Generalized projector for task priority transitions during hierarchical control

Redundant robots performing multiple tasks of different priority levels are often handled by hierarchical control frameworks. This paper proposes a general hierarchical control approach that can handle not only a single standard lexicographic hierarchy, but also a complex priority network involving both strict and non-strict task priorities. In this approach, priorities can be defined by pairs of tasks and are encoded by a priority matrix. Priority modulations are achieved by the regulation of a novel generalized projector, which takes the priority matrix as input. This projector allows a task to be completely projected in the null-space of a set of tasks, while partially projected in those of some other tasks. Such a projector can be used to achieve multiple priority rearrangements simultaneously. The effectiveness of this approach is demonstrated on a KUKA LWR robot performing task priority rearrangements as well as task insertion and deletion.