Time-Optimal Trajectory Planning With Motion Stabilization Limits For Manipulator

Optimal trajectory planning is a research hotspot in the field of robotics and has a wide range of applications.Motion stabilization and time optimality are the two most important optimization objectives in the optimal trajectory planning of robots.Based on the theoretical analysis,this paper studies the time-optimal trajectory planning with motion stabilization limits for manipulator by means of Levenberg-Marquardt iteration(LM iteration),B-spline interpolation and convex optimization.The inverse kinematics problem is the basis of solving the trajectory planning problem of the multi-axis serial manipulator,and the numerical method is widely used in the solving process because of its good universality.However,the conventional numerical method to the inverse kinematics problem of the serial manipulator has the problems of slow convergence speed and easy to appear non-convergence.According to above problems,an improved numerical method to the inverse kinematics of multi-axis serial manipulator is proposed,and the iterative strategy of parameter factor in LM iterative method is improved,and the additional factor is set to improve the iterative convergence speed.In the process of converting path from works pace to the joint space,the default path in work space corresponds to multiple paths in joint space due to the existence of multiple solutions to the inverse kinematics problem of the multi-axis serial manipulator.In order to work out above problem,a solution to minimum rotation angle path in joint space which is helpful to promote time optimality is established based on improved numerical method,multi-segment directed graph and shortest path search algorithm.After the minimum rotation angle path in joint space of the multi-axis serial manipulator is obtained,there is an error between the path in joint space and the default path in work space.According to above problem,the factors influencing the error are investigated.Under the premise of 5-order B spline interpolation,there is a negative exponent between the number of path points(interpolation points)and the error between the path in joint space and the path in work space negative exponent.Based on the negative exponent,an error reduction strategy of "determining negative exponential relationship-dividing path point encryption region-reselecting path point" is established,which can guide the selection of path points in the process of solving the minimum rotation angle path in joint space.Finally,a method to plan high-speed and stable trajectory of multi-axis serial manipulator based on convex optimization is proposed.This method is able to obtain the time-optimal trajectory satisfying the motion stabilization constraints(jerk constraints).In this method,switch points between the maximum acceleration/deceleration are searched based on optimal control theory.Based on the assumption that the motion between adjacent path points is uniform acceleration/deceleration motion,the iterative formulas of velocity and acceleration between adjacent path points are derived.The nonlinear jerk constraints in optimization problem are equivalently convert to the linear acceleration constraints,which ensures both the convexity and the computational speed of optimization problem.By solving the convex optimization problem at each path point,the maximum velocity satisfying the jerk constraints is calculated.Eventually,the time-optimal trajectory satisfying the motion stabilization limits of the multi-axis serial manipulator is obtained.In the process of studying the time-optimal trajectory planning with motion stabilization limits for manipulator,all solving methods and planning methods to the problems can be transplanted to the solver and controller of the multi-axis serial manipulator.These methods can be used to plan the time-optimal trajectory with motion stabilization limits,which is helpful to promote the development of the control and tracking field of the multi-axis serial manipulator.