Abstract: Based on the Legendre pseudospectral method, the optimal control of free floating space robots path planning problems are studied. Free floating is the working status for the space robots in task and path planning is the foundation for them to fulfil a complex space task. Because the space robots have no fixed pedestal and there are nonholonomic constraints between the manipulator and the carrier, and it makes the path planning for free floating space robots different from those on the ground. In this paper, the Legendre pseudospectral method which can realize the optimal control of free floating space robots path planning problem is presented. Firstly, a dynamic model of free floating space robots is established by using multi-body dynamics theory. The path planning problem of Bolza with certain initial and terminal stance is then obtained. Here, we select the minimum joint dissipation as performance index and consider the actual control input saturation. Then, by applying the Legendre pseudospectral method, the state and control variables are discretized at Legendre-Gauss-Lobatto (LGL) point and Lagrange interpolation polynomials are constructed to approximate the state and control variables. The problem of continuous path optimization is discretized to solve a nonlinear programming problem. Finally, results of the numerical simulation show that using the application of Legendre pseudospectral method to solve the problem of free floating space robot path planning can get the optimal trajectory of manipulator and carrier. It can fit various constraint conditions well. And this method is with fast simulation calculation, high accuracy and good real-time performance.