Controlling the exact Cartesian stiffness values of a robot end-effector (EE) is troublesome because of difficulties associated with estimating the stiffness and controllability of a full Cartesian stiffness matrix. However, most practical applications require only quantitative (high/low) stiffness values in the EE motion direction (or perpendicular direction). Full control of the stiffness matrix requiring too many control inputs which is hardly possible in practical applications. To ensure the efficiency of execution for a range of redundant robots, we present an algorithm for shaping a robot’s Cartesian stiffness ellipsoid, a more intuitive and visual stiffness representation, using a nonlinear sequential least square programming optimization. The algorithm is designed to optimize the joint stiffness values and the trajectory of the robot’s joints, using null-space exploration, for a given task. Using eigenvalue decomposition of the stiffness matrix, the algorithm minimizes the orientation difference between the major axis of the current and the desired stiffness ellipsoid and specify a scaling factor between the major and the minor axis. The presented approach allows the user to better understand and control of a robot, regardless of the user’s knowledge of the achievable stiffness range and the interdependencies of the Cartesian stiffness matrix elements.

控制机器人末端执行器 (EE) 的精确笛卡尔刚度值很麻烦，因为估计完整笛卡尔刚度矩阵的刚度和可控性很困难。然而，大多数实际应用仅需要 EE 运动方向（或垂直方向）上的定量（高/低）刚度值。完全控制刚度矩阵需要太多的控制输入，这在实际应用中几乎是不可能的。为了确保一系列冗余机器人的执行效率，我们提出了一种使用非线性顺序最小二乘编程优化来塑造机器人笛卡尔刚度椭球体的算法，这是一种更直观和视觉化的刚度表示。该算法旨在针对给定任务，使用零空间探索来优化关节刚度值和机器人关节的轨迹。该算法使用刚度矩阵的特征值分解，最小化当前的长轴和所需刚度椭球体之间的方向差异，并指定长轴和短轴之间的比例因子。所提出的方法允许用户更好地理解和控制机器人，无论用户是否了解可实现的刚度范围和笛卡尔刚度矩阵元素的相互依赖性。