Research On The High Precision Posture Control Of Parallel Manipulator Driven By Pneumatic Muscles

Pneumatic muscle is a new type of flexible pneumatic actuator with the same out-put characteristics as human muscle, and is designed according to motion principle ofhuman muscle. It has not only the advantages of cleanliness, lightweight, cheapnessand easy maintenance possessed by pneumatic actuators, but also the special feature ofhigher power/weight ratio and power/volume ratio as well as good compliance ow-ing to its force-length characteristics similar to human muscle when compared withthe pneumatic cylinder. The parallel manipulator has the characteristics of high loadingcapability, no accumulative errors, high accuracy and fast response. The parallel manip-ulator driven by pneumatic muscles proposed in this dissertation is a new applicationof pneumatic muscle, which consists of three pneumatic muscles connecting the mov-ing platform to its base platform. Multiple degrees-of-freedom (DOF) rotation motion ofthe parallel manipulator can be realized by using cheap fast switching valves to regulatethe pressure inside each pneumatic muscle. Integrating the advantages of both pneu-matic muscle and parallel manipulator, such a test-rig has the characteristics of compactstructure, easy assembly, cheapness, smooth movement, good natural compliance andsafety operation, higher power/weight ratio and power/volume ratio, which will havepromising wide applications in robotics, industrial automation, and bionic devices.However, there are not only severe nonlinearity and time-varying parameters ex-isting in the pneumatic muscles but also the MIMO coupling effect and large uncertain-ties existing in the parallel manipulator. These factors bring a challenge for the highprecision posture controlling of the parallel manipulator driven by pneumatic muscles.Firstly, the relationship among contractive force, contractive length and inner pressureis highly nonlinear, and the accurate contractive force is not easily obtained. Frictionforce and hysteresis of pneumatic muscle are influenced by its pressure and tempera-ture etc., and the characteristics of the friction force are difficult to obtain. The innerpressure dynamics of the pneumatic muscle is nonlinear. If we regard it as polytropicprocess, this inaccurate model will bring disturbances to controlling of parallel manipu-lator. Furthermore, though the pressure in tube may be assumed to be uniform, the tem-perature in tube is non-uniform. Secondly, the method for calculating flow rate through fast switching valves is based on the steady-state measurement, thus the instantaneousflow rate through them could not be obtained resulting in large model errors. There aresome disadvantages of controlling the system from fast switching valves, such as pul-satory flow rate, delay time of opening and closing fast switching valves. Thirdly, theparallel manipulator is a MIMO coupling nonlinear system, and the accurate parame-ters are difficult to obtain. There also exist unknown external disturbance moments inthe parallel manipulator.Research object of this doctoral dissertation is a parallel manipulator driven bypneumatic muscles, and research aim is to realize the high precision posture trajectorytracking of the parallel manipulator. With the help of theoretical analysis and experi-mental research, the high precision control strategies of the parallel manipulator drivenby pneumatic muscles are investigated systemically and thoroughly step-by-step.In order to tackle the deteriorated consistency of tracking accuracy due to timevarying operating points induced by redundancy, an equivalent-average-stiffness-likeconstraint is integrated into the adaptive robust controller to remove the redundancy,and the equivalent average stiffness is optimized through minimizing measurementnoise gain. Thus, not only high precision posture trajectory tracking is achieved butalso control chattering is reduced. In order to solve the problem of parameter adapta-tion without pressure sensors, a nonlinear pressure observing method is presented inthe pneumatic system with multiple actuators coupling. An adaptive robust controllerbased on the above pressure observer is developed to compensate and attenuate theadded uncertainties from pseudo-decoupling process, the dynamic uncertainties fromobservation errors of pressure and the uncertainties of model itself for achieving highprecision posture trajectory tracking of the parallel manipulator without pressure sen-sors. In order to deal with large transient tracking errors in the process of changingdirection, a new parameter estimation algorithm based on composite error minimiz-ing criterion is proposed for the first time to obtain reliable and reasonable parame-ter estimation results for the dynamic equation with redundancy. Integrating the newalgorithm with adaptive robust control, an integrated direct/indirect adaptive robustcontroller is developed. This controller achieves excellent experimental results of thesteady-state error being less than 0.01°and average tracking error less than 0.1°andmaximum tracking error less than 0.3°during tracking sinusoidal trajectory. Main research contents of this doctoral dissertation are divided into the followingchapters.In Chapter 1, development course, main characteristics and usage form of the pneu-matic muscle are introduced. The domestic and foreign research stage of pneumaticmuscle is discussed on the mathematical model, related characteristics, control methodand system application. Finally, necessity, difficulties and main contents of this projectare summarized concisely.In Chapter 2, the mechanism and hardware components of the parallel manipulatordriven by pneumatic muscles are introduced briefly. According to the valid modelingassumptions, the full nonlinear mathematical models of the parallel