Singularity And Control Of Underactuated Multi-joint Manipulator

An underactuated system is a system that the number of independent control inputs is less than its degrees of freedom.For underactuated manipulator,there is joint in the manipulator in which no drive is installed.Owing to the reduction of drive,underactuated systems with light weight,low cost,low energy consumption and many other advantages,the application prospect is very broad.Nonholonomic constraints with underactuated characteristics,many of the underactuated system are essentially nonholonomic system.Nonholonomic systems presents some complex properties because of motion coupling.Smooth nonliner feedback can't be used to achieve its asymptotic stability and input-state linearization can't be achieved,the system research had became one of the most challenging problem in the control field.This thesis mainly research about the motion planning and related control experiment for a nonholonomic underactuated manipulator.The underactuated multi-joint manipulator consists of a kind of nonholonomic mechanism.It was proved that the manipulator is controllable,and then a method of chained form conveition was proposed based on the kinematics model of underactuated manipulator.A motion planning algorithm for underactuated manipulator was proposed based on the chained model.Time polynomial was adoped as control input in the chained system,by solving the constraint equations that established by boundary conditions of manipulator to got control input of chained system,then the trajectories of state variables in the chained space was accessible.Finally obtained the motion trajectories of joints angles in joint space through inverse chained form conversion.To avoid the singular configuration and optimize the trajectories of joints,a linear evaluation function was established to optimize the inverse kinematics of the manipulator.The concept of motion planning to path through angular zero was presented based on the controllable condition of the manipulator,and then explained the necessity of motion planning to path through angular zero by analyzing the working space of the manipulator.In order to control joints of the manipulator to path through angular zero,the motion planning method of symmetric position was proposed based on the symmetry of structure and path planner.When the end executor of manipulator mechanical lies in the asymmetrical position,three trajectories were used for motion planning,by improving the time polynomial motion planner and using time scale transform to achieve the continuous of velocity when switching,and finally all joints can path through angular zero.Several experiments were processed on the motion control platform to verify the feasibility of the proposed motion planning algorithm.Using UMAC as motion controller to control two servo motors to drive the manipulator.The actual angular displacement of each joint was obtained through the motor encoder and the angular displacement sensor.The feasibility of the zero-motion planning method was proved through comparison with the theoretical calculation results.In summary.This thesis dealt with the motion planning algorithm of nonholonomic manipulator which proceeds from mechanical principle and the chained form conversion properties of manipulator.It provides a way to study the motion planning of complex nonholonomic underactuated system and to avoid the obstacle constraints...