tailieunhanh - Advances in Robot Manipulators Part 15

Tham khảo tài liệu 'advances in robot manipulators part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 552 Advances in Robot Manipulators above there is a need of a detailed and practical two-link planar robotic system modeling with the practically distributed robotic arm mass for control. Therefore this chapter develops a practical and detailed two-link planar robotic systems modeling and a robust control design for this kind of nonlinear robotic systems with uncertainties via the authors developing robust control approach with both H V disturbance rejection and robust pole clustering in a vertical strip. The design approach is based on the new developing two-link planar robotic system models nonlinear control compensation a linear quadratic regulator theory and Lyapunov stability theory. 2. Modeling of Two-Link Robotic Systems The dynamics of a rigid revolute robot manipulator can be described as the following nonlinear differential equation 1 2 6 10 Fc M q q V q q q N q q N q q G q Fdq Fs q where M q is an n X n inertial matrix V q q an n X n matrix containing centrifugal and coriolis terms G q an n X 1 vector containing gravity terms q t an n X 1 joint variable vector Fc an n X 1 vector of control input functions torques generalized forces Fd an n X n diagonal matrix of dynamic friction coefficients and Fs q an n X 1 Nixon static friction vector. However the dynamics of the robotic system 1 in detail is needed for designing the control force . especially what matrices M q V q q and G q are. Consider a general two-link planar robotic system in Fig. 1 where the system has its joint mass m1 and m2 of joints 1 and 2 respectively robot arms mass m1r and m2r distributed along arms 1 and 2 with their lengths 71 and 12 generalized coordinates q1 and q2 . their rotation angles q q1 q2 control torques generalized forces f1 and f2 Fc f1 f2 . Fig. 1. A two-link manipulator ROBUST CONTROL DESIGN FOR TWO-LINK NONLINEAR ROBOTIC SYSTEM 553 Theorem 1. A general two-link planar robotic system has its dynamic model as in 1 with M q M 11 M 21 M12 M22 2 M11 m1 Ỉ1mr1 m2