manipulator drivenby pneumatic muscles are obtained through respectively establishing dynamic equationof the parallel manipulator, the contractive force equation of pneumatic muscle, the dif-ferential equation of pressure, the differential equation of temperature and the averageflow rate equation. Then, according to the added assumptions, the simplified nonlinearmathematical models that are convenient to design nonlinear controller are obtained.The characteristics of the system and the influence of model parameters on the perfor-mance are analyzed through linearizing the nonlinear mathematical models to obtainthe operating points of static equilibrium and simulating the system under the condi-tion of open-loop control.In Chapter 3, according to the stiffness definition of a general parallel manipulator,both static stiffness and dynamic stiffness of the parallel manipulator driven by pneu-matic muscles are deduced, and moreover, the static stiffness under different posturesand the influence of static stiffness on the performance are analyzed. An equivalentaverage stiffness of parallel manipulator driven by pneumatic muscles is defined forthe first time, and then the principle of utilizing the equivalent average-stiffness-likedesired constraint in the posture controller to remove the control redundancy of theparallel manipulator is developed. Moreover, it is presented that the choosing prin-ciples of the equivalent average stiffness respectively from three aspects of adjustablerange, optimization method and the relation between equivalent average stiffness andequivalent average pressure. Furthermore, attention points of utilizing the equivalentaverage stiffness are also given.In Chapter 4, a three-order dynamic equation with pseudo-decoupling between the control inputs and the state variables is established for the parallel manipulator drivenby pneumatic muscles. An output differential observer is constructed to obtain velocitysignals and acceleration signals. A full order sliding-mode controller with boundarylayer and linear switching function is designed and two reduced order sliding-modecontrollers with boundary layer and nonlinear or linear switching function are also de-signed respectively. The relations of tracking errors to switching function of sliding-mode controller, control parameters and model uncertainties are analyzed. And theinfluence of boundary layer and supply pressure on the performance is also discussed.In Chapter 5, the system model in form of parametric uncertainties is derived atfirst. Then, a discontinuous projection-based adaptive robust controller (ARC) is de-signed, which utilizes the parameter adaptation to compensate large parametric uncer-tainties from unknown parameters in the system model, and uses the robust feedback toattenuate rather severe nonlinear uncertainties, and applies the equivalent average stiff-ness to remove control redundancy and determine the operating points of the systemso that the problem of consistency of tracking accuracy deteriorating is solved while theproblem of control chattering is reduced. In addition, the influence of control param-eters on the performance is analyzed theoretically. Finally, the influence of equivalentaverage stiffness on performance (especially on the control chattering) is analyzed ex-perimentally.In Chapter 6, for enhancing the system reliability and saving the system cost, pres-sure sensors are canceled, so there are not only the large parametric uncertainties andrather severe nonlinear uncertainties in the system but also the added dynamic uncer-tainties from unknown pressures. A single-input-single-output (SISO) pseudo-decouplingmodel of the single driving-unit is derived for constructing a nonlinear pressure ob-server and estimating unknown pressure. Then, a pressure observer based adaptiverobust controller is developed to accomplish high precision posture trajectory trackingof the parallel manipulator driven by three pneumatic muscles without pressure sen-sors. Finally, the influence of supply pressure on the performance is analyzed.In Chapter 7, in order to obtain more accurate model of the system, the dynamicequation of the parallel manipulator is described as the modified model in the form ofparametric linearization to express unmodeled errors. A new parameter estimation al-gorithm based on composite error minimizing criterion is presented, then the discrete parameter estimation algorithm is proposed to obtain the initial values of parametersin the modified model and the continuous parameter estimation algorithm is proposedto realize on-line parameter adaptation. The flow rate equation is modified throughcontrolling the constant contractive length of a single pneumatic muscle. On the abovebasis, an integrated direct/indirect adaptive robust controller is developed to solve theproblem of large transient tracking errors when the direction of motion in the paral-lel manipulator is changed, and the reliable and reasonable parameter estimation isachieved.In Chapter 8, the integrated direct/indirect adaptive robust controller is tested onthe parallel manipulator driven by pneumatic muscles under various experimental con-ditions. The experimental results of step response, sinusoidal trajectory tracking andarbitrary continuous trajectory tracking are given. The robustness of the system is ver-ified through applying sudden disturbance on a position transducer. The influence ofsupply pressure, the theoretical contractive force, the weights of error criterion and theequivalent average stiffness on the performance are analyzed.In Chapter 9, main research work, conclusions and innovation points of this doc-toral dissertation are summarized. At the same time, future development of parallelmanipulator driven by pneumatic muscles is predicted in order to provide referencesfor the further research on this project.