Shortest Path Set Induced Vertex Ordering and its Application to Distributed Distance Optimal Multi-agent Formation Path Planning
Abstract
For the task of moving a group of indistinguishable agents on a connected graph with unit edge lengths into an arbitrary goal formation, it was previously shown that distance optimal paths can be scheduled to complete with a tight convergence time guarantee, using a fully centralized algorithm. In this study, we show that the problem formulation in fact induces a more fundamental ordering of the vertices on the underlying graph network, which directly leads to a more intuitive scheduling algorithm that assures the same convergence time and runs faster. More importantly, this structure enables a distributed scheduling algorithm once individual paths are assigned to the agents, which was not possible before. The vertex ordering also readily extends to more general graphs - those with non-unit capacities and edge lengths - for which we again guarantee the convergence time until the desired formation is achieved.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2012
- DOI:
- 10.48550/arXiv.1205.0207
- arXiv:
- arXiv:1205.0207
- Bibcode:
- 2012arXiv1205.0207Y
- Keywords:
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- Computer Science - Robotics;
- Computer Science - Systems and Control
- E-Print:
- Extended the earlier version to 8 Pages, complete with literature review. One additional section on a distributed scheduling algorithm is added