A method is described for collision-free motion planning of a first manipulator with closed kinematics. The method includes defining a dynamic optimization problem, solving the optimization problem using a numerical approach, and determining a first movement path for the first manipulator based on the solution of the optimization problem. The dynamic optimization problem includes a cost function that weights states and control variables of the first manipulator, a dynamic that defines states and control variables of the first manipulator as a function of time, and at least one inequality constraint for a distance to collisions. Furthermore, the optimization problem includes at least one equality constraint for the closed kinematics.