無人搬運車(AGV)的階層式架構模型，包含運動學、機械運動子系統和直流馬達動力學，而虛擬期望的輸入(VDI) (即馬達需要的電流)是經由第一個Lyapunov定理得到，其組成為第一滑動曲面的二次函數，是無人搬運車姿態的線性動態誤差 ，接著，階層路徑追蹤控制(HPTC)是由第二Lyapunov定理得到，其組成為第二滑動曲面的二次函數，是VDI的線性動態追蹤誤差。如此一來，使得直接輸出(即馬達電流)漸進或有界地追蹤虛擬期望的輸入(VDI)，緊接著，使得AGV追上想要的路徑(即所規劃的AGV任務)。VDI和HPTC都具有等效控制與增強模糊動態滑動控制(IFHSMC)，其中等效控制乃是處理標稱動態系統(Nominal Dynamic System)，而IFDSMC乃是處理系統的不確定項(例如:由不同的地面條件、不同的載重所產生的摩擦力或力矩)。因此提出整合VDI和HPTC的階層增強模糊動態滑動控制(HIFDSMC) ，並以階層概念的Lyapunov穩定性定理驗證閉迴路系統的穩定性。最後，將HIFDSMC應用於裝配線上的AGV，進行載重的圓形路徑和分段直線路徑追蹤。此外，為了驗證本論文所提出之控制系統的有效性與強健性，並和階層模糊分散路徑追蹤控制 (HFDPTC)進行相關實驗之比較。

Due to the hierarchical architecture of the derived model of the automatic guided vehicle (AGV), i.e., kinematics, mechanical motion subsystem, and electrical dc motor dynamics, the virtual desired input (VDI) (i.e., the desired motor current) is at the outset designed by the 1st Lyapunov function, which is a quadratic function of the first sliding surface, set as the linear dynamic pose error of the AGV. In sequence, the hierarchical path tracking control (HPTC) is designed by the 2nd Lyapunov function, which is made up by the quadratic function of the second sliding surface, i.e., the linear dynamic tracking error of the VDI. Thus, the direct output (i.e., the motor current) either asymptotically or boundedly tracks the VDI. In this situation, the asymptotic or bounded tracking of the indirect outputs (i.e., the pose of AGV) is achieved. Both VDI and HPTC contain equivalent control and improved fuzzy dynamic sliding-mode control (IFDSMC). The nominal dynamic system is tackled by equivalent control; on the other hand, IFDSMC deals with the system uncertainties (e.g., friction force or torque caused by different ground conditions, different payloads). The integration of VDI and HPTC is the proposed hierarchical improved fuzzy dynamic sliding-mode control (HIFDSMC). The stability of the closed-loop system is also verified by Lyapunov stability theory using hierarchical concept. Finally, the application to the assembly line of the AGV with payload for tracking circular path and piecewise straight-line path by the proposed HIFDSMC are compared with the hierarchical fuzzy decentralized path tracking control (HFDPTC).

[1] C. L. Hwang and N. W. Chang, “Fuzzy decentralized sliding-mode control of car-like mobile robots in a distributed sensor-network space,” IEEE Trans. Fuzzy Syst., vol. 16, no. 1, pp. 97-109, Feb. 2008.
[2] E. J. Jung, J. H. Lee, B. J. Yi, J. Park, S. Yuta, and S. T. Noh, “Development of a laser-range-finder-based human tracking and control algorithm for a Marathoner service robot,” IEEE/ASME Trans. Mechatronics, vol. 19, no. 6, pp. 19963-1976, Dec. 2014.
[3] G. Ishigami, K. Iagnemma, J. Overholt, and G. Hudas, “Design, development, and mobility evaluation of an omnidirectional mobile robot for rough terrain,” Journal of Field Robotics, vol.32, no. 6, pp. 880-896, 2015.
[4] C. L. Hwang and W. L. Fang, “Global fuzzy adaptive hierarchical variable structure control for trajectory tracking of a mobile robot with huge uncertainties,” IEEE Trans. Fuzzy Syst., to be appeared, 2016. [5] H. S. Kim and J. B. Song, “Multi-DOF counter balance mechanism for a service robot arm,” IEEE/ASME Trans. Mechatronics, vol. 19, no. 6, pp. 1756-1763, Dec. 2014.
[6] S. I. Han and J. M. Lee, “Balancing and velocity control of a unicycle robot based on the dynamic model,” IEEE Trans. Ind. Electron., vol. 62, no. 1, pp. 405-413, Jan. 2015.
[7] R. Loureiro, S. Benmoussa, Y. Touati, R. Merzouki, and B. O. Bouamama, “Integration of fault diagnosis and fault-tolerant control for health monitoring of a class of MIMO intelligent autonomous vehicles,” IEEE Trans. Veh. Technol., vol. 63, no. 1, pp. 30-39, Jan. 2014.
[8] J. C. L. Barreto S., A. G. S. Conceic˜ao, C. E. T. D´orea, L. Martinez, and E. R. de Pieri, “Design and implementation of model-predictive control with friction compensation on an omnidirectional mobile robot,” IEEE/ASME Trans. Mechatronics, vol. 19, no. 2, pp. 467-476, Apr. 2014.
