tailieunhanh - Control of Robot Manipulators in Joint Space - R. Kelly, V. Santibanez and A. Loria Part 12

Tham khảo tài liệu 'control of robot manipulators in joint space - r. kelly, v. santibanez and a. loria part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 324 14 Introduction to Adaptive Robot Control Mutjl mil ll m-2 íị 2 2 i C2 005 72 Il I Mu q m-2 2 Mo2 cos 72 h M21 q m-2 2 Mo2 cos 72 h M q m2ll2 h Cu q q -m2lilC2 sin ợ2 Ợ2 CÚ2 q q -iWUc2 8111 72 qi 72 CMq q m2lilc2 sin 72 qi C 22 q q 0 gi q míỈA m2Ỉí gsin cli -rm l g sin qi 72 72 q m2lc2g sin 7 72 . For tills example we have selected as parameters of interest the mass m2 the merttals end thelneatino nt the center nt mats nt the second link. lc2. In contoart to the previous example where the dynamic niotlt l pA6 v f4-la wat writtee directly in terms of the dynamic varametam hete ht is necessary to determine the latter as functions of the parameters of interest. To spal end depqs 1ia t tha rectors u a u2 Cl to U 1 w2 V w Thedevelxpment of the parameterization in this example leads to M q e u c qpv e ỡ o c hte am i w 21 In ta2 3 91 Ớ2 h3 Atot e co q w ho2 e ha . . sin h2 2- qq. . . Z1 or _ Z1 sinteKii -Il wi 12 V2 7 sin qi 72 13 Ui U2 21 0 I2Q. 2 21 cos to eHt otih 7 sin 71 7q 23 U1 2 h te Ớ1 rn Ớ h p L sJ m 2 2 te The Adaptive Robot Control Problem 325 M0 q co q w ỡo q 0 0 0 0 o 0 0 mJc sin i 0 Notice that effectively the vector of dynamic parameters 0 depends exclusively on the parameters of interest 7712 Il and C2. Ộ The Adaptive Robot Control Problem mu. We have presented and discussed so far the fundamental property of linear parameterization of robot manipulators. All the adaptive controllers that we study in the followmg phapters rely on the assumption that this property holds. Also it is assumed that liiiceWtiiiily in the model of the manipulator consists only of th0 lact of knowledge of the numerical values of the elements of 0. Hence the structural form of the model of the manipulator is assumed to be exactlyknown that is thematrices t r n it w Mo q Cij q w and the nertor at q wrensqnmedtobcknown. Formally the control problem that we address in this text may be stated in the following terms. Consider the dynamic equation of n-DOF robots