Analysis of the discontinuities in prioritized tasks-space control under discreet task scheduling operations

This paper examines the control continuity in hierarchical task-space controllers. While the continuity is ensured for any a priori fixed number of tasks -even in ill-conditioned configurations-, the control resulting from a hierarchical stack-of-task computation may not be continuous under some discrete events. In particular, we study how the continuity of the stack-of-task control computation is affected under discreet scheduling operations such as on-the-fly priority switching between tasks, or tasks insertion and removal, which changes the number of tasks in the stack controller. Different ways to formulate a hierarchy of tasks are presented together with their continuity properties, which is thoroughly analyzed under such discreet scheduling operations.