A Riemannian metric for geometry-aware singularity avoidance by articulated robots

Articulated robots such as manipulators increasingly must operate in uncertain and dynamic envi-ronments 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 our 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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

Articulated robots, such as manipulators, need to operate in uncertain and dynamic environments, where interaction with human coworkers is necessary. A new singularity index introduced in the paper provides an effective measure of proximity to singular configurations and avoids the failure modes and difficulties of common indices. Experimental results show that optimization based on the new index outperforms traditional manipulability maximization techniques for reaching and path following tasks.