氣動肌肉外文翻譯--氣動肌肉驅動并聯(lián)機器人的自適應性魯棒姿態(tài)控制（英文）

1、ADAPTIVE ROBUST POSTURE CONTROL OF A PNEUMATIC MUSCLES DRIVEN PARALLEL MANIPULATOR 1Xiaocong Zhu ? Guoliang Tao ? Jian Cao ?Bin Yao ?,??? The State Key Laboratory of Fluid Power Transmission and Control Zhejiang Universi

2、ty, China ?? School of Mechanical Engineering Purdue University, West Lafayette, IN 47907, USAAbstract: Considering rather severe parametric uncertainties and nonlinear un- certainties exist in the dynamic model of pneum

3、atic muscles driven parallel manipulator, a discontinuous projection-based adaptive robust control strategy (ARC) is adopted to effectively handle the effect of various parameter variations of the system and hard-to-mode

4、l nonlinearities such as the friction forces of the pneumatic muscles and external disturbances of the entire pneumatic system to achieve remarkably precise posture trajectory control. Experimental results are obtained t

5、o illustrate the effectiveness of the proposed adaptive robust controller.Keywords: Pneumatic muscle,Parallel manipulator,Adaptive robust control1. INTRODUCTIONPneumatic muscle is a new kind of flexible actu- ator simila

6、r to human muscle, which is made up of rubber tube and cross-weave sheath material. Its basic working principle is as follows: when the rubber tube is inflated, the cross-weave sheath experiences lateral expansion, resul

7、ting in axial contractive force and the change of the end point position of pneumatic muscle. Thus, the position or force control of a pneumatic muscle along its axial direction can be realized by regulating the inner pr

8、essures of its rubber tube. The parallel manipulator driven by pneumatic muscles (PM by PM) studied in this paper is a new application of pneumatic muscles, which consists of three pneu-1 This work is supported by Festo

9、Inc. through an inter- national cooperation. The last author is supported by the National Natural Science Foundation of China (NSFC) un- der the Joint Research Fund (grant 50528505) for Overseas Chinese Young Scholars.ma

10、tic muscles connecting the moving arm of the parallel manipulator to its base platform as shown in Fig.1. By controlling the lengths of three pneu- matic muscles, any three-DOF rotation motion of the parallel manipulator

11、 can be realized. Such a parallel manipulator combines the advantages of compact structure of parallel mechanisms with the adjustable stiffness and high power/volume ratio of pneumatic muscles, which will have promising

12、wide applications in robotics, industrial automa- tion, and bionic devices.Severe nonlinearity and time-varying parameters exist in the pneumatic muscle dynamic model; examples include various frictions, hysteresis and t

13、he contractive force on the temperature (Lilly, 2003). These factors made the precise position control of a pneumatic muscle alone a signifi- cant challenge, which has received great attentions during the past several ye

14、ars. Though significant researches have been done on the control of pneu- matic muscles(Lilly, 2003; Bowler et al., 1996;764From Eq.1, define the drive moment of the parallel manipulator in task-space as τ =JT p (θ)F m a

15、nd differentiate it to obtain the actuator dynamics.˙ τ = f τ(θ, ˙ θ, p) + gτ(θ)Kq(p)u + dτ(t) (5)where f τ(θ, ˙ θ, p) = ˙ J Tp (θ, ˙ θ) ¯ F m + JT p ? ¯ F m?xm ˙ xm ?JT p ? ¯ F m ?p Af(xm, ˙ xm, p)λa , gτ

16、(θ)=JT p ? ¯ F m ?p Ag(xm)×diag(λb), ¯ F m = F m ? δF is the calculable part of F m, dτ(t) represents all the unknown distur- bances in driving unit space (muscle-space) and Kq is a matrix of nonlinear flo

17、w gain function deduced from Eq.3.Thus, define a set of state variables as x =[xT 1 , xT 2 , xT 3 ]T = [θT, ˙ θ T, τ T]T, the entire system can be expressed in state-space form as ? ??˙ x1 = x2 ˙ x2 = I?1 p (x1)[x3?Bp(x1