[9] C. M. Lin and Y. J. Mon, “Decoupling control by hierarchical fuzzy sliding-mode controller,” IEEE Trans. Contr. Syst. Technol., vol. 13, no. 4, pp. 593-598, Jul. 2005.
[10] W. Wang, X.D. Liu, and J.Q. Yi, “Structure design of two types of sliding-mode controllers for a class of under-actuated mechanical systems,” IET Control Theory Appl., vol. 1, no. 1, pp. 163-172, Jan. 2007.
[11] C. L. Hwang, C. C. Chiang, and Y. W. Yeh, “Adaptive fuzzy hierarchical sliding-mode control for the trajectory tracking of uncertain under-actuated nonlinear dynamic systems,” IEEE Trans. Fuzzy Syst., vol. 22, no. 2, pp. 286-297, Apr. 2014.
[12] A. Mohammadzadeh, O. Kaynak, and M. Teshnehlab, “Two-mode indirect adaptive control approach for the synchronization of uncertain chaotic systems by the use of a hierarchical interval type-2 fuzzy neural network,” IEEE Trans. Fuzzy Syst., vol. 22, no. 5, pp. 1301-1312, Oct. 2014.
[13] K. Chu, M. Lee, and M. Sunwoo, “Local path planning for off-road autonomous driving with avoidance of static obstacles,” IEEE Trans. Intell. Transp. Syst., vol. 13, no. 4, pp. 1599-1616, Dec. 2012.
[14] A. K. Pamosoaji and K. S. Hong, “A path-planning algorithm using vector potential functions in triangular regions,” IEEE Trans. Cybern., vol. 43, no. 3, pp. 832- 842, Jul. 2013.
[15] R. Zou, V. Kalivarapu, E. Winer, J. Oliver, and S. Bhattacharya, “Particle swarm optimization-based source seeking,” IEEE Trans. Autom. Sci. & Engrg., vol. 12, no. 3, pp. 865-875, Jul. 2015.
[16] J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control: A survey,” IEEE Trans. Ind. Electron., vol. 40, no. 1, pp. 2-22, Feb. 1993.
[17] Q. Gao, G. Feng, Y. Wang, and J. Qiu, “Universal fuzzy models and universal fuzzy controllers for stochastic nonaffine nonlinear systems,” IEEE Trans. Fuzzy Syst., vol. 21, no. 2, pp. 328-341, Apr. 2013.
[18] B. S. Chen, H. C. Lee, and C. F. Wu, “Pareto optimal filter design for nonlinear stochastic fuzzy systems via multiobjective H2/H∞ optimization,” IEEE Trans. Fuzzy Syst., vol. 23, no. 2, pp. 387-399, Apr. 2015.
[19] J. T. Huang, T. V. Hung, and M. L. Tseng, “Smooth switching robust adaptive control for
omnidirectional mobile robots,” IEEE Trans. Contr. Syst. Technol., vol. 23, no. 5, Sep. 2015.
[20] Y. H. Chang, C. W. Chang, C. L. Chen, and C. W. Tao, “Fuzzy sliding-mode formation control for multirobot systems: design and implementation,” IEEE Trans. Syst. Man & Cybern., Pt. B, vol. 42, no. 2, pp. 444-457, Apr. 2012.
[21] B. Ranjbar-Sahraei, F. Shabaninia, A. Nemati, and S. D. Stan, “A novel robust decentralized adaptive fuzzy control for swarm formation of multiagent systems,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 3124-3134, Aug. 2012.
[22] M. S. Park, D. Chwa, and M. Eom, “Adaptive sliding-mode antisway control of uncertain overhead cranes with high-speed hoisting motion,” IEEE Trans. Fuzzy Syst., vol. 22, no. 5, pp. 1262-1271, Oct. 2014.
[23] P. Salaris, A. Cristofaro, L. Pallottino, and A. Bicchi, “Epsilon-optimal synthesis for vehicles with vertically bounded field-of-view,” IEEE Trans. Autom. Contr., vol. 60, no. 5, pp. 1204-1214, May 2015.
[24] B. Kehoe, S. Patil, P. Abbeel, and K. Goldberg, “A survey of research on cloud robotics and automation,” IEEE Trans. Autom. Sci. Eng, vol. 12, no. 2, pp. 398–409, Apr. 2015.
[25] B. J. Choi, S. W. Kwak, and B. K. Kim, “Design and stability analysis of single-input fuzzy logic controller,” IEEE Trans. Syst. Man & Cybern., Pt. B, vol. 30, no. 2, pp. 303-309, Apr. 2000.
[26] Y. S. Kung, R. F. Fung, and T. Y. Tai, “Realization of a motion control IC for X−Y table based on novel FPGA technology,” IEEE Trans. Ind. Electron., vol. 56, no. 1, pp. 43-52, Jan. 2009.
[27] F. Taeed, Z. Salam, and S. M. Ayob, “FPGA implementation of a single-input fuzzy logic controller for boost converter with the absence of an external analog-to-digital converter,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 1208-1217, Feb. 2012.
[28] C. L. Hwang, “Neural-network-based variable structure control of electrohydraulic servosystems subject to huge uncertainties without the persistent excitation,” IEEE/ASME Trans. Mechatronics, vol. 4, no.1, pp. 50-59, Jan. 1999.
[29] H. K. Khalil, Nonlinear Systems, Prentice-Hall, 2nd Ed., 1996.