Extending Harmonic Function Methods via Root Locus for Coordinated Path Generation

Engineering notes

Engineering notes will be added by the Robot Papers editorial team.

Chinese explanation / 中文解读

中文解读待补充：本站会优先为 VLA、具身智能、人形机器人控制、机器人操作等高价值论文补充中文说明。

Original abstract

We consider the offline generation of coordinated paths for N interchangeable robots and N goals in planar environments with polygonal obstacles. After a conformal map to a circular domain, starts and goals become the poles and zeros of a rational function R, and the paths are the branches of its Generalized Root Locus (GRL), i.e. the streamlines of the logarithmic potential -log R. We show that, for every phase outside a finite set of critical phases and a set of boundary phases, the induced gradient motion drives each robot to a distinct goal along pairwise disjoint paths that never reach the obstacles; the robot-goal assignment is produced by the construction, and with the gain used as a clock all robots move as the closed-loop roots of the GRL and arrive together at a prescribed time. Obstacles become streamlines through successive Milne-Thomson reflections, and for a finite number of reflections a finite test certifies safety for the potential that is actually computed. Reciprocal root-locus planning is recovered as a special case. The method is illustrated on two polygonal workspaces, 100 random instances compared with independent harmonic planning and artificial potentials, and a scene with ten robots and ten obstacles.

Links and sources

• Official / arXiv page
• PDF from original source

Comments