In recent years robots have been moving from their places within cages and from behind safety curtains closer to the workspace of humans. Robots are up to become part of people's workspace. Robots are up to become part of our every day live. Therefore, future mobile robots need to be suited for operation in every day environments with regard to flexibility, maneuverability and robustness. In this context a central role is taken by the motion-apparatus of a robot. Non-holonomic, omnidirectional undercarriages composed by steered standardwheels promise to provide a solid compromise between these requirements. In this context, due to the actuator coupling via the non-holonomic bindings, exact coordination of all actuators emerges as especially important. Within this work the kinematic modeling and control of this class of non-holonomic, omnidirectional undercarriages are addressed. Grounded on the seminal works by Campion and Thuilot a state-spacerepresentation that implicitly represents the constraints emerging from the non-holonomic bindings is developed. It will be shown that the spherical coordinate representation of the twist forms a basis of such a state-space. In fact, it will be shown that the spherical coordinate representation of the twist is a local diffeomorphism to the instantaneous center of motion. Furthermore, it will be shown that the singularities which are inherent to this state-space can be divided into removable and physical singularities. The removable singularities will be resolved by providing an expanded state-space formulation and designing an appropriate observer. To tackle the problems associated to the physical singularities three different approaches are devised. A potential-field based and a model predictive control approach to avoid the singular regions are developed. Therefore, the fitness criterias of the controllers are adapted such that the singularities are taken into account within the applied control sequence. However, these approaches imply constraining the accessible workspace and thus a reduction of the systems flexibility. To resolve these drawbacks a third approach is devised based on controller switching. This approach is grounded in the fact, that it can be shown that a set of appropriately transformed state-spaces can form an atlas of the entire valid configuration space. This Atlas is free of singularities. With this approach it is for the first time possible to use the full flexibility of these non-holonomic, omnidirectional undercarriages without violating the non-holonomic bindings. The three proposed approaches are discussed with respect to stability and solvability of the underlying optimization problem. Finally, the approaches are qualitatively and quantitatively compared to each other and a further reference-controller. The reference controller is designed to optimize control time under violation the non-holonomic bindings if necessary. To ensure reproducibility and comparability al controllers are integrated into a common simulation environment. The simulated test-system is the undercarriage of the Care-O-bot® 3 developed at Fraunhofer IPA. The obtained results show that all three approaches outperform the reference-controller with respect to actuator-coordination and adherence to the non-holonomic bindings. It also becomes apparent that the approach via controller switching does in fact allow passing through the singular regions of the system. Thus the switching based controller provides the shortest control times except for the reference-controller and the highest possible flexibility that is possible when adhering to the non-holonomic bindings.
Kinematische Modellierung und Regelung omnidirektionaler, nicht-holonomer Fahrwerke
2013
Theses
Electronic Resource
German
Kinematische Modellierung und Regelung omnidirektionaler, nicht-holonomer Fahrwerke
Tema Archive | 2013
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