Mathematical Modeling And Optimal Trajectory Planning Of A Parallel Robot

Under the development trend of modern industrialization and intelligence,robot technology has developed rapidly in various fields,especially the theoretical research and industrial application of parallel robots occupy a certain position.This thesis takes the3-PPR parallel robot in the laboratory as the research object,considering the kinematic constraints of the parallel robot,and proposes a method to optimize the task trajectory of the parallel robot under the limited motion space.The main content and innovative research can be summarized as:First,taking the parallel robot as the research object to analyze the mechanical structure and working principle,simplify the structure and establish the corresponding coordinate system according to the research requirements.Using the homogeneous coordinate transformation method derives the kinematics forward solution and kinematics inverse solution of the parallel robot,using the first-order influence coefficient method to solve the Jacobian matrix of the parallel mechanism and analyzing the working space and singularity of the mechanism.The rigid body dynamics model of the parallel parallel robot is derived by Lagrangian method.Through the comparative analysis of ADAMS model simulation and MATLAB numerical simulation,the established kinematics and dynamics models are verified.Second,an optimization model is established to solve the problem that the movement space of the parallel robot is limited in the actual application process.The friction and wear during the joint movement affect the system accuracy and energy consumption.Finite rectangular space boundary is modeled,constructing anti-collision constraints.Then,introduce the corresponding kinematic constraints in the model by combining the mechanism characteristics.Subsequently,according to the actual motion planning requirements,the comprehensive optimization model of time and joint friction energy consumption is established by a suitable friction model to obtain the joint friction energy consumption of the motion branch chain.In the joint space,the particle swarm algorithm is used to solve the optimal value of the optimization model.Different interpolation functions are selected to obtain the driving joint motion curve and the motion of the moving platform.And then analyze the performance of the motion trajectory.Third,in view of the fact that the initial and final pose of the moving platform is close to the limited motion boundary,the optimal solution of the traditional trajectory planning method is sparse or does not exist so that the optimal trajectory without collision cannot be solved.Combined with the movement of the parallel alignment platform characteristics and optimization model,a trajectory planning method with task space partition and joint space segment interpolation is proposed.The motion space of the moving platform’s geometric center is divided into different regions.The motion strategies in different regions are specified.Different partitions are mapped to the joint space for segmental interpolation to realize trajectory planning under any initial pose and end pose in the limited space.The results of simulation experiments show that this method can guarantee a collision-free trajectory under the optimization objective and have certain practical value.