# Stability Criterion for Dynamic Gaits of Quadruped Robot
## 1 Introduction  
Legged robots that imitate animals have flexible joints and interact with the ground intermittently through their feet, giving them excellent environmental adaptability, which makes them suitable for working in complex environments such as mountains, disaster sites, and warehouses. Compared with other legged robots, quadruped robots have better maneuverability and load capacity. Over the past several decades, there has been an increasing interest in quadruped robots [1; 2; 3; 4]. When considering the dynamic motion of legged robots, one must pay attention to their stability. It is very important for robots to complete the assigned task while maintaining balance and moving on an even keel. Researchers have proposed a variety of static- and dynamic-stability-analysis methods to evaluate the stability of legged robot. The static-stability criteria and margins are only applicable for analyzing low-speed static gaits rather than the dynamic motion because they do not consider inertial forces or external impacts [5]. [PERSON] and [PERSON] proposed a stability criterion named wide stability margin (WSM) [6]. They hypothesized that a robot can maintain its balance if the projection of the center of mass (CoM) of the body is within the support polygon formed by the projection of the current support and swing feet on the horizontal plane; the shortest distance from this projectionpoint to the boundaries of the support polygon is used to evaluate the robot's stability. This stability criterion, in essence, is a static-stability criterion, and it is not suitable for analyzing the stability of high-speed motion. The rationality of the definition of the support polygon has not been explained; there is no experiment to verify that this stability criterion and margin can accurately evaluate the robot's stability. Many dynamic-stability criteria have been presented to address the limitations of static-stability criteria. The main idea behind the dynamic-stability criterion is that, at a certain state, the motion of the robot is considered to be stable if the torque caused by the ground-reaction force can prevent the robot from tumbling around any support boundary. The most common dynamic-stability criteria are based on the zero-moment point (_ZMP_) or the center of pressure (CoP). _ZMP_ refers to a point on the ground where the net torque in the direction parallel to the ground caused by the gravity and inertial forces of each part of the robot is zero. _ZMP_ shows the tendency of the robot to tumble. Researchers believe that the robot is stable if _ZMP_ is located inside the support polygon, which is connected to the support feet. The minimum distance between _ZMP_ and the support boundaries is used as the stability margin. The larger the minimum distance is, the better the stability that the robot can achieve [7; 8; 9; 10]. CoP refers to the point where the net torque caused by the ground-reaction forces is zero; it coincides exactly with _ZMP_ when the robot is dynamically stable [11; 12]. The traditional _ZMP_-based-stability criteria can only be applied to planar motion, and some researchers have made improvement to analyze the motion on irregular terrain by adjusting the support plane [11; 13; 14]. The stability criteria based on _ZMP_ do not consider the influence of the robot's current speed on its stability, but speed is very important for dynamic stability [15]. Methods using the leg-end-supporting moment (LSM) and tumble stability margin (TSM) [13; 16; 17; 18; 19], among others, directly consider the resultant moment around each support boundary. The robot will be stable if the resultant moments can counteract the torque which makes the robot tumble. A simpler stability criterion is the force-angle-stability measure (FASM) [20], which considers the angle between the resultant force of gravity, inertial force, and other external forces at the CoM and the perpendicular line from CoM to the support boundary.