A Hierarchical Structure Control Strategy Based on MPC for a Six-DOF Flexible Joint Manipulator

The six-degree-of-freedom flexible joint manipulator is a complex system that suffers from the problem that the trajectory planning results are inconsistent with the control results. To keep the planned trajectory within the control range of the manipulator, a hierarchical structure control strategy is designed, which consists of a trajectory planning layer, a model predictive control layer, and a bottom control layer. Specifically, first, the target joint angles are obtained by a time-optimal trajectory planning algorithm based on a genetic algorithm in the trajectory planning layer. Second, in the model predictive control layer, considering the system physical constraints, the model predictive controller is adopted to provide the set points for the Proportion-Differentiation (PD) controllers. Finally, in the bottom control layer, the manipulator moves along the target trajectory under the PD controllers with the feedback control law. The simulation results show that, compared with the PD control strategy, the hierarchical structure control strategy can achieve better control performance and reduce the tracking error of the terminal trajectory by 33.70%.

Adaptive boundary control of a flexible-link flexible-joint manipulator under uncertainties and unknown disturbances

In this article, we consider the trajectory tracking and vibration suppression of a flexible-link flexible-joint manipulator under uncertainties and external time-varying unknown disturbances. The coupled ordinary differential equation and partial differential equation model dynamic of the system is presented by employing the Hamilton principle. Using the singular perturbation theory, the dynamic is decomposed into a no-underactuated slow ordinary differential equation and fast partial differential equation subsystem, which solves the problem of the underactuated ordinary differential equation subsystem of the ordinary differential equation and partial differential equation cascade and reduces the analytical complexity. For the slow subsystem, to guarantee the trajectory tracking of the joint, an adaptive global sliding mode controller without gain overestimation is designed, which can guarantee the global stability of the slow system and reduce the chattering of the sliding mode control. For the fast subsystem, an adaptive boundary controller is developed to suppress the elastic vibration of the flexible link during the trajectory tracking. The stability of the whole closed-loop system is rigorously proved via the Lyapunov analysis method. Simulation results show the effectiveness of the proposed controller.

Constraint-Following Servo Control for the Trajectory Tracking of Manipulator with Flexible Joints and Mismatched Uncertainty

Trajectory tracking is a common application method for manipulators. However, the tracking performance is hard to improve if the manipulators contain flexible joints and mismatched uncertainty, especially when the trajectory is nonholonomic. On the basis of the Udwadia–Kalaba Fundamental Equation (UKFE), the prescribed position or velocity trajectories are creatively transformed into second-order standard differential form. The constraint force generated by the trajectories is obtained in closed form with the help of UKFE. Then, a high-order fractional type robust control with an embedded fictitious signal is proposed to achieve practical stability of the system, even if the mismatched uncertainty exists. Only the bound of uncertainty is indispensable, rather than the exact information. A leakage type of adaptive law is proposed to estimate such bound. By introducing a dead-zone, the control will be simplified when the specific parameter enters a certain area. Validity of the proposed controller is verified by numerical simulation with two-link flexible joint manipulator.

A model-based PID-like motion control method for flexible-joint manipulator with harmonic drives

A novel control method is proposed to achieve high trajectory tracking precision, for flexible-joint manipulators. The method consists of three major parts: joint torque generator, joint torque tracker and motor position controller. The expected torque is generated by a PID controller based on the manipulator’s rigid dynamics model. In the torque tracker, motor position is corrected in both feedback and feedforward ways. Finally, the motor position controller is responsible to track the corrected motor trajectory to achieve the torque and position control. To suppress nonlinear friction, a disturbance observer is also implemented. The method is verified with a seven-DOFs manipulator. Simulation and experimental results show that, the proposed method is efficient and practical to suppress vibration caused by flexible transmission and disturbance due to friction. As result, high positioning accuracy is achieved in a certain wide working speed range. The no-load motion accuracy is better than 0.6 mm with a manipulator whose length is 1.8 meter, and the motion error is less than 3 mm with loading of four kilograms.

Experimental Application of Robust and Converse Dynamic Control for Rotary Flexible Joint Manipulator System

Performance evaluation of trajectory tracking for a rotary flexible joint system is demonstrated in this paper. The robust and converse dynamic (RCD) technique is proposed and implemented for this evaluation. This control methodology is of the left inversion type, i.e., the control inputs are obtained by means of plant output error feedback. RCD control encompasses the baseline inverse (BI) control and sliding mode control-based discontinuous control element. The baseline inverse controller enforces the prescribed servo (virtual) constraints that represent the control objectives. The control objectives of the baseline inverse controller are enclosed in the form of servo (virtual) constraints which are inverted using Moore–Penrose Generalized Inverse (MPGI) to solve for the baseline control law. To boost the robust attributes against parametric uncertainties and disturbances, a discontinuous control function is augmented with baseline controller such that semiglobal practical stability is guaranteed in the sense of Lyapunov. To exhibit the effectiveness of RCD control in terms of tracking performance, computer simulations are conducted in Simulink/Matlab environment. Furthermore, the practical implementation is also investigated through a real-time experiment on Quanser’s rotary flexible joint manipulator system. The experimental results obtained by RCD are compared to the conventional sliding mode and fractional-order control techniques.