摘要
气动肌肉是一种具有类似人类肌肉输出特性的柔性执行器，它是根据人类肌肉的运动原理设计而成。气动肌肉既具有清洁、质量轻、价格低、易维护等气动元件的优点，与气缸相比，还具有较大的功率／体积比和功率／质量比，并且由于其力—位移关系特性与人类肌肉特性相似而具有很好的柔顺性。并联关节机构具有承载能力强、无累积误差、精度高和反应速度快等优点。我们提出一种结构简单的气动肌肉并联关节，采用三根气动肌肉连接运动平台和基座，使用成本低的高速开关阀来控制气动肌肉的充气量实现气动肌肉收缩，从而达到多自由度的关节转角控制。该机构充分发挥气动肌肉与并联关节机构的优点，具有功率／重量比和功率／体积比大、结构紧凑、安装方便、成本低、运动平滑、自然柔顺性好、不易损害操作对象等诸多优点，在机器人、工业自动化、仿生机械等领域中具有较好的应用前景。
但是，气动肌肉的强非线性和参数时变性以及并联关节的多输入多输出耦合影响和模型不确定，给气动肌肉并联关节的高精度控制带来挑战。首先，气动肌肉的收缩力、收缩位移和内部压力之间具有复杂的非线性关系，其收缩力不易精确获得；气动肌肉的摩擦力和滞回受压力、温度等多种因素影响，其特性很难获得：气动肌肉内部压力微分方程的非线性，假定气体为多变过程，这将造成模型的不准确对控制量带来干扰，而且，虽然气腔内的压力可假定为均匀的，但温度却是不均匀的。其次，经过阀口的流量计算方法都是基于稳态流量测试标准，不能测试阀口的瞬态流量，存在较大的模型误差；高速开关阀存在流量脉动、开关延迟等多种不利控制因素。再者，气动肌肉并联关节为多输入多输出且耦合的非线性系统，各种参数不易精确获得；且存在未知的外部干扰力矩。
本论文以气动肌肉并联关节为研究对象，以实现高精度轨迹跟踪控制为研究目标，采用理论分析与试验研究相结合的方法，系统地且逐层深入地研究了气动肌肉并联关节位姿的高精度控制方法。
针对冗余的控制自由度使得工作点时变从而导致轨迹跟踪精度一致性变差的问题，提出在基于反步法的自适应鲁棒控制中加入期望等效平均刚度约束来消除冗余的控制自由度，并根据测量噪声增益对等效平均刚度进行优化设计，既保证了高精度的位姿轨迹跟踪又减少了控制量振荡。针对无压力传感器时的参数自适应问题，提出多执行器耦合气动系统的非线性自适应压力观测方法，并与自适应鲁棒控制策略相结合将伪解耦过程中新增的不确定、压力观测误差产生的动态不确定和模型本身的不确定一起进行抑制与补偿，从而实现无压力传感器时气动肌肉并联关节的高精度位姿轨迹跟踪。针对并联关节运动方向改变时瞬态跟踪误差较大的问题，提出基于复合误差最小化准则的参数估计方法获得具有冗余特征系统动力学方程的可靠且合理的参数估计，并与自适应鲁棒控制相结合，设计了直接／间接复合自适应鲁棒控制器。此控制方法获得的稳态误差小于0.01°，正弦轨迹跟踪的平均误差小于0.1°和最大跟踪误差小于0.3°。
本论文的主要研究分为九章，现分述如下：
第一章，介绍了气动肌肉的发展历程、主要特点和使用形式；探讨了国内外在气动肌肉的数学模型、相关特性、控制方法和系统应用等方面的研究现状；最后概述了本课题的研究意义、研究难点以及研究内容。
第二章，描述了气动肌肉并联关节系统实验装置的机构原理与硬件组成；根据数学建模的假设条件，通过建立并联关节的动力学模型、气动肌肉收缩力模型和压力微分方程、温度微分方程、平均流量方程，获得气动肌肉并联关节系统完整的非线性模型；根据附加的简化假设条件，将并联关节和执行器的动力学模型进行简化，获得气动肌肉并联关节系统简化的非线性模型以便设计非线性控制器；通过数学模型线性化、求取静平衡状态的系统工作点和进行开环控制下的系统仿真，分析系统的特性和各模型参数对系统性能的影响。
第三章，根据并联关节的一般刚度定义，推导出气动肌肉并联关节的静态刚度和动态刚度，分析了不同位姿点的静态刚度和静态刚度对系统性能的影响；首次定义了气动肌肉并联关节的等效平均刚度，并给出了使用等效平均刚度作为约束来消除冗余控制自由度的原理；从等效平均刚度的可调范围、优化方法和等效平均刚度与等效平均压力的关系三个方面，分析了等效平均刚度的选取原则，并给出其应用时的注意事项。
第四章，建立了气动肌肉并联关节的控制量和状态量互相伪解耦的三阶动态系统模型；构造了输出微分观测器以获取速度信号和加速度信号；分别设计了带边界层线性切换函数的全阶滑模控制器和带边界层线性或非线性切换函数的降阶滑模控制器；分析了跟踪误差与滑模切换函数、控制参数和系统不确定量之间的关系；探讨了边界层的影响和气源压力的影响。
第五章，导出了参数不确定形式的系统模型；设计了基于非连续参数投影映射的自适应鲁棒控制器，通过自适应参数估计来补偿因系统模型中某些参数未知而引起的参数不确定，通过鲁棒反馈抑制系统模型中的严重非线性不确定，通过优化的等效平均刚度消除冗余控制自由度以确定系统的工作点从而解决轨迹跟踪精度的一致性变差问题和减少控制量的振荡；从理论上分析了控制器的参数对系统控制性能的影响；从实验上分析了等效平均刚度对系统控制性能特别是归一化的控制变化量的影响。
第六章，为提高可靠性和降低成本而取消压力传感器，这样不仅存在气动肌肉并联关节系统的参数不确定和严重非线性不确定，而且新增了压力未知导致的动态不确定；导出了单支路的单输入单输出伪解耦模型以便构造压力观测器来估计未知的压力；设计了基于压力观测的自适应鲁棒控制器实现气动肌肉并联关节无压力传感器时的高精度轨迹跟踪；分析了气源压力对系统控制性能的影响。
第七章，为获得气动肌肉并联关节系统的精确模型，将并联关节的动力学模型表示为参数线性化的修正模型以便把未建模误差表示出来；提出基于复合误差最小化准则的参数估计算法，给出离散形式的参数辨识获取修正模型参数的初始值，给出连续形式的参数辨识以便实现在线的自适应参数估计；通过单根气动肌肉收缩长度的定长控制对流量模型进行了修正。在此基础上，设计了基于参数投影映射的直接／间接复合自适应鲁棒控制器以解决气动肌肉并联关节运动方向改变时瞬态跟踪误差较大的问题，同时获得了可靠且合理的参数估计。
第八章，在气动肌肉并联关节上对直接／间接复合自适应鲁棒控制器进行了各种试验测试；给出了阶跃位姿响应、正弦轨迹跟踪、任意连续轨迹跟踪的试验结果；通过施加突变干扰测试了控制器的鲁棒性；分析了气源压力、气动肌肉理论收缩力、误差准则权值和等效平均刚度对系统控制性能的影响。
第九章，总结归纳了本博士论文的主要工作、研究结论和创新点，同时对气动肌肉并联关节的未来发展进行了展望与预测，为本方向的后继研究提供了参考。
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.
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