Optimal point-to-point motion planning of heavy-duty industry robot with indirect method

Optimal point-to-point motion planning of heavy-duty industry robot was critical between two points in the prescribed time. The dynamic modeling was derived though Lagrange formulation and Spong model; then based on the Pontryagin´s minimum principle, optimal point-to-point motion planning problem was constructed considering the gravity effect. Indirect method integration with homotopy mapping was developed to expand the convergence domain of initial costate vector, also the Broyden method was adopted for the differentiation calculation to reduce computation burden. At last, the simulation was carried out on a 4 d.o.f. heavy-duty industry robot, compared with the line motion of quintic time polynomial, the proposed method could guarantee motion accuracy, velocity and acceleration continuity in starting and end point, and can also reduce the sizing of motors and reducers.