## 1 Introduction  
Researchers who study human walking have attempted the quantitative evaluation of various factors, including stride velocity, stride length, step information (length, width, angle, and time), joint angles, muscle force, and so on. [PERSON] et al. [1] described the categorization of gait parameters based on clinical application, sport, and recognition. Of these, clinical application requires the greatest number of gait parameters, because gait disorders affect a large percentage of the world's population. Clinical application or rehabilitation has been focused on walking parameters related to balance, stability, symmetry, etc., for the purpose of recovering healthy gait. These factors include the trajectory of joints, the symmetry of left and right, COG (center of gravity), COP (centre of pressure), ZMP, and so on. The mentioned indices are extremely important as individual walking features, but one index alone is not enough to judge personal walking. Therefore, many researchers have studied the use of one or more indices for the analysis of human walking [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. Prior to discussing the various indices, it is important to understand the two basic models of human walking. The first is an earlier and dominant perspective. From this view of point, walking is described as a continuous sequence of cyclic joint rotations of limbs and the trunk [15; 16; 17; 18; 19; 20]. This concept is typically applied to robot systems to mimic human walking motion with left and right symmetry. Additionally, the stability index is always estimated by monitoring whether the expected performance remains stable. Imitation of walking, however, is restricted by the complexity of the body structure and its controls. On the other hand, a less widely held viewpoint is that walking can be defined as the forward translation of the body system through a total locomotion. This movement results from the compositive interplay between gravity, inertia, joint rotations, and the cyclic contraction of numerous muscles [21; 22; 23]. Thus, above all, walking balance and symmetry are regarded as important for maintaining walking translation performed by individual parts of body. However, it has been difficult to produce a quantitative index to describe balance and symmetry, even though many studies have been performed in this area. In fact, walking balance can be defined as any condition in which all acting forces are cancelled out by each other, resulting in a stable balance system [24]. The concept of balance in walking is, generally, projected onto the COG and ZMP in order to judge the stability state by considering forces such as gravity and inertial forces. Here, COG is defined as a hypothetical point at which the force of gravity works on the human body. When the COG falls outside the BOS (base of support), a reaction is essential in order to stay balanced. The BOS refers to the area beneath the robot or person, including every point of contact between the robot or person and the ground, where the ZMP is determined. Meanwhile, [PERSON] et al. [25] evaluated two kinds of walking. The first was the symmetrical gait of 80 healthy people, and the other was the asymmetrical gait of 141 stroke patients. The method for analyzing symmetry and asymmetry is based on the comparison of five spatiotemporal parameters, including step length, swing time, stance time, DS time and SW/ST by using ratio (a symmetry ratio), SI (symmetry index), GA (gait asymmetry), SA (symmetry angle). As a result, only the ratio affects the easy analysis, while the other symmetry indices show no obvious advantages for the defined analysis. This research is limited to quantifying the symmetry feature as indices, although left and right symmetry in walking is described by the detected data. Thus, we tried to find a numerical index that connotes symmetry, balance, and side effects, together with the conventional stability indices, the COG and the ZMP.