Research On Kinematics And Time Optimal Trajectory Planning Of Redundant Manipulators

Manipulators play an important role in automation and intelligent manufacturing,and advances in related technologies can promote the development of manufacturing industry in China.The manipulator with kinematic redundancy is more flexible thanks to its characteristic of redundancy.Research on its inverse kinematics and trajectory planning considering dynamics will make a difference to making full use of the advantages of kinematic redundancy and improving its efficiency.This paper forces on redundant manipulators and conducts research on inverse kinematics,identification of dynamics parameters and time optimal trajectory planning.The main contents are as follows:(1)The inverse kinematics problem of redundant manipulators is studied and solution algorithms are proposed.First,the local optimal solution method of kinematic redundancy is analyzed.Then,based on the augmented Jacobian matrix method,the problem of computational complexity of the augmented part when the number of manipulator's joints is large is solved from the form and calculation method of the augmented part.The computational efficiency of the algorithm meets the requirement of real-time control,and it can ensure the repeatability of the manipulator when tracking a closed trajectory.Finally,a global optimal inverse kinematics solution method is proposed.After the entire path is segmented,it is optimized from two levels to improve the solving efficiency.(2)The identification of dynamics parameters of manipulators is studied and the dynamics parameters of a seven-degree-of-freedom redundant manipulator are identified.First,the Newton-Euler method is used to establish the dynamics model of the manipulator.Then,the minimum condition number of the observation matrix in the linearized dynamics model is utilized as the objective function to optimize the excitation trajectory.According to the data collected when the manipulator tracks the excitation trajectory,the dynamics parameters are identified by the least square method.Finally,the manipulator tracks other trajectory and the actual torque is compared with the torque obtained through the identification model to verify the identification results.(3)The time optimal trajectory planning is studied and a trajectory planning method considering jerk constraints is proposed.First,the B-spline curve is used to interpolate and fit the path points and the parameterized path is obtained.Then,the time optimal trajectory planning problem considering dynamic constraints is constructed and the convex relaxation method is used to convert it into a convex optimization problem.In order to improve the solution accuracy at the head and end points,while controlling the number of discrete points,a piecewise continuous non-uniform discrete strategy is proposed.On the basis of the discrete optimization problem that has been constructed,linearized jerk constraints are added,and a time optimal trajectory planning problem considering jerk constraints is constructed.After solving this problem,a smooth acceleration trajectory is obtained.(4)The effectiveness of proposed algorithms is validated through the experiment.First,a manipulator experiment platform is built from both hardware and software aspects.After the experiment path is obtained by fitting discrete points,the solution of inverse kinematics and the planned trajectory are simulated and verified.After the requirements are met,the trajectory is sent to the seven-degree-of-freedom manipulator for execution.Finally,the actual results of the manipulator show that algorithms proposed in this paper have a good performance.