Rational B-Splines) are the traditional parametric curves [27; 28], and their applications related to gait analysis are most common in the aspects of robot motions and gait recognition [29; 30].