The novel conceptual model of the antagonistic variable stiffness actuator based on the equivalent nonlinear torsion spring and the friction damper is demonstrated. For the dynamic model of the antagonistic variable stiffness actuator in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance, and input saturation constraints, using the coordinate transformation, the state space model of the antagonistic variable stiffness actuator with composite disturbances and input saturation constraints is transformed into an extended integral chain-type pseudo-linear system with input saturation constraints. Subsequently, a combination of the linear extended state observer, sliding mode control, and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the antagonistic equivalent nonlinear torsion spring-based variable stiffness actuator. Under the proposed controller, the semi-global uniformly ultimately bounded stability of the closed-loop system has been proved via Lyapunov stability analysis. Simulation studies demonstrate the effectiveness and the robustness of the proposed robust adaptive tracking control method for the antagonistic variable stiffness actuator.
This paper is concerned with the design of a robust adaptive tracking control scheme for a class of variable stiffness actuators (VSAs) based on the lever mechanisms. For these VSAs based on the lever mechanisms, the AwAS‐II developed at Italian Institute of Technology (IIT) is chosen as the study object, and it is an enhanced version of the original realization AwAS (actuator with adjustable stiffness). Firstly, for the dynamic model of the AwAS‐II system in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance and input saturation constraints, by using the coordinate transformations and the static state feedback linearization, the state space model of the AwAS‐II system with composite disturbances and input saturation constraints is transformed into an uncertain multiple‐input multiple‐output (MIMO) linear system with lumped disturbances and input saturation constraints. Subsequently, a combination of the feedback linearization, disturbance observer, sliding mode control and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the AwAS‐II system. Under the proposed controller, the semi‐global uniformly ultimately bounded stability of the closed‐loop system has been proved via Lyapunov stability analysis. Simulation results illustrate the effectiveness and the robustness of the proposed robust adaptive tracking control scheme.
The variable stiffness joint (VSJ) has the characteristics of independent and controllable position and stiffness. The variable stiffness characteristics and inherent flexibility make the VSJ suitable to be used as the actuation joint of the physical human-robot interaction application robot, so as to improve the task adaptability of the robot and physical human-robot interaction safety. The VSJ based on equivalent lever mechanism has the advantages of low energy consumption in stiffness adjustment, so there are many researches on this type of VSJ. The tracking control of output link angular position and joint output stiffness are two basic control targets of the VSJ. For the system dynamic model of the VSJ based on equivalent lever mechanism, considering the unknown parametric perturbations, the unknown friction torques acting on the drive units, the unknown external disturbance acting on the output link and the control input saturation constraints, a robust tracking controller based on feedback linearization, disturbance observer with antiwindup measures, sliding mode control and estimation error compensator is designed to improve the tracking control accuracy of the position and stiffness of the VSJ. The simultaneous tracking control of position and stiffness of the VSJ can be achieved by the designed controller, and the simulation results show the effectiveness and robustness of the proposed controller. Moreover, the simulation results show that the proposed estimation error compensator for the disturbance observer with fixed preset observation gain can effectively reduce the system output tracking error and improve the anti-disturbance characteristics of the controller.
The variable stiffness actuator (VSA) is an open research field. This paper introduces the conceptual design and analysis of four types of novel variable stiffness actuators (VSAs). The main novelty of this paper is focused on the convenience control of the torque and stiffness of the actuator. We do not need to design complicated control strategies to achieve the desired actuating torque and output stiffness. This feature is beneficial for real-time control. In order to achieve this advantage, three types of approximate quadratic springs and four types of stiffness regulation mechanisms are presented. For the first VSA, the relationship between the output stiffness and angular deflection is close to linear, and the fitted quadratic spring is easy to implement and compact. For the second VSA, the output stiffness is only related to the working radius, and the relationship between the exerted torque and angular deflection is linear. For the third VSA, two equivalent quadratic torsion springs are used. Compared with the existing quadratic torsion springs, the design method is simple and the structure size is compact. The stiffness and torque is a linear function of the kinematic parameters of the VSA. The novelty of the fourth VSA is the use of the tension spring set. The approximate quadratic tension spring is compact and easy to implement. The relationship between the output stiffness and the angular deflection is fairly linear. The conceptual layouts and working principles are elaborated for the four actuators. The characteristics of torque and stiffness of the VSAs are presented, and the mechanical solutions are illustrated.
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.
Accurate estimation of battery state of charge (SOC) is of great significance to improve battery management and service life. An unscented Kalman filter (UKF) method is used to increase the accuracy of SOC estimation in this paper. Firstly, a battery model that the parameters are identified by using the least squares algorithm is established, which is foundation of the two-order RC equivalent circuit model. Secondly, SOC is estimated by UKF. In order to validate the method, experiments have been carried out under different operating conditions for LiFePO4 batteries. The obtained results are compared with that of the extended Kalman filter. Finally, the comparison shows that the UKF method provides better accuracy in the battery SOC estimation. Its estimation error is less than 2%, which is better than EKF algorithm. An effective method is provided for state estimation for battery management system.
Among many types of flexible robot actuators, the variable stiffness actuator (VSA) is an actuator that can adjust the compliance of the actuator output shaft by adjusting the equivalent stiffness of its internal elastic element. Compared with the traditional rigid actuators, the VSAs have inherent flexibility and adjustable stiffness because they contain elastic elements and stiffness adjusting mechanisms. They have advantages in human-robot physical interaction security and task adaptability. The independent controllability of position and stiffness and the ability of stiffness adjustment make the VSAs have research value and application prospects in the fields of rehabilitation training equipment, prosthetics, wearable devices and so on. The mechanical scheme design of the VSA is an open research field. At present, there is no perfect mechanical structure design of any type of VSA. Optimizing and improving the mechanical structure design of the VSA is helpful to improve its actuation characteristics and application value. Due to the limitation of the mechanical structure design, most of the existing VSAs have limited rotation angle range of the output shaft, which limits their application. The purpose of this paper is to design the parallel driven VSA whose rotation angle range of output shaft is not limited. Moreover, inspired by the mechanical structure design ideas of some stiffness adjustment mechanisms with good implementation schemes and elastic elements with good force transmission characteristics, this paper makes some improvement, synthesis and innovation in the mechanical structure design of the VSA, so as to improve the structural compactness design, assembly modular design, mechanical transmission reliability design and actuation characteristics. In this paper, six types of parallel driven VSAs with different mechanical structure design schemes are proposed. Their common point is that the rotation angle range of the output shaft is not limited, and the differences are that they have different implementation schemes of variable stiffness mechanisms and elastic elements. The transmission structure diagrams of the designed VSAs show the working principle and stiffness adjustment principle. The actuation characteristics of the designed VSAs are analyzed and their differences are compared. The detailed mechanical structure design of the VSA is shown. In the designed VSAs, the model of the VSA based on the symmetrical Archimedes spiral cam groove mechanism is printed and assembled to show the feasibility of the implementation of the designed mechanical structure scheme. Finally, a manual adjustment experiment verifies the stiffness adjustment ability of the assembled VSA model, and shows that the rotation angle range of the output shaft of the assembled VSA model is unlimited.INDEX TERMS variable stiffness actuator, variable stiffness mechanism, output shaft with unlimited rotation angle range, parallel driven structure, mechanical structure scheme design, actuation characteristics I. INTRODUCTION
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