Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile Robots
In this paper, we evaluate theoretical aspects of a distributed system of noncooperative robots controlled by a distributed model predictive control scheme, which operates in a shared space. Here, for collision avoidance, the future predicted state trajectories are projected on a grid and exchanged...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-02-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/10/3/1007 |
| _version_ | 1819118596851236864 |
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| author | Tobias Sprodowski Jürgen Pannek |
| author_facet | Tobias Sprodowski Jürgen Pannek |
| author_sort | Tobias Sprodowski |
| collection | DOAJ |
| description | In this paper, we evaluate theoretical aspects of a distributed system of noncooperative robots controlled by a distributed model predictive control scheme, which operates in a shared space. Here, for collision avoidance, the future predicted state trajectories are projected on a grid and exchanged via discrete cell indexes to reduce the communication burden. The predicted trajectories are obtained locally by each robot and carried out in the continuous space. Therefore, the quantisation does not impose the quality of the solution. We derive sufficient conditions to show convergence and practical stability for the distributed control system by using an idea of a temporary roundabout derived from crossing patterns of street traffic rules, which is established in a fixed and flexible circle size. Furthermore, a condition for the sufficient prediction horizon length to recognise necessary detours is presented, which is adapted for the occupancy grid. The theoretical results match with the trajectory patterns from former numerical simulations, showing that this pattern is naturally chosen as an overall solution. |
| first_indexed | 2024-12-22T05:51:24Z |
| format | Article |
| id | doaj.art-2cc31d75c46b486283328d6d26d2912a |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-12-22T05:51:24Z |
| publishDate | 2020-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-2cc31d75c46b486283328d6d26d2912a2022-12-21T18:36:52ZengMDPI AGApplied Sciences2076-34172020-02-01103100710.3390/app10031007app10031007Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile RobotsTobias Sprodowski0Jürgen Pannek1Faculty of Production Engineering, Hochschulring 20, University of Bremen, 28359 Bremen, GermanyFaculty of Production Engineering, Hochschulring 20, University of Bremen, 28359 Bremen, GermanyIn this paper, we evaluate theoretical aspects of a distributed system of noncooperative robots controlled by a distributed model predictive control scheme, which operates in a shared space. Here, for collision avoidance, the future predicted state trajectories are projected on a grid and exchanged via discrete cell indexes to reduce the communication burden. The predicted trajectories are obtained locally by each robot and carried out in the continuous space. Therefore, the quantisation does not impose the quality of the solution. We derive sufficient conditions to show convergence and practical stability for the distributed control system by using an idea of a temporary roundabout derived from crossing patterns of street traffic rules, which is established in a fixed and flexible circle size. Furthermore, a condition for the sufficient prediction horizon length to recognise necessary detours is presented, which is adapted for the occupancy grid. The theoretical results match with the trajectory patterns from former numerical simulations, showing that this pattern is naturally chosen as an overall solution.https://www.mdpi.com/2076-3417/10/3/1007distributed model predictive controlquantisationstabilityprediction horizon lengthmobile robots |
| spellingShingle | Tobias Sprodowski Jürgen Pannek Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile Robots Applied Sciences distributed model predictive control quantisation stability prediction horizon length mobile robots |
| title | Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile Robots |
| title_full | Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile Robots |
| title_fullStr | Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile Robots |
| title_full_unstemmed | Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile Robots |
| title_short | Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile Robots |
| title_sort | analytical aspects of distributed mpc based on an occupancy grid for mobile robots |
| topic | distributed model predictive control quantisation stability prediction horizon length mobile robots |
| url | https://www.mdpi.com/2076-3417/10/3/1007 |
| work_keys_str_mv | AT tobiassprodowski analyticalaspectsofdistributedmpcbasedonanoccupancygridformobilerobots AT jurgenpannek analyticalaspectsofdistributedmpcbasedonanoccupancygridformobilerobots |