Hierarchical Sliding Mode Control of Flexible Joint RobotBased on Friction Compensation

For the nonlinear friction in flexible joint robot, a hierarchical sliding mode control method based on friction compensation is proposed. Firstly, the friction of flexible joint robot is modeled by linearizing the parameters, and an adaptive law is designed for the unknown parameters in the model to realize the estimation of friction. Then, an observer is designed to estimate the error of the friction model. Combining the adaptation of friction and estimation of model error, the friction compensation is realized. Finally, the position error and the velocity error of the motor side and the joint side are used to design the first order sliding mode surface. Then, the second order sliding mode surface is designed based on the first order sliding mode surface. Consequently, a hierarchical sliding mode controller is constructed, which realizes the position trajectory tracking control of the flexible joint robot. The convergence of the robot joint trajectory tracking error is proved via Lyapunov function. The simulation results show that with the proposed control method the friction can be effectively compensated by combining the parameter adaptation and the model error observer. Meanwhile, the position trajectory tracking of the flexible joint robot to the desired position trajectory can be realized in finite time.