In order to explore the optimal relationship between discretization accuracy and energy cost index of robotic arm in the process of sorting,a mathematical model of robotic arm was established according to D-H matrix,and Euler-Lagrange equation was used to describe the dynamics equation of the robotic arm.The system constraint equations were constructed based on the necessary conditions of optimal control,and the optimal energy cost index function of robotic arm was established accordingly.Finally,direct collocation and nonlinear programming was used to transform the two-point boundary value problem into a general nonlinear programming problem in order to obtain the optimal solution of the system.The relationship between the discretization accuracy and the cost index was discussed.The results show that the finer the discretization is,the more accurate the cost function value is;however,when the discretization reaches certain extends,the optimal energy cost index is no longer reduced.