Mechanical Design And Tracking Control Of The Variable Stiffness Joints

Adjustable output stiffness and inherent passive flexibility of the variable stiffness joints(VSJs)can improve task adaptability,energy efficiency,robustness and physical human-robot interaction security of robots.The variable transmission rate VSJs,which adjust the output stiffness by changing the pivot position,have the advantages of low energy consumption in stiffness adjustment and can theoretically adjust the output stiffness from zero to infinite.However,due to the mechanical limitation of the movable range of lever pivot position,the existing this type of VSJs often have the problem of limited adjustable range of output stiffness,and the structural design needs to be optimized.The design of variable transmission rate VSJs with compact structure,high modularity and wider adjustable range of output stiffness will help to improve the task adaptability and collision safety of this type of VSJs.Compared with variable transmission rate VSJ,antagonistic VSJ consumes more energy when adjusting joint stiffness,but antagonistic VSJ has modular design of nonlinear elastic element,simple implementation of variable stiffness mechanism,no additional rotational inertia of output shaft,and strong adaptability of space installation structure.Most of the existing antagonistic VSJs have the problems of large volume of nonlinear elastic elements,large volume of the joints,limited ranges of rotation angle of the output shafts or the low flexibility of joints.The design of antagonistic VSJs with compact structure,high flexibility,simple control method of output stiffness and unlimited rotation angle of output shaft will be beneficial to the construction of multi-DOF manipulator system driven by antagonistic VSJs.Considering the dynamic model of the VSJ system in the presence of parametric uncertainties,unknown friction torques,unknown external disturbance and input saturation constraints,it is necessary to design a robust control scheme.Disturbance observer(DOB)and linear extended state observer(LESO)are two effective methods to deal with disturbance.However,there are few studies on robust tracking control of VSJs based on these two methods.Therefore,for the simultaneous position and stiffness tracking control of the VSJs,it is necessary to design the novel robust control schemes based on the two disturbance processing methods and consider input saturation compensation and estimation error compensation to improve the tracking accuracy.In order to design the new mechanical schemes of VSJs and the novel robust control schemes for simultaneous position and stiffness tracking of the VSJs,the main research contents are as follows.(1)Referring to the existing design scheme of spring mounting structure with better force transfer characteristics,a new elastic output module with compact structure,high modularity of assembly and wider movable range of lever pivot position is designed.Referring to the existing implementation scheme of variable stiffness mechanism which adjusts the joint output stiffness by changing the pivot position,and combining with the new elastic output module,the mechanical design schemes of three types of variable transmission rate VSJs with series configuration are presented.Compared with the existing VSJs,the designed elastic output module has better force transfer characteristics,the adjustable range of joint output stiffness is wider,and both structural compactness design and modular design are considered in mechanical design.This design is conducive to improving the adaptability and safety of the variable transmission rate VSJ.In order to design the variable transmission rate VSJ with convenient output stiffness control,a new type of equivalent lever mechanism with adjustable arm length is designed based on screw nut mechanism and connecting rod slider group.The output stiffness of VSJ based on this mechanism is only related to the arm length of equivalent lever mechanism,and it is independent of the angle deviation and load of the joints,and the control method of the joint output stiffness is simple.In order to design the equivalent nonlinear spring with simple structure,two kinds of approximate quadratic nonlinear spring mechanical design schemes based on linear spring group are proposed.Based on the designed approximate quadratic spring,two spring pretension VSJs with series configuration structure are constructed.The application of the spring group is conducive to the measurement and control of the output stiffness of this type of variable stiffness joint.(2)In order to design an antagonistic VSJ with compact structure,high flexibility and unlimited rotation angle range of output shaft,a new equivalent nonlinear torsion spring mechanical design scheme with desired torque-angular displacement relationship and simple calculation method was proposed.Considering the possibility that the antagonistic VSJ with compact structure and easy control of stiffness can be used to construct a multi-DOF manipulator and the different actuating requirements and design requirements of the shoulder joint,upper arm joint,elbow joint and forearm joint of the manipulator,four types of equivalent quadratic torsion springs(EQTSs)are designed,and the corresponding antagonistic VSJs with rotational degrees of freedom and swinging degrees of freedom are constructed according to their actuation requirements,in details:1)Shoulder joint(base joint)of the manipulator should have the characteristics of high flexibility and stability.For this reason,the EQTS with large