Increasing the degrees of freedom of robotic systems makes them more versatile and flexible. This usually renders the system kinematically redundant: the main manipulation or interaction task does not fully determine its joint maneuvers. Additional constraints or objectives are required to solve the under-determined control and planning problems. The state-of-the-art approaches arrange tasks in a hierarchy and decouple lower from higher priority tasks on velocity or torque level using projectors. We develop an approach to redundancy resolution and decoupling on position level by determining subspaces of the configurations space independent of the primary task. We call them \emph{orthogonal foliations} because they are, in a certain sense, orthogonal to the task self-motion manifolds. The approach provides a better insight into the topological properties of robot kinematics and control problems, allowing a global view. A condition for the existence of orthogonal foliations is derived. If the condition is not satisfied, we will still find approximate solutions by numerical optimization. Coordinates can be defined on these orthogonal foliations and can be used as additional task variables for control. We show in simulations that we can control the system without the need for projectors using these coordinates, and we validate the approach experimentally on a 7-DoF robot.

翻译：增加机器人系统的自由度使其更具通用性和灵活性，这通常会导致系统在运动学上具有冗余性：主要的操作或交互任务无法完全确定其关节运动。需要额外的约束或目标来解决欠定的控制与规划问题。现有技术通过投影仪在速度或力矩层面将任务分层解耦，分离低优先级任务与高优先级任务。我们提出一种在位置层面进行冗余度求解与解耦的方法，通过确定与主要任务无关的构型空间子空间来实现。我们将其称为**正交叶状结构**，因为在某种意义下它们与任务自运动流形正交。该方法能更深入地揭示机器人运动学与控制问题的拓扑性质，提供全局视角。我们推导了正交叶状结构存在的条件。若条件不满足，仍可通过数值优化找到近似解。可在这些正交叶状结构上定义坐标，并将其作为额外的控制任务变量。仿真实验表明，使用这些坐标无需投影仪即可控制系统，并在一个7自由度机器人上进行了实验验证。