Handling and Describing String-Tying Operations Based on Metrics Using Segments Between Crossing Sections

Abstract

Many robotics researchers are currently addressing the challenge of string-tying operations. Actual knot-tying tasks require metrics, such as the positions, sizes, and shapes of the knots, as well as the segment lengths of the knots. In this letter, we propose unified expressions for string-tying operations based on metrics and a method of realizing knot-tying tasks considering these metrics. Unified expressions, which are needed for the actual knot-tying task, are described using crossing sections and the segments between them. The realization method is the movement perturbation method, which first realizes a topological knot-tying task as a special solution to the task while considering the metrics; it determines where perturbations can be applied by means of sensitivity analysis, and extends the special solution using the movement perturbations. These allow us to realize knot-tying tasks by considering the metrics and relying on the results of topologically realized previous studies. Through experiments, we show the efficacy and limitations of our method.