Robust tracking control for two classes of variable stiffness actuators based on linear extended state observer with estimation error compensation

Abstract

In this article, a novel robust tracking control scheme based on linear extended state observer with estimation error compensation is proposed for the tracking control of the antagonistic variable stiffness actuator based on equivalent nonlinear torsion spring and the serial variable stiffness actuator based on lever mechanism. For the dynamic models of these two classes of variable stiffness actuators, considering the parametric uncertainties, the unknown friction torques acting on the driving units, the unknown external disturbances acting on the output links and the input saturation constraints, an integral chain pseudo-linear system with input saturation constraints and matched lumped disturbances is established by coordinate transformation. Subsequently, the matched lumped disturbances in the pseudo-linear system are extended to the new system states, and we obtain an extended integral chain pseudo-linear system. Then, we design the linear extended state observer to estimate the unknown states of the extended pseudo-linear system. Considering the input saturation constraints in the extended pseudo-linear system and the estimation errors of the linear extended state observer with fixed preset observation gains, the adaptive input saturation compensation laws and the novel estimation error compensators are designed. Finally, a robust tracking controller based on linear extended state observer, sliding mode control, adaptive input saturation compensation laws, and estimating error compensators is designed to achieve simultaneous position and stiffness tracking control of these two classes of variable stiffness actuators. Under the action of the designed controller, the semi-global uniformly ultimately bounded stability of the closed-loop system is proved by the stability analysis of the candidate Lyapunov function. The simulation results show the effectiveness, robustness, and adaptability of the designed controller in the tracking control of these two classes of variable stiffness actuators. Furthermore, the simulation comparisons show the effectiveness of the proposed estimation error compensation measures in reducing the tracking errors and improving the disturbance rejection performance of the controller.

Robust Tracking Control of Variable Stiffness Joint Based on Feedback Linearization and Disturbance Observer With Estimation Error Compensation

“…When the VSJ is used as the actuation joint of the robot, its variable stiffness characteristics and the independent controllability of the joint position and stiffness will be conducive to improving the adaptability of the robot task and the safety of physical human-robot interaction. The VSJ with series configuration based on equivalent lever mechanism has the advantages of low energy consumption in joint stiffness adjustment, so there are many researches on this type of VSJs at present [1,4,7,8,9,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]37]. For the existing VSJs with series configuration based on the equivalent lever mechanisms [4,[11][12][13][14][15][16]37], although they usually have different model parameters, elastic actuation torque functions and reaction torque functions, this type of VSJs all have the same structural type of the system dynamics model [36], as shown in equation (1).…”

“…A robust tracking controller based on feedback linearization, disturbance observer (DOB) and sliding mode control is designed for the simultaneous tracking control of the position and stiffness of the AwAS-II, and the effectiveness of the controller has been illustrated by simulation results [20]. A robust tracking control scheme based on linear extended state observer with estimation error compensation is proposed for the tracking control of the antagonistic VSJ based on equivalent nonlinear torsion spring and the serial VSA based on the equivalent lever mechanism, and the effectiveness of the proposed controller is verified by simulation results [21]. A DOB based composite controller is developed to achieve the tracking control of the stiffness and position of the SVSA, and the effectiveness of the controller is experimentally verified [22,23].…”

Data-Driven Position and Stiffness Control of Antagonistic Variable Stiffness Actuator Using Nonlinear Hammerstein Models

“…For an inflatable soft robot, the performances of the MPC and SMC approaches were compared in [16]. A linear extended state observer with estimation error compensation was applied to AVSA for the robust tracking control of position and stiffness [30]. The decoupled nonlinear adaptive control of position and stiffness for a pneumatic soft robot with a McKibben muscle was proposed in [31].…”