Research On Designing And Motion Planning For A Underactuated Four-joint Manipulator

As the development and application of robot technology is advancing,the study of underactuated robotic systems is attracting extensive attention.Underactuated robots refer to mechanical system which's independent control input dimension less than the number of degrees of freedom,so that it can completes the complicated work.However,underactuated systems often have strong coupling,nonlinear characteristics,which can not achieve input-state linearization,and can not use smooth nonlinear feedback to achieve its progressive stability,so it undoubtedly added to the difficulty of its motion planning.In order to deeply explore the motion planning problem of the underactuated system,a new four-joint underactuated manipulator is presented which uses the idea of fusing the structure design and control theory.Through theoretical deduction,simulation analyzing and experimental test,This paper analyzes the motion characteristics of the manipulator and studies its motion planning method.A set of friction disc mechanisms are provided at each joint of the manipulator to drive the next joint which is capable of achieving continuous control of the motor-togear ratio by changing the relative configuration of the disc to the turntable.The gear ratio changes follow the trigonometric function.Based on the analysis of the motion characteristics of the underactuated manipulator,it is proved that the system has controllability and nonholonomic.The kinematic model of the triangular mathematical structure is deduced.The motion model is transformed into a chain system by coordinate transformation,The nonlinear mapping relationship of coordinate transformation is studied from the perspective of Cartesian product change.Based on the Newton iteration method,the undetermined coefficients of the time polynomial input control method are solved in the chain space,and the motion planning of the underactuated manipulator is simulated.The joint motion trajectories and the input control quantities are obtained.And the singularity avoidance method is proposed by increasing the constraint configuration in the singular part.Based on the previous theoretical deduction and simulation analysis,the experimental device of four-joint underactuated manipulator is designed and manufactured.The underactuated manipulator uses two servo motors as control inputs,and the servo motor is controlled by the UMAC motion controller.The angular displacement of each joint is measured by the angle sensor.The results of the final experiment are in good agreement with the calculated results,which proves the the motion transmission of the underactuated manipulator is feasible and the motion planning method is effective,that realizes the configuration control of the nonholonomic system.