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.

We presented our works relative to anthropomorphic motions. We performed task recognition, full-dynamic motion generation, motion retargeting and editing in a unified framework: the stack of tasks. Thanks to the genericity of the task function formalism, our works can be further extended. For example, for the recognition, the use of the task function formalism applied to human motion is currently investigated. Also, preliminary results on the real robot for the retargeting and editing method have been obtained.

Efficient methods to perform motion recognition have been developed using statistical tools. Those methods rely on primitive learning in a suitable space, for example, the latent space of the joint angle and/or adequate task spaces. Learned primitives are often sequential: A motion is segmented according to the time axis. When working with a humanoid robot, a motion can be decomposed into parallel subtasks. For example, in a waiter scenario, the robot has to keep some plates horizontal with one of its arms while placing a plate on the table with its free hand. Recognition can thus not be limited to one task per consecutive segment of time. The method presented in this paper takes advantage of the knowledge of what tasks the robot is able to do and how the motion is generated from this set of known controllers, to perform a reverse engineering of an observed motion. This analysis is intended to recognize parallel tasks that have been used to generate a motion. The method relies on the task-function formalism and the projection operation into the null space of a task to decouple the controllers. The approach is successfully applied on a real robot to disambiguate motion in different scenarios where two motions look similar but have different purposes.