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This paper proposes a two-stage planning algorithm for 3-leg free-climbing robots. The algorithm consists of global path planner and local motion planner. Firstly, the proposed algorithm distributes climbing points to Delaunay triangle mesh. The global planner plans a sequence of Delaunay triangles from the start configuration to goal configuration. Then, the latter plans the transition configurations between two adjacent triangles of the trajectory. The local motion algorithm uses the inverse Jacobian matrix to derive the positions and angles of joints for all configurations. Since the proposed algorithm directly uses spatial information of the workspace to plan a path, it is more efficient than configuration-space based approaches. Simulation results show that the proposed algorithm works well.