An asymptotic stable proportional derivative control with sliding mode gravity compensation and with a high gain observer for robotic arms

The major contributions of this paper are as follows: 1) A proportional derivative control with sliding mode for the gravity compensation for robotic arms is proposed. In the proposed control, it is not necessary to know the dynamics of the robotic arms. It is proven that the closed loop system of the proportional derivative control with sliding mode gravity compensation applied to robotic arms is asymptotic stable. 2) A high gain observer is used to estimate the joint velocities to avoid the necessity of the velocity measures. It is proven that the high gain observer applied to the robotic arms is uniformly stable. 3) A proportional derivative control with sliding mode gravity compensation that uses the high gain observer to estimate the joint velocities for robotic arms is proposed. It is proven the closed loop system of the proportional derivative control with sliding mode gravity compensation with the high gain observer applied to robotic arms is asymptotic stable. The simulations give the effectiveness of the suggested control.