## 1 Introduction  
In recent years, legged robots have become a research hotspot in robotics due to their excellent terrain adaptability [1, 2]. Among the existing legged robots, the hexapod robots have higher walking stability and anti-tipping ability compared with quadruped and biped robots [3]. Therefore, they have received increasingly extensive attention in fields such as disaster relief [4]. Among the existing motion control methods for hexapod robots, control based on dynamic models can significantly improve the motion performance of hexapod robots [5]. The walking stability of legged robots is deeply affected by the impact between the foot-end and the ground when they perform tasks in different terrains. In current academic research, reducing the impact of the foot-end touching the ground through compliant control is an important research direction [6]. Compliant control can be further divided into passive and active compliant control [7]. Passive compliant control relies on mechanical structural components. [PERSON] et al. added series elastic actuators (SEAs) to the robot leg to improve motion compliance [8]. However, its compliance is limited by the material selection, processing, and stiffness and deformation range of the elastomer. Active compliance control adjusts the force-position relationship of the robot in real time through sensor feedback and control algorithms to adapt to the external environment. [PERSON] proposed two classic impedance control methods [9; 10], the force-based and position-based impedance methods (also known as admittance control). Both methods establish a relationship between the end-effector position and the touchdown force of the robot and indirectly control the contact force with the environment by using the change in the end-effector pose. The team of [PERSON] from the Italian Institute of Technology (IIT) researched force-based impedance control for hydraulic legs [11]. By modeling and analyzing the valve control system and combining force loop compensation, they improved the response speed of force-based impedance control, but it has not been verified on electrically driven robots. The team of [PERSON] proposed a new controller that integrates feed-forward contact force and impedance control for the robot and verified its excellent impedance adjustment ability in high dynamic motion through experiments [12]. [PERSON] et al. achieved a good force-tracking response based on admittance control in a known environment, with the steady-state error being almost zero and a fast response speed [13]. In post-disaster rescue operations, hexapod robots often encounter local ground collapses or slippage when their feet contact the terrain [14], which can lead to a loss of stability during locomotion. Therefore, when unexpected events such as foot misplacement occur under different gaits, it is essential to first assess the robot's stability. A state ma-chine should then be employed to adjust the control strategy in real time based on the status flags, thereby enhancing overall stability. Since hexapod robots exhibit distinct dynamic characteristics under different gaits [15], the impact of foot misplacement on overall stability also varies with the gait type. At present, the mainstream methods for real-time stability monitoring include the zero moment point (ZMP) method, the force-angle stability margin (FASM), and the moment-height stability (MHS) method. ZMP is defined as the minimum distance from the equivalent zero-moment point--where the moments in the x and y directions are zero on the horizontal plane to the edge of the support polygon, and this distance is used as the stability margin at the current moment. [PERSON] et al. [16] applied the FASM method, which evaluates dynamic stability based on the relationship between the resultant force and the support polygon. FASM has become one of the dominant approaches for stability assessment in legged robots.