Research On The Dynamical Servo Control Problem For A Class Of Underactuated Mechanical Systems

With the progress of society and development of industrial application, a specialkind of mechanical system named underactuated mechanical system(UMS) graduallyemerges in robotics, aerospace and transportation and other areas. Different from tra-ditional fullyactuated mechanical systems. This special systems have fewer actuatorthan degree of freedom, which include not only strong nonlinear and coupling factorsbut also actuator missing and nonholonomic constraint property, which makes motioncontrol of UMS become an extremely challenging hotspot and difficulty in controlresearch.A special motion control problem can be abstracted from the"bio-brachiationmotion control"of Bio-Primates robot. Different from traditional point stabilizationcontrol or trajectory tracking control, it only care about accessibility of target pointand not concrete realization ways and the final trajectory is periodic and dynamical,so it is called"dynamical servo control(DSC)"."Dynamic servo control"not just existin the primate bio-robot, but also widely exists in a class of UMS such as Acrobot,TORA and vertical planar underactuated manipulator. Taking Acrobot (underactuatedtwo-arm brachiation robot) as the application object, relying on the National NaturalScience Foundation project"The bio-brachiation of Bio-Primates robot and its controlstrategy", this dissertation will systemically study the involved trajectory planning andtrajectory tracking control problem to realize dynamical servo control of a class ofUMS.Dynamic equations of general mechanical systems and Acrobot are model byLagrange equation. Based on such models, definitions of fullyactuated mechanicalsystem and UMS are given in mathematics. According to whether there exists secondorder nonholonomic constraints and converse force in the underactuated freedom, theUMS are classified to first order nonholonomic UMS, non-conservative second ordernonholonomic UMS, conservative second order nonholonomic UMS. By analyzingthe controllability and accessibility of second order nonholonomic UMS, charactersof the class of UMS suitable for dynamical servo control are given. Definition ofdynamical servo control is given and analyzed and is divided into two subtypes: basicdynamical servo control and point-to-point dynamical servo control. Through periodic motion analysis of conservative system, an energy based dy-namical servo trajectory planning method is proposed, which uses both the actuatedfreedom and system energy to determine an orbit passing through the target point. Toovercome shortcoming that the planned trajectory is unique and cannot be improved, avirtual constraints based method is proposed, which uses general virtual contraints andorbit function instead of constant constraints on actuated freedom and system energyfunction to character the trajectory. By caculating and judging whether the trajectoryis periodical, it is easy to gain periodic orbit passing through the target point. Basedon this work, a direct search method is proposed to solve the point-to-point trajectoryplanning problem.Trajectories planned by the energy based and virtual constraints based methodare determined by virtual constraint function and orbit function, thus trajectory track-ing problem can be transformed to output stabilization problem. On this basis, Lya-punov based trajectory tracking control method are proposed separately. To makefully use of the limited inputs, partial linearization method is used to stabilize virtualconstraints function by constructing virtual inputs. According to the relation betweenthe orbit function and virtual inputs, a cascade control law is designed to stabilizeboth the orbit function and virtual constraints function. Simulation results show theeffectiveness of the proposed two dynamical servo control method.Then, dynamical servo control experiments are performed on the dSPACE basedAcrobot platform. The experiments include energy based dynamical servo control,virtual constraints based dynamical servo control and robust experiments. Experi-ments results prove the proposed design method is effective.Finally, virtual constraints based trajectory planning and dynamical servo con-trol method for Acrobot is extended to a class consertive second order nonholonomicn DOF UMS with (n ? 1) inputs. To solve the complexity problem of the extenedcontrol method, a simplified control strategy is introduced. The improved method areapplied in the TORA and RRR underactuated manipulator in vertical plane. Simula-tion results show that the proposed dynamical servo control design process is correctand the simplified control strategy is effective.