In this thesis various control theoretic questions from the field of autonomous robotics are investigated. Those questions range from motion planning and control to modeling and analysis of complex control systems based on hybrid automata theory.
A path planning method is proposed for generating smoothing splines that are optimal with respect to an energy functional at the same time as they drive the output of a given, linear control system close to desired waypoints. These curves are furthermore numerically inexpensive to produce, which suggests that they can be used on-line for refining or updating paths as a reaction to unexpected events in the environment.
A stable and model-independent control strategy for making mobile platforms track reference paths is also proposed. The control algorithm is based on a parameterization of the reference trajectory in such a way that the motion of the point on the trajectory, tracked by the robot, is governed by a differential equation containing error feedback. This makes the method robust to disturbances and measurement errors.
The third topic covered in this thesis concerns the integration of continuous controllers into one, complex control system. These types of complex control architectures can for instance be found in a behavior based robot system, where different continuous robot behaviors are influenced by events in the environment or controlled transitions between different behaviors. This combination of continuous and discrete phenomena makes it possible to model the system as a hybrid automaton. It is furthermore shown in this thesis how chattering between different behaviors can be avoided within this framework by exploiting regularization techniques that basically involves adding extra nodes to the hybrid automaton.