The objective of this Master's thesis is to design a controller for a twelve-dimensional bipedal walking robot with hybrid dynamics. To ensure a stable and physically realizable walking gait, certain constraints have to be satisfied. We propose a new approach to control bipedal robots by reducing the dynamics via a linearizing feedback controller and applying abstraction-based control on the remaining two-dimensional zero dynamics, which enables us to provide formal guarantees for the satisfaction of the constraints of the full order robot. This new approach allows us to overcome the problem of applying abstraction-based control for high-dimensional systems and might be used for other systems.

To use abstraction-based control for hybrid systems, we propose a new method to efficiently compute abstractions for a certain class of hybrid systems, which includes the reduced walking robot model. Simulation results illustrate the improved walking performance and the constraint satisfaction on the full order robot.