angular displacement range is designed,and two types of friction dampers are designed to reduce the vibration that may occur during the rotation of output shaft,2)The upper arm joint of the manipulator should have higher elastic actuating torque;smaller radial dimension and compact structure design.Based on the small size linear compression spring group and the spatial cylindrical cam-roller mechanism with two lift profiles,the EQTS with compact structure,small radial dimension and large elastic actuating torque is designed,and the corresponding antagonistic VSJ is constructed.3)The elbow joint of the manipulator should pay attention to the lightweight design(to increase the payload of the base joint)and the motion stability(to improve the motion precision of the end joint).It should have the degree of freedom of swing and avoid the continuous energy consumption to maintain the joint stiffness.Therefore,in the design of the EQTS,the wire rope is directly used to compress the spring to reduce its weight and structure size.A self-locking worm-wheel mechanism is used to transmit power to avoid continuous energy consumption to maintain joint stiffness,and a friction damper is added to the swinging elbow joint to improve its motion stability.4)The forearm joints of the manipulator should have a compact structural design and high elastic actuating torque.In order to reduce the radial dimension of the EQTS,several groups of small-size linear compression springs are used,and two unidirectional lifting profiles are designed to improve the elastic actuating torque of the EQTS.(3)Considering the parameter uncertainties,unknown bounded friction torque and unknown bounded external disturbance in the dynamic model of VSJ system,a tracking controller based on feedback linearization and disturbance observer with anti-windup measures is designed.Simulation results show the effectiveness and robustness of the controller.Firstly,the nonlinear state space model of VSJ with composite disturbance is transformed into a linear system model with lumped disturbance by coordinate transformation and feedback linearization.Considering the influence of input saturation constraints on the estimation performance of disturbance observer,an anti-windup scheme is designed for disturbance observer.Simulation results show that the designed controller has better reference trajectory tracking performance and disturbance rejection ability than the feedback linearization controller with integral term.Furthermore,the simulation results show that the anti-windup measure designed for the disturbance observer can reduce the output tracking error caused by input saturation constraints.(4)To deal with the problem of input saturation constraints in VSJ tracking controller design,two types of tracking control schemes with input saturation compensation(ISC)are proposed.The simulation results show that the effectiveness and robustness of the controller and the designed input saturation compensation measures are helpful to reduce the system output tracking error.Control scheme 1:Firstly,by using the coordinate transformations and the feedback linearization,the nonlinear state space model of the VSJ with composite disturbances and input saturation constraints is transformed into a linear system with lumped disturbances and input saturation constraints.Subsequently,the DOB with anti-windup measure is used to estimate the lumped disturbances.To solve the input saturation compensation problem and prove the semi-global ultimate uniformly bounded stability of the closed-loop system based on Lyapunov function stability analysis,an adaptive ISC law with sliding mode surface as input is designed and a sliding mode control law with ISC term is given.Control scheme 2:Using coordinate transformation,the nonlinear state space model of VSJ with composite disturbances and input saturation constraints is transformed into the integral chain-type pseudo-linear system with input saturation constraints and matched lumped disturbance.Subsequently,the matched lumped disturbances are extended to the new system states and the extended integral chain pseudo-linear system is obtained.A LESO with input saturation constraints is used to estimate the system states.In order to solve the input saturation compensation problem and prove the semi-global ultimate uniformly bounded stability of the closed-loop system based on Lyapunov function stability analysis,an adaptive ISC law with sliding mode surface as input is designed and the expression of the sliding mode control law with input saturation compensation term is given.The simulation results show the effectiveness and robustness of the two control schemes mentioned above respectively.Furthermore,the simulation results show that,compared with the feedback linearization conrtrol scheme based on DOB with anti-windup measure,the tracking control scheme based on LESO is more suitable for dealing with time-varying external disturbance under the allowable large state observation gain setting.(5)Aiming at the problem that the disturbance observer and the linear extended state observer with fixed preset observing gain may have estimation error,the compensation measures for the estimation error of the disturbance observer and the linear extended state observer are designed respectively.The simulation results show that the proposed estimation error compensation method is helpful to reduce the tracking errors of the system outputs.Moreover,the estimation error compensation method has limited influence on the response of the control inputs of the VSJs.