Paper Title
Robust Lyapunov-Based Pid Control of Robot Manipulators with Elastic Joints in The Task-Space

Robot arms are programmed and controlled in order to enable them to track a trajectory in the task space. Also, designing control system for a flexible joint robot (FJR) in the task-space needs desirable trajectory to be transformed from joint-space to task-space. This problem becomes hypersensitive since we require to solving the inverse kinematic problem of obtaining the desired trajectory in the joint space. The main contribution of this paper is investigation a robust Lyapunovbased PID control scheme in the task-space. The control structure composed by two fast and slow control subsystem. Fast control assurances that the fast dynamics remains asymptotically stable and related to integral manifold keeps constant. Slow control involves a robust PID designed established on the rigid model and a corrective term designed based on the reduced flexible model. The stability analysis is verified by the Lyapunov direct method. Simulation results on a 2 link flexible joint robot are rendered to verify the effectiveness of the control method. Keywords - Flexible Joint Robot, Task-Space, Robust PID control, Stability analysis.