tailieunhanh - Control of Robot Manipulators in Joint Space - Part 3

Part III Motion Control Hãy xem xét mô hình năng động của một tay máy robot với mức độ tự do n, các liên kết cứng nhắc, không có ma sát ở các khớp và cơ cấu truyền động lý tưởng, (3,18), mà chúng ta lặp lại ở đây cho dễ tham khảo: | Part III Motion Control Introduction to Part III Consider the dynamic model of a robot manipulator with n degrees of freedom rigid links no friction at the joints and with ideal actuators which we repeat here for ease of reference M q q C q q q g q T . In terms of the state vector qT qT these equations are rewritten as d q q di _q_ _M q -1 r t - C q q q-g q _ where M ợ G IR X is the inertia matrix C q q q G IR is the vector of centrifugal and Coriolis forces g G IR is the vector of gravitational torques and T G IR is a vector of external forces and torques applied at the joints. The veetora a é iR G IRC denote theposition velocityandjointacceleration respectively. The ptelotemirf motíoneenteol tracking control for robot manipulators may be formulated in the follow ng terms consider the dynamic 1 n-DOF robot III. 1 . Given a set of vectorial bounded functions qd and qd referred to as desired joint positions velocities and accelerations we wish to find roectoria1 fuvetiop ptucfo thfot theppedfonsqjeesedatedtp jhe robot s joint coordinates follow qd accurately. In more forinal tenne the objective of motion control consists in finding T such that n lim q f 0 p . i ei . . o r I where ỘG vee stcnhsfoc tie ooifot positionarrors crctos eo issimvCycalled veaitfop essOT avd is hrfinePPp eiej 9d - eM 224 Part III Considering the previous definition the vector q i qd i q i stands for the velocity error. The control objective is achieved if the manipulator s joint variables follow asymptotically the trajectory of the desired motion. The computation of the vector T involves in general a vectorial nonlinear function of q q and q. This function is called control law or simply controller . It is important to recall that robot manipulators are equipped with sensors to measure position and velocity at each joint henceforth the vectors q and q are measurable and may be used by the controllers. In some robots only measurement of joint position is available and joint .