Research On Trajectory Planning And Control Of The Cable-driven Parallel Mechanism

The cable-driven parallel mechanism is a new type of parallel mechanism that uses cable instead of rigid rods as connecting elements.With its simple construction,light weight,low inertia and high load carrying capacity,it is widely used in medical rehabilitation,sports simulation,material handling and astronomical observation.However,the unidirectional force and flexibility of the rope reduce the stability of trajectory planning and the accuracy of trajectory tracking control.To address these problems,the thesis investigates the kinematics,dynamics,trajectory planning and trajectory tracking of the cable-driven parallel mechanism.The main research works in the thesis are as follows:(1)The kinematics and dynamics of the cable-driven parallel mechanism are analysed and its workspace is solved.The inverse kinematic solution model of the cable-driven parallel mechanism is established by applying the vector closure principle and verified by simulation;the positive kinematic solution model is solved by applying the Newton-Raphson method;the dynamics model of the cable-driven parallel mechanism is established by applying the Lagrangian method;the workspace of the cable-driven parallel mechanism is solved and analysed by applying the numerical method.The theoretical basis for the study of trajectory planning and trajectory tracking control of the cable-driven parallel mechanism is laid.(2)An improved quintuple polynomial trajectory planning method is proposed.When using the traditional trajectory planning method for trajectory planning,there are problems such as rope vibration,unstable motion of the end-effector and excessive speed during the process of starting,stopping and changing direction of the cable-driven parallel mechanism,etc.The thesis proposes an improved quintuple polynomial trajectory planning method and optimizes it based on the time-optimality principle.It is verified through simulation experiments that when the method is applied to the trajectory planning of the cable-driven parallel mechanism,the velocity curve and acceleration curve of the end-effector show continuity and the running time is short,meeting the requirements of maximum velocity and maximum acceleration.(3)A fuzzy PID control strategy based on particle swarm optimization is proposed.For the trajectory tracking problem of the cable-driven parallel mechanism,a PID controller,a fuzzy PID controller and a fuzzy PID controller optimised by particle swarm algorithm are designed respectively.For the problem that the parameters of the PID controller are not easily adjustable,the fuzzy PID controller is proposed by combining fuzzy control with PID control,which can adjust the parameters of the PID controller in real time;for the problem that the fuzzy control rules in the fuzzy PID controller rely too much on expert experience,the particle swarm algorithm is used to optimise the quantization factor and proportionality factor parameters in the fuzzy control,a fuzzy PID controller based on the particle swarm algorithm is designed.The virtual prototype model of the cable-driven parallel mechanism was established in ADAMS software,and the simulation model was combined with Simulink software to verify the trajectory tracking control effect of the designed controller.The experimental result shows that the trajectory tracking control effect of the fuzzy PID controller based on particle swarm algorithm for the cable-driven parallel mechanism is better than PID controller and fuzzy PID controller.(4)The experimental platform of the cable-driven parallel mechanism was built,and the kinematic verification experiments and trajectory tracking control experiments were carried out.The mechanical structure,control system hardware and control system software of the cable-driven parallel mechanism are proposed and implemented.The calculation results are compared with the experimental results to verify that the kinematic model established in the thesis is accurate;the particle swarm algorithm based optimised fuzzy PID controller is used to carry out the unidirectional linear trajectory tracking control of the cable-driven parallel mechanism.The maximum offset of the end-effector in X,Y and Z directions are 2mm,2mm and 3mm respectively.The result shows that the controller can improve the accuracy of the trajectory tracking of the cable-driven parallel mechanism and reduce the error.