Cooperative robots require the capability of external force detection to ensure the safety and convenience of human-machine interaction. Although installing force sensors provides more accurate external force detection, a sensorless external force estimation method eliminates concerns related to zero point drift, collision overload, stiffness reduction, and high cost. It plays a crucial safety role in case the force sensor fails. However, the force control system faces significant challenges regarding the accuracy of the friction model, nonlinearity when switching between static and sliding friction, and time-varying factors. This article proposes an exciting current-based identification method to improve the precision of static friction identification. A continuous friction model between static friction and sliding friction is modified to avoid the overestimation of external torque. An improved external torque estimator is proposed to ensure the stability of switching static and sliding friction models. Furthermore, a linear-active disturbance rejection control-based sensorless force control is proposed to improve the response speed of the control system. The proposed algorithms are verified through contrast experiments, and the results indicate that they can effectively ensure stability and improve the response speed of the sensorless force control system, especially when a joint is at near-zero velocity.