A Lunar Construction starts from Earth. We should develop and perfect legged and armed construction robots that are also utilized on Earth mining and construction. Space Agencies are still investing on wheeled rovers and plan to send humans to assist them. Simply send legged and armed robots !
The lunar dust is very sharp and very hard. Which is not good for moving parts. Therefore I propose the use of springy joints instead of bearing based joints. All the motors would be housed inside the robot body. The sections of the legs will be controlled by carbon nanotube cables. These cables would have shield tubes covering them. Once the robot is in position it can lock the joints and use no power to maintain the posture. The arms of the robot would have similar design to that of the legs.
The arms and legs should have redundancy, for example the leg count should be more 6 or more. The legs and arms should be removable and replaceable by the robot itself. Therefore if one limb malfunctions the robot should be able to replace it with a working one. Also depending on the task a specialized limb would be attached to improve the efficiency. This modular design should include the replaceable multi batteries as well. The robot itself should be able to replace the depleted battery with a full one by itself without effecting the operation of the other arms and legs. Battery may transfer its energy wirelessly to avoid contact problems. These batteries would also be used to store the renewable energy when they are not available.