基于摩擦补偿的柔性关节机器人分级滑模控制

针对柔性关节机器人中存在的非线性摩擦问题，提出一种基于摩擦补偿的柔性关节机器人分级滑模控制方法。首先，通过线性化参数的方法对柔性关节机器人受到的摩擦进行建模，并对模型中未知参数设计自适应律以实现摩擦的估计；然后，针对摩擦模型的误差，进一步设计观测器进行估计，结合摩擦的自适应和模型误差估计实现对摩擦的补偿；最后，利用电机侧和关节侧的位置误差和速度误差设计一级滑模面，再根据一级滑模面设计二级滑模面，从而得到分级滑模控制器，进一步实现柔性关节机器人的位置轨迹跟踪控制。通过Lyapunov函数证明了机器人关节轨迹跟踪误差的收敛性。仿真结果表明：该控制方法结合参数自适应和模型误差观测器可以有效地对摩擦进行补偿，在有限时间内实现柔性关节机器人的位置轨迹对期望位置轨迹的跟踪。

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.