When a robotic system is redundant with respect to a given task, the remaining degrees of freedom can be used to satisfy additional objectives. With current robotic systems having more and more degrees of freedom, this can lead to an entire hierarchy of tasks that need to be solved according to given priorities. In this paper, the first compliant control strategy is presented that allows to consider an arbitrary number of equality and inequality tasks, while still preserving the natural inertia of the robot. The approach is therefore a generalization of a passivity-based controller to the case of an arbitrary number of equality and inequality tasks. The key idea of the method is to use a Weighted Hierarchical Quadratic Problem to extract the set of active tasks and use the latter to perform a coordinate transformation that inertially decouples the tasks. Thereby unifying the line of research focusing on optimization-based and passivity-based multi-task controllers. The method is validated in simulation.

翻译：当机器人系统对于给定任务存在冗余时，剩余自由度可用于满足额外目标。随着当前机器人系统自由度的不断增加，这将导致需要根据给定优先级解决整个任务层级。本文首次提出一种兼顾机器人自然惯性的柔顺控制策略，可同时处理任意数量的等式与不等式任务。因此，该方法是将基于无源性的控制器推广至任意数量等式与不等式任务的情形。其核心思想是利用加权分层二次规划提取活动任务集，并基于该任务集执行坐标变换以实现任务的惯性解耦，从而统一了基于优化与基于无源性的多任务控制器研究路线。通过仿真验证了该方法的有效性。