By Warren Dixon PhD, Darren M. Dawson PhD, Erkan Zergeroglu MSc, Aman Behal BS Elec Eng (auth.)

This publication examines the keep watch over challenge for wheeled cellular robots. numerous novel keep watch over ideas are built and the soundness of every controller is tested using Lyapunov strategies. The functionality of every controller is both illustrated via simulation effects or experimental effects. the ultimate bankruptcy describes how the keep an eye on concepts built for wheeled cellular robots might be utilized to resolve different issues of comparable governing differential equations (e.g., dual rotor helicopters, floor vessels). numerous appendices are incorporated to supply the reader with the mathematical historical past used in the regulate improvement and balance research. appendices also are incorporated that supply particular info with reference to the variations that have been performed to commercially to be had cellular robots (e.g., a K2A synthetic through Cybermotion Inc. and a Pioneer II synthetic through Activemedia) to experimentally exhibit the functionality of the torque enter controllers.

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66) where el, Tol(el) E N 1 are positive constants. 60) have been used. 67) by v2(t) and then integrating the resulting equation, we obtain the following expression 1 vo (t) 1 ~ot ~ot2klW2(Cr) vo (0) = 4k~davo (a) da. 70), and the fact that lim t--cOO vo(t) ----O, we can prove by contradiction that lim w2(t) = 0. 72) To2 (E2) E R 1 are positive constants. 74) and c2 T < w2 3c2 <-V Vt>To2(2). 75), we can conclude that ~)0(t) is nonnegative as shown below > 1 =klc2vo >_ 0 W > To. 62 3. 65). 71) leads to a contradiction, we can conclude that lim w2(t) = 0 t---*OO lim t--~Oo w(t) = 0.

667 [m] denotes the length of the axis between the wheels, and the dynamic and static friction elements are denoted by Fsl, Fs2, Fal, and Fd2. 5t) [rad/sec]. 2. 01 ]T. 47) The best-guess estimates for the mass and inertia were selected to be 50% 44 2. 2. 19)). 5. 75. 48) to facilitate the "tuning" process. 4 represent the torques applied after the gearing mechanism). 85 [Deg]. 48) were found as a result of "tuning" the controller until the position and orientation tracking error improved. Note that similar results may be obtained by "tuning" the controller in a slightly different manner.

Jiang, "Iterative design of time-varying stabilizers for multi-input systems in chained form", Systems and Control Letters, Vol. 28, pp. 255-262, 1996. [13] Z. Jiang and H. Nijmeijer, "Tracking Control of Mobile Robots: A Case Study in Backstepping", Automatica, Vol. 33, No. 7, pp. 13931399, 1997. [14] Z. Jiang and H. Nijmeijer, "A Recursive Technique for Tracking Control of Nonholonomic Systems in the Chained Form", IEEE Transactions on Automatic Control, Vol. 44, No. 2, pp. 265-279, Feb. 1999.

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