tailieunhanh - Giáo trình robot - Phần 4

Tham khảo tài liệu 'giáo trình robot - phần 4', kỹ thuật - công nghệ, tự động hoá phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 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 .