In recent decades, robotic systems have moved from structured industrial settings into dynamic, unstructured environments. A central challenge in this transition is non-smooth dynamics, which emerges from the interplay of discrete and continuous actions. Examples include contact-making and breaking or obstacle planning in legged locomotion, mode-switching in vehicles that rely on hydrodynamics, or on/off thruster actuation in spacecrafts used for space debris removal. To achieve dynamic movements with such systems, controllers must solve these mixed problems at a high control frequency, while the estimators must be able to recognize the discrete states of a system. Existing model-based methods often delegate discrete decisions to heuristics, which are hard to tune and nonoptimal, or relax them to continuous problems that yield untrackable solutions. Integrating non-smooth decisions directly into the control problem can provide optimality, but is usually too computationally expensive for online use. Pure learning-based approaches, while capable of discovering control policies from data, demand extensive training, are prone to local minima, and face large sim-to-real gaps. Moreover, they typically lack guarantees on optimality, robustness, and constraint satisfaction, limiting their use in safety-critical settings.
To overcome these drawbacks, the goal of this thesis is to develop methods for dynamic control of systems with hybrid dynamics in the real world. Two main application cases are considered: (1) A free-floating system with on/off thruster serves as an example for systems with discrete actions. (2) Legged robots, namely quadrupedal and bipedal robots, serve as an example for systems with non-smooth states. I already compared model-based methods that use heuristics on their computational traceability for quadrupedal and bipedal robots. In the next step, I want to remove the heuristics to optimize the discrete decisions directly within the controller. Thereby, I want to investigate learning-based techniques to accelerate computation and enable real-time control of both legged robots and on/off-actuated free-floating systems. Finally, my goal is to extend the developed methods to develop a contact implicit state estimation in order to complete the control stack. In summary, this PhD thesis contributes to the development of methods for controlling systems with non-smooth dynamics where the methods are both computationally trackable and experimentally validated.