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Proving Feasibility of a Docking Mission: A Contractor Programming Approach

Author

Listed:
  • Auguste Bourgois

    (Forssea Robotics, 130 Rue de Lourmel, 75015 Paris, France)

  • Simon Rohou

    (Lab-STICC, ENSTA Bretagne, 2 rue François Verny, 29200 Brest, France)

  • Luc Jaulin

    (Lab-STICC, ENSTA Bretagne, 2 rue François Verny, 29200 Brest, France)

  • Andreas Rauh

    (Group: Distributed Control in Interconnected Systems, Department of Computing Science, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany)

Abstract

Recent advances in computational power, algorithms, and sensors allow robots to perform complex and dangerous tasks, such as autonomous missions in space or underwater. Given the high operational costs, simulations are run beforehand to predict the possible outcomes of a mission. However, this approach is limited as it is based on parameter space discretization and therefore cannot be considered a proof of feasibility. To overcome this limitation, set-membership methods based on interval analysis, guaranteed integration, and contractor programming have proven their efficiency. Guaranteed integration algorithms can predict the possible trajectories of a system initialized in a given set in the form of tubes of trajectories. The contractor programming consists in removing the trajectories violating predefined constraints from a system’s tube of possible trajectories. Our contribution consists in merging both approaches to allow for the usage of differential constraints in a contractor programming framework. We illustrate our method through examples related to robotics. We also released an open-source implementation of our algorithm in a unified library for tubes, allowing one to combine it with other constraints and increase the number of possible applications.

Suggested Citation

  • Auguste Bourgois & Simon Rohou & Luc Jaulin & Andreas Rauh, 2022. "Proving Feasibility of a Docking Mission: A Contractor Programming Approach," Mathematics, MDPI, vol. 10(7), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1130-:d:785134
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    References listed on IDEAS

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    1. Le Mézo, Thomas & Jaulin, Luc & Zerr, Benoît, 2018. "Bracketing the solutions of an ordinary differential equation with uncertain initial conditions," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 70-79.
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