• quadrupedal robots
• optimal control
• model-based control
• whole-body controller
• soft contacts

Legged robots represent a new category of mobile robots that have recently attracted a lot of attention from the scientific community. The research efforts received have resulted in massive improvements in several aspects of legged locomotion, from control techniques to design choices.
Guided by bio-inspired design principles, some researchers attempted to further improve legged robots by developing soft and adaptive feet. But the research in this direction is still in its infancy.
This thesis investigates the state of the art of controllers for quadrupedal robots, focusing on robots traversing compliant environments or implementing soft elements. It also examines existing foot designs and compares them with the innovative SoftFoot-Q.
Furthermore, I present a novel model-based whole-body controller. This represents the first controller explicitly addressing locomotion with non-rigid feet. In addition to the whole-body controller, two motion planners and a state estimator are developed and used in conjunction with a ROS 2 interface for the implementation on the SOLO 12 platform. These comprise all the software components necessary for the locomotion of a teleoperated legged robot. Consequently, an additional contribution of this thesis consists in the development of a modular framework upon which further research on legged robots can be conducted.
Finally, the controller's performance is validated using multiple quadrupedal robots and feet designs.