Détail de l'offre

Safety for uncertain high-order systems with delays: Application to UAVs

Offre du 16/12/2022

Beyond stability and convergence, safety is among the most important properties to analyze for a general control system. Assuring safety for the system consists in designing the input u so that the closed-loop solutions starting from a given set of initial conditions Xo never reach a given unsafe region Xu .
Depending on the considered application, reaching the unsafe set Xu can correspond to the impossibility of applying a prede ned feedback law or, simply, colliding with a physical obstacle, another system, or a human operator.
Analogous to Lyapunov theory for stability, control barrier functions are useful to design an adequate candidate set K that can be rendered forward invariant.
Control barrier functions for safety are used in many applications, including multi-robots collision avoidance , adaptive cruise control , bipedal locomotion , and drones, among many others. This extensive use has lead to the following research directions:

1. Control design for safety-critical high-order systems In mechanical systems, for examples, the safety requirements (i.e., the sets Xo and Xu) are usually expressed in terms of positions; hence, a natural choice of the barrier function would involve the vector of positions only. However, since the input u does not appear in the positions'dynamics, it will not appear in the safety condition; thus, the latter cannot be enforced.

2. The presence of delays in the control loop.
Note that the transfer of information from the sensors to the controller and from the latter to the actuator is always a ected by delays, which can be of di erent types (constant, time-varying, bounded, unbounded). This phenomena is usually neglected in the applied literature of safety, especially in the context of drones. The few results on the analysis of safety in the presence delays concern only control systems with relative-degree one.

3. Digital implementation of safe controllers.
Few existing results studied safety under intermittent or digital control implementations
(sample data, event-triggered, self triggered) . They often consider control systems with relative-degree one and assume either strong regularities on f or boundedness of the set K.

4. Safety despite of the system's uncertainties and perturbations.
Usually, the models we use are useful only after taking into account some uncertainties and perturbations. As an example, we can cite drones operating in uncertain environments or subject to winds or other disturbances. Hence, it is important to adapt the design procedure to parametric uncertainties and disturbances.

The goal of this masters internship is to propose a rigorous framework to study safety for control systems  u, for which, the relative degree is larger than one. Such models are representative in the context of AUVs and drones, where delays as well as uncertainties are unavoidable, in addition to digital control implementations. The obtained solutions will be validated on the drone set up available at GIPSA lab.

Laboratory : Gipsa-lab, Grenoble, France
Address: 11 rue des Math ematiques, Grenoble, FRANCE, Campus BP46, F-38402 SAINT
Team: COPERNIC/ MODUS / In nity
Mohamed Maghenem, CNRS researcher
e-mail : mohamed.maghenem@grenoble-inp.fr
Ahmed Hably, Associate Professor Grenoble-INP - HDR
e-mail: ahmad.hably@grenoble-inp.fr
Jonathon Dumon, Ingénieur d'études CNRS
e-mail: jonathan.dumon@gipsa-lab.grenoble-inp.fr
Keywords: Control theory; Delayed systems; High-order systems; Safety; Barrier functions; Autonomous navigation; drones.

Gipsa-lab (Grenoble images parole signal automatique)



Type de Contrat

  • Stage
  • Fonction

    • Ingénieur.e
    • Diplômes

      • Bac +5 (M2, Ingénieur, etc.)
      • Expérience

        • Débutant
        • Compétences Techniques

          • Navigation
          • Drone