Research On Time Optimal Trajectory Planning And Trajectory Tracking Control Based On Reachability Analysis

With the aggravation of industrial production tasks and the continuous change of production demand,the user's requirements for robots are also increasing,and robots are no longer simply replacing manual labor.Nowadays,modern factories put forward more stringent requirements for the rapidity,accuracy and safety of robots.Therefore,aiming at various Cartesian space paths,this paper studies the optimal time,accurate trajectory and safe operation.Firstly,the robot is analyzed and modeled from kinematics and dynamics,which is the mathematical basis of trajectory planning and trajectory tracking.In this paper,the forward kinematics model of the robot is established according to the geometric structure characteristics of the robot.According to the feature that the last three joints of the robot intersect at one point,Euler angle transformation method and algebraic method are used to establish the inverse kinematics model of the robot.In the aspect of kinematics,the singularity problem is also analyzed.In order to avoid singularity,the damping coefficient is added to the singular parameters,and the effectiveness of the method is verified by simulation experiments.In the aspect of dynamics,the Newton Euler method is used to establish the dynamic model of the robot.Secondly,based on the kinematic and dynamic constraints,a time optimal trajectory planning algorithm is designed to achieve the goal of rapid movement and safe operation of the robot.For single path such as straight line,arc and spline curve,the path velocity decomposition framework is adopted to complete the steps of parameterization,calculation of feasible region and reachable set,adjustment of interpolation points,trajectory smoothing and trajectory generation.A new idea is proposed for the distribution of interpolation points.First,rough the path length,and then adjust the trajectory according to the acceleration and curvature information after calculating the reachable set.In addition,when solving the reachable set,the forward and inverse search algorithm is proposed,which is more efficient than the traditional search algorithm.For the multi segment path,this paper focuses on the case of multi line splicing.The straight line segment and mixed segment are treated separately,and a continuous multi segment continuous motion algorithm is designed.Then,simulation experiments are designed to verify the effectiveness of the algorithm.Finally,the experimental platform is built to test the effect of the algorithm.The results show that the algorithm has a great time advantage over the traditional algorithm,and the time is close to the foreign level.Finally,in order to achieve the goal of accurate operation of the robot,a feed-forward control scheme based on PID control is designed.Firstly,the joint friction model is established,and experiments are designed to identify the friction.Then,the least square method is used to identify the friction parameters.Then,the friction compensation is carried out to improve the dynamic model.Under the precise dynamic model,a feed-forward control scheme based on PID control is designed.The co simulation platform of Adams and Simulink is built,and the simulation experiment is designed to verify the effect of feed-forward control.Then,the trajectory tracking experiment at high speed is carried out,and the position accuracy is in a reasonable range.