Optimal Time-Invariant Distributed Formation Tracking for Second-Order Multi-Agent Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910774511796224 |
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| author | Fabris, Marco Fattore, Giulio Cenedese, Angelo |
| author_facet | Fabris, Marco Fattore, Giulio Cenedese, Angelo |
| contents | This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton's method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_12235 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal Time-Invariant Distributed Formation Tracking for Second-Order Multi-Agent Systems Fabris, Marco Fattore, Giulio Cenedese, Angelo Systems and Control This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton's method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies. |
| title | Optimal Time-Invariant Distributed Formation Tracking for Second-Order Multi-Agent Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2307.12235 |