A Riemannian Metric for Geometry-Aware Singularity Avoidance by Articulated Robots

TL;DR

This paper introduces a Riemannian metric-based singularity index for articulated robots that improves safety and adaptivity by accurately measuring proximity to singularities and enabling better control in uncertain environments.

Contribution

A novel geometry-aware singularity index using Riemannian metrics that enhances singularity avoidance and is compatible with optimization-based control methods.

Findings

Index outperforms traditional manipulability measures in experiments.

Ensures singularity-robust motions during reaching and path following.

Facilitates differentiation for use in local optimization algorithms.

Abstract

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.