A robot system with a robot configured for locomotion about a space using ground reaction force (GRF) to provide a first level of balancing. The robot system includes force generators located on or in the robot's body or offboard in the space that act to generate balancing forces to provide a second level of balancing for the robot using non-conventional physics. Clamping of a robot's feet to a support surface is provided whenever the feet are in contact with the support surface using electromagnets in the feet and a layer of ferrous material on the support surface or using mechanical coupling techniques to temporarily anchor the foot to the support surface. A balance controller processes output of balance sensors and responds by generating control signals to operate force generators onboard the robot such as electric fans or inertial reaction wheels.