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Roboclimber is a service robot designed to replace human workers in the highly dangerous task of rocky wall consolidation. It can walk on steep terrains by means of four legs and two ropes. The robot must perform missions requiring displacements on steep rocky walls and operations involving a strong interaction with the environment, semiautonomous control strategies driven by teleoperation are suitably employed. The system proposed is very complex; the motion of the robot is obtained by coordinating step-by-step the leg displacements and the rope tensions. Intrinsic stability is an essential requirement for the operational security of the robot, and the work presented proposes quasi-static motion control strategies that improve the system reliability based on actual stability knowledge.