To overcome the shortcomings of underactuated mechanical systems which are unable to track arbitary point and trajectory, give full play to the resource and energy comsuming advantage and enlarge the application area, the dynamical servo control problem for a class of underactuated mechanical systems was studied. The dynamcal servo control aims to realize reaching any point in configuration space by planning and tracking specific trajectory. The virtual constraints method was used to plan the dynamcial servo trajectory. By constructing the constraint relation between freedoms and analysing the system zero dynamics , periodic orbits meeting system dynamics were gained easily. Using the inner connection between the virtual constraints and orbit function, a orbit tracking controller was designed based on Lyapunov stability theory. The experiment was performed on the Acrobot Platform and experiment results shows the effectiveness of the trajectory planning method and control method．
CHENG Hong-tai, ZHANG Xiao-hua. Virtual constraints based dynamical servo control for a class of underactuated mechanical systems. J4, 2011, 45(5): 818-824.
［1］ SPONG M W. The swing up control problem for the Acrobot ［J］. IEEE Control Systems Magazine, 1995,15(1):49-55． ［2］ XIN X, KANEDA M. The swing up control for the Acrobot based on energy control approach ［C］∥Proceeding of the 41st IEEE Conferenceon Decision and Control. Las Vegas: IEEE, 2002,1 :3261-3266． ［3］ BERKEMEIER M D, FEARING R S. Tracking fast inverted trajectories of the underactuated Acrobot ［J］. IEEE Trans. on Robotics and Automation, 1999, 15(4):740-750． ［4］ 张晓华, 程红太, 赵旖旎. 基于能量的Acrobot动态伺服控制［J］. 控制与决策,2008,23(11), 1258-1262． ZHANG Xiaohua, CHENG Hongtai, ZHAO Yini. Energy based dynamical servo control for the Acrobot ［J］. Control and Decision,2008,23(11): 1258-1262． ［5］ CHUNG C C, HAUSER J. Nonlinear control of a swinging pendulum ［J］.Automatica, 1995, 31 (6) : 851-862． ［6］ 程红太, 赵旖旎,张晓华,Acrobot动态伺服控制及其对称虚约束方法研究［J］,自动化学报,2010,36(11):1594-1600． CHENG Hongtai, Zhao Yini, Zhang Xiaohua. Study of dynamical servo control for the acrobot and symmetrical virtual constraints method ［J］. ACTA AUTOMATICA SINICA,2010,36(11): 1594-1600． ［7］ SHIRIAEV A, PERRAM J W, CANUDAS DE WIT. Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach ［J］. IEEE Trans. on Automatic Control, 2005, 50(8): 1164-1176． ［8］ METTIN U, LA HERA P, FREIDOVICH L, et al. Generating humanlike motions for an underactuated threelink robot based on the virtual constraints approach ［C］∥ Proceeding of the 46th IEEE Conference on Decision and Control. New Orleans: IEEE, 2007, 1:5138-5143． ［9］ SHIRIAEV A, PERRAM J, ROBERTSSON A, et al. Explicit formulas for general integrals of motion for a class of mechanical systems subject to virtual constraints ［C］∥ Proceeding of the 43rd IEEE Conference on Decision and Control. Nassau, Bahamas: IEEE, 2004, 2:1158-1163． ［10］ SHIRIAEV A, SANDBERG A, CANUDAS DE WIT. Motion planning and feedback stabilization of periodic orbits for an acrobat ［C］∥Proceeding of the 43rd IEEE Conference on Decision and Control. Nassau, Bahamas: IEEE, 2004 , 1:290-295． ［11］ SHIRIAEV A, FREIDOVICH L, ROBERTSSON A. Virtual constraints based design of stable oscillations of furuta pendulum: Theory and experiments ［C］∥ Proceeding of the 45th IEEE Conference on Decision and Control. San Diego, CA, USA:IEEE, 2006. 1:6144-6149． ［12］ SLOTINE J J, LI W, Applied nonlinear control ［M］. Englewood Cliffs, NJ: Prentice Hall, 1991:207-213．
