In various application scenarios of the manipulator,reasonable trajectory planning of the manipulator can better exert its working ability.As the production becomes more complex,the end trajectory of traditional straight lines or arcs can no longer meet the production needs,and more and more tasks require the end of the manipulator to move along an irregular curve,such curves are often not described mathematically,therefore,it is necessary to establish a mathematical expression of the end path to plan the smooth trajectory of the end.In addition,considering the running speed and stability of the manipulator,the time-optimized planning of trajectories is necessary,and the angular velocity and angular acceleration of each joint are within the limit.In order to establish the mathematical expression of the end path,this thesis proposes a Bspline iterative fitting method based on vertical distance estimation.This method uses the Bspline interpolation method to fit the data points of the end path,so as to establish the mathematical expression of the end path,mainly including interpolation point selection,node vector calculation,fitting error calculation and adding new interpolation points based on the fitting error.In the interpolation point selection,this thesis uses the improved DOM method to select the initial interpolation points.In knot vector calculation,this thesis proposes point index parameterization instead of chord length parameterization.In the fitting error calculation,this thesis proposes the vertical distance estimation method to calculate the vertical error between the fitting curve and the data point,and proposes a center diffusion algorithm to determine the error estimation triangle.In adding interpolation points,this thesis determines the position of the newly added interpolation points in the data points based on the maximum vertical distance.Through MATLAB simulation,it is proved that under the same error conditions,the iterative fitting method based on vertical distance estimation method proposed in this thesis has higher curve fitting efficiency than the fitting method based on Euler distance.In order to plan the time-optimal trajectory of the Cartesian space of the manipulator,this thesis converts the time-optimal trajectory planning problem of the manipulator into a nonlinear optimal value search problem under multi-constraint conditions,and uses the minimum maximum rule to avoid the situation that the algorithm falls into the local optimal situation in the optimization process.To solve the above problem,an adaptive search algorithm based on fuzzy control is also proposed to search the shortest time.Through MATLAB simulation,the time optimization of a straight trajectory and a weld trajectory of the robotic arm is carried out,and the shortest time of the trajectory is solved by using the bisection algorithm,the traditional gradient descent method and the algorithm proposed in this thesis.The efficiency of the proposed algorithm is proved by comparing the execution time of these three algorithms. |