A main problem in the control of flexible-joint robots and in the precise positioning of their end-effector, is synchronization between the turn angles of the robots' joints and the turn angles of the motors that provide actuation to these joints. In this article, a nonlinear optimal (H-infinity) control method is proposed for multi-DOF robotic manipulators with flexible joints. The dynamic model of these robotic manipulators is shown to be underactuated and to satisfy differential flatness properties. The state-space description of these robots undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. The linearization procedure makes use of first-order Taylor-series expansion and relies on the computation of Jacobian matrices. For the approximately linearized model of these multi-DOF robotic systems an H-infinity feedback controller is designed. This controller stands for the solution of the robots' optimal control problem under model uncertainty and external disturbances. The computation of the controller's feedback gain requires the solution of an algebraic Riccati equation, which is performed again at each time-step of the control algorithm. The stability properties of the control scheme are proven trough Lyapunov analysis. First, it is confirmed that the controller satisfies the H-infinity tracking performance criterion which ascertains its robustness. Moreover, it is proven that the control loop is globally asymptotically stable. Finally, to implement sensorless control for such robotic systems the H-infinity Kalman Filter is used as a robust state estimator. The proposed control method for multi-DOF robotic manipulators with flexible joints retains the advantages of linear optimal control, that is fast and accurate tracking of its reference setpoints under moderate variations of the control inputs.

中文翻译：

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具有柔性关节的多自由度机器人机械手的非线性优化控制

柔性关节机器人的控制及其末端执行器的精确定位中的一个主要问题是机器人关节的转角与为这些关节提供驱动的电机的转角之间的同步。在本文中，针对具有柔性关节的多自由度机器人机械手提出了一种非线性最优（H-无穷大）控制方法。这些机器人操纵器的动态模型被证明是欠驱动的，并且满足微分平坦度特性。这些机器人的状态空间描述围绕临时操作点进行近似线性化，该操作点在控制方法的每次迭代中重新计算。线性化过程利用一阶泰勒级数展开并依赖于雅可比矩阵的计算。对于这些多自由度机器人系统的近似线性化模型，设计了 H 无穷大反馈控制器。该控制器代表模型不确定性和外部干扰下机器人最优控制问题的解决方案。控制器反馈增益的计算需要求解代数 Riccati 方程，该方程在控制算法的每个时间步长处再次执行。通过李雅普诺夫分析证明了控制方案的稳定性特性。首先，确认控制器满足确定其鲁棒性的 H 无穷大跟踪性能标准。此外，证明控制回路是全局渐近稳定的。最后，为实现此类机器人系统的无传感器控制，H 无穷大卡尔曼滤波器用作稳健的状态估计器。所提出的具有柔性关节的多自由度机器人操纵器的控制方法保留了线性最优控制的优点，即在控制输入的适度变化下快速准确地跟踪其参考设定点。