Articulated robots such as manipulators increasingly must operate in uncertain and dynamic environments where interaction (with human coworkers, for example) is necessary. In these situations, the capacity to quickly adapt to unexpected changes in operational space constraints is essential. At certain points in a manipulator's configuration space, termed singularities, the robot loses one or more degrees of freedom (DoF) and is unable to move in specific operational space directions. The inability to move in arbitrary directions in operational space compromises adaptivity and, potentially, safety. We introduce a geometry-aware singularity index, defined using a Riemannian metric on the manifold of symmetric positive definite matrices, to provide a measure of proximity to singular configurations. We demonstrate that our index avoids some of the failure modes and difficulties inherent to other common indices. Further, we show that this index can be differentiated easily, making it compatible with local optimization approaches used for operational space control. Our experimental results establish that, for reaching and path following tasks, optimization based on our index outperforms a common manipulability maximization technique and ensures singularity-robust motions.
翻译:电动机器人(如操纵者)越来越多地必须在不确定和动态的环境中操作,这种环境中必须(例如与人类同事)互动。在这种情况下,迅速适应操作空间限制意外变化的能力至关重要。在操纵者配置空间的某些点上,即所谓的奇点,机器人失去了一个或多个自由度(DoF),无法在特定的操作空间方向上移动。在操作空间的适应性和潜在安全性方面,无法任意朝着操作空间的任意方向移动。我们引入了几何-能见的单点指数,在对称正数确定矩阵的方位上使用里伊曼测量度来定义,以提供与单点配置相近的量度。我们证明我们的指数避免了其他通用指数固有的一些失败模式和困难。我们进一步表明,该指数可以很容易地区分,使其与用于操作空间控制的本地优化方法相匹配。我们的实验结果证明,为了达到和遵循任务,基于我们的指数的优化超过了共同的人工最大化技术,并确保单点-硬度运动。