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可使其更具通用性和灵活性，但这通常会导致系统出现运动学冗余：主要操作或交互任务无法完全确定其关节运动。解决欠定控制与规划问题需要引入额外约束或目标函数。现有方法通过投影器在速度或力矩层面对任务进行分层解耦，将低优先级任务与高优先级任务分离。本文提出一种在位置层级实现冗余度求解与解耦的新方法，通过确定与主任务无关的构型空间子空间来实现。我们将这些子空间称为"正交叶状结构"，因为它们在一定意义上正交于任务的自运动流形。该方法能更深入地揭示机器人运动学与控制问题的拓扑特性，从而提供全局视角。我们推导了正交叶状结构存在性条件；若不满足该条件，仍可通过数值优化求得近似解。可在这些正交叶状结构上定义坐标，并将其作为额外任务变量用于控制。仿真实验表明，使用这些坐标无需投影器即可实现系统控制，并通过七自由度机器人实验验证了该方法的有效性。