18、)?dp(t)] ˙ x3 = f τ(x1, x2, p)+gτ(x1)Kq(p)u+dτ(t) (6)and p = f p(x1, x3) is the inverse function of τ.3. ADAPTIVE ROBUST CONTROLLER3.1 Design Issues,Assumptions and NotationsGenerally the system is subjected to parametri

19、c uncertainties due to the variation of Cs, Ip, λa, λb and unknown nonlinearities dp and dτ. Prac- tically, dp and dτ may be composed of two parts, a nominal part denoted by dpn and dτn which is constant or slowly changi

20、ng and be dealt with by parameter adaptation, and a fast changing part denoted by ? dp and ? dτ, which have to be attenuated by the robust feedback.It can be seen that the major difficulties in con- trolling are: (a)The

21、system has severe parametric uncertainties represented by the lack of knowledge of the changing damping coefficients Cs and the polytropic exponents λa and λb. Hence on-line parameter adaptation method should be adopted

22、to reduce parametric uncertainties. (b)The sys- tem has a large extent of lumped modeling error like unknown disturbances and unmodeled fric- tion forces, which are contained in dp and dτ. So the approach with certain ro

23、bustness should be used to handle the uncertain nonlinearities for improving effectively performance. (c)The model uncertainties are mismatched, i.e. both paramet- ric uncertainties and uncertain nonlinearities ap- pear

24、in the dynamic equations that are not di- rectly related to the control input u. Therefore the backstepping design technology should be em- ployed to overcome design difficulties for achieving asymptotic stability.Since

25、the extents of parametric uncertainties and uncertain nonlinearities are known, the paramet- ric uncertainties and uncertain nonlinearities aresupposed to satisfy β ∈ ?β = {β : βmin ≤β ≤ βmax}, and ? dp ≤ dpmax, ? dτ ≤ d

26、τmax in which βmax and βmin are the maximum and mini- mum parameter vectors and dpmax and dτmax are known vectors.Let ? β denote the estimate of β and ? β=? β?β the estimation error. A discontinuous projection can be def

27、ined as Eq.7 in order to guarantee that the parameters and their derivatives are bounded in the whole process of adaptive robust control.(Yao et al., 2000)Proj? β(? i)=? ??0, if ? βi=βimax and ?i > 00, if ? βi=βimin a

28、nd ?i 0 is a diagonal matrix and σ is an adaptation function to be synthesized later.The projection mapping used in Eq. 8 guaranteed that P1: ? β ∈ ?β = {β : βmin ≤ β ≤ βmax} and P2: ? β T [Γ?1Proj? β(Γσ) ? σ] ≤ 03.2 AR

29、C Controller DesignThe design parallels the recursive backstepping design procedure in task-space and muscle-space via ARC Layapunov functions as follows. (Yao et al., 2000)1).Step1: Define a switching-function-like quan

30、- tity as z2 = ˙ z1 + Kcz1 (9)where z1=x1?yd is the trajectory tracking error vector and Kc is a positive diagonal feedback matrix. If z2 converges to a small value or zero, then z1 will converge to a small value or zero

31、 since the transfer function from z1 to z2 is stable. Then, differentiating Eq.9 while noting Eq.6,˙ z2 = I?1 p (τ ? Bpx2 ? dp) ? ¨ yd + Kc ˙ z1 (10)The unknown parameter vector in task-space is βp=[cs1, cs2, cs3, d

32、pn1, dpn2, dpn3]T and the term of parametric uncertainties in task-space is described as ? Bpx2 + ? dpn = ??T 2 ? βp (11)in which ?2=[?diag(GTGx2), ?I]T is a regressor for parameter adaptation.If τ is treated as the inpu

33、t to Eq.10, a virtual control law τ d is synthesized such that z2 is as small as possible. τ d consists of two terms given by τ d = τ da + τ ds (12)τ da = Ip(¨ yd ? Kc ˙ z1) ? ?T 2 ? βp (13)in which τ da functions a