tailieunhanh - Robotics 2010 Current and future challenges Part 3

Tham khảo tài liệu 'robotics 2010 current and future challenges part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Modeling and Control of Mechanical Systems in Terms of Quasi-Velocities 59 Appendix B Consider the following positive-definite function 1 V 2 Hen2 In view of Remark 2 the time-derivative of the above function along the error trajectory 40 is obtained as V eT rre eT K e T Kde which gives V 2Amin Kd V. Thus V V 0 e 2Amin Kd t which is equivalent to 41 . Appendix C Consider the following positive-definite function V 1 0 2 49 whose time-derivative along 42 gives V è T Kp 0 T B e e 0T B 0 B 0d vd. From 44 and 43 we can find a bound on V as V Amin Kp 0 2 Cb 0 e Cjcv 0 2 50 272V Cb VzV e which is in the form of a Bernoulli differential inequality. The above nonlinear inequality can be linearized by the following change of variable U vV . U i 2U IH0 e n1t 51 In view of the comparison lemma Khalil 1992 p. 222 and 41 one can show that the solution of 51 must satisfy U U 0 e n2t Cb1 11 yt e n2 t T n1 TdT which is equivalent to 45 . 60 Robotics 2010 Current and Future Challenges 6. References Aghili F 2005 . A unified approach for inverse and direct dynamics of constrained multibody systems based on linear projection operator Applications to control and simulation. IEEE Trans. on Robotics 21 5 834-849. Aghili F. 2008 . A gauge-invariant formulation for constrained robotic systems using squareroot factorization and unitary transformation. In IEEE RSJ Int. Conf. on Intelligent Robots and Systems. Nice France. pp. 2814-2821. Aghili F. 2009 . A gauge-invariant formulation for constrained mechanical systems using square-root factorization and unitary transformation. ASME Journal of Computational and Nonlinear Dynamics Vol. 4 No. 3. Aghili Farhad 2007 . Simplified lagrangian mechanical systems with constraints using square-root factorization. In Multibody Dynamics 2007 ECCOMAS Thematic Conference. Milano Italy. Angeles J. 2003 . A methodology for the optimum dimensioning of robotic manipulators. Memoria del 5o. Congreso Mexicano de Robótica. UASLP San Luis Potosí SLP Mexico. pp.