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The Dodecacopter: a Versatile Multirotor System of Dodecahedron-Shaped Modules

Kévin Garanger, Thanakorn Khamvilai, Jeremy Epps, Eric Feron

Abstract

With the promise of greater safety and adaptability, modular reconfigurable uncrewed air vehicles have been proposed as unique, versatile platforms holding the potential to replace multiple types of monolithic vehicles at once. State-of-the-art rigidly assembled modular vehicles are generally two-dimensional configurations in which the rotors are coplanar and assume the shape of a "flight array". We introduce the Dodecacopter, a new type of modular rotorcraft where all modules take the shape of a regular dodecahedron, allowing the creation of richer sets of configurations beyond flight arrays. In particular, we show how the chosen module design can be used to create three-dimensional and fully actuated configurations. We justify the relevance of these types of configurations in terms of their structural and actuation properties with various performance indicators. Given the broad range of configurations and capabilities that can be achieved with our proposed design, we formulate tractable optimization programs to find optimal configurations given structural and actuation constraints. Finally, a prototype of such a vehicle is presented along with results of performed flights in multiple configurations.

The Dodecacopter: a Versatile Multirotor System of Dodecahedron-Shaped Modules

Abstract

With the promise of greater safety and adaptability, modular reconfigurable uncrewed air vehicles have been proposed as unique, versatile platforms holding the potential to replace multiple types of monolithic vehicles at once. State-of-the-art rigidly assembled modular vehicles are generally two-dimensional configurations in which the rotors are coplanar and assume the shape of a "flight array". We introduce the Dodecacopter, a new type of modular rotorcraft where all modules take the shape of a regular dodecahedron, allowing the creation of richer sets of configurations beyond flight arrays. In particular, we show how the chosen module design can be used to create three-dimensional and fully actuated configurations. We justify the relevance of these types of configurations in terms of their structural and actuation properties with various performance indicators. Given the broad range of configurations and capabilities that can be achieved with our proposed design, we formulate tractable optimization programs to find optimal configurations given structural and actuation constraints. Finally, a prototype of such a vehicle is presented along with results of performed flights in multiple configurations.

Paper Structure

This paper contains 51 sections, 83 equations, 18 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Dodecacopter-based modular vehicles
  3. Dodecacopter description
  4. The dodecahedron frame
  5. Connection between modules
  6. Geometry of Achievable Configurations
  7. Feasible module positions and orientations
  8. Orientation of module's rotors
  9. Definition of modular configurations
  10. Dynamics
  11. Equations of motion
  12. Scaling of unmodeled forces and moments
  13. Control allocation
  14. The control allocation matrix method
  15. Control allocation matrix choice
  16. ...and 36 more sections

Figures (18)

  • Figure 1: Representation of a module frame and its propeller.
  • Figure 2: Connection between modules. Connecting faces are represented with thicker lines. Connecting vertices are circled. Vertices from one module to the other can be obtained via a translation along the dashed arrow or a rotation of $\pi$ radians around the dashed line.
  • Figure 3: Restricted set of module connections. Vertices used for connections are circled. Dashed lines join the pairs of vertices used to make a connection at every face and form a cube. Dotted arrows represent the translation vectors induced by each connection.
  • Figure 4: Examples of conventional configurations recreated with Dodecacopter modules.
  • Figure 5: Tilt angles inducing a positive thrust allowed by the different possible module orientations.
  • ...and 13 more figures

Theorems & Definitions (30)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • proof
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • proof
  • proof
  • ...and 20 more