The inspection of underground sewer networks is subject to several constraints that limit its scope and reliability: limited access through manholes, irregular pipe geometries, and degraded radio communications due to depth, reinforced concrete, and the lack of direct line of sight. A teleoperated robot may progressively lose contact with its operator as it moves deeper into the network. Deploying a fleet of robots, some of which can act as communication relays, addresses this limitation but raises a new challenge: coordinating the robots so as to maintain an appropriate formation along the network while ensuring communication continuity. This thesis proposes an original approach based on a unified geometric representation of the robot fleet. Rather than considering individual robot trajectories, the fleet is described by a planar Pythagorean hodograph (PH) curve whose Lagrange nodes correspond to the positions of the robots. The degree of the curve is directly determined by the size of the fleet. This representation makes it possible to analytically compute the length of the corridor and, consequently, determine the spacing between robots directly from the curve coefficients. The first contribution concerns the algebraic characterization of PH curves satisfying interpolation, tangency, and arc-length constraints. Using a Legendre basis, these constraints are formulated in matrix form, making it possible to characterize the entire family of admissible trajectories. Existence conditions are established as a function of the curve degree and, consequently, of the number of robots forming the fleet. The second contribution addresses fleet control and coordination. The curve coefficients are incorporated into the state vector within a new framework, referred to as PHoCS (Pythagorean Hodograph Curve-based State-space). A control law is then designed to drive the fleet configuration towards a prescribed reference, with asymptotic convergence established through a Lyapunov-based argument. This approach coordinates the robots through a common representation, without requiring explicit coordination rules between vehicles. It is validated through simulations involving fleets of eight to twelve robots and experimentally on a fleet of four mobile robots. The third contribution extends this approach to the mechanical modelling of the cable connecting the leader robot to the operator. The cable is considered as a deformable element guided and supported by the follower robots. A Lagrangian and subsequently a port-Hamiltonian model is developed to account for cable length, curvature, and torsion. A distributed energy-shaping control strategy is proposed, with each robot relying only on information exchanged with its neighbouring robots. Overall, the thesis establishes a unified framework linking fleet geometry, trajectory generation and control, robot synchronization, and the mechanical dynamics of the communication cable. The proposed approach provides an original theoretical and experimental framework for coordinating robotic fleets operating in confined environments and subject to severe communication constraints.
- M. Rochdi MERZOUKI Professeur des universités Université de Lille Directeur de thèse, - M. Sueur CHRISTOPHE Professeur des universités Centrale Lille Co-directeur de thèse, - M. Frédéric BOYER Professeur IMT Atlantique Examinateur, - Mme Reine TALJ-KFOURY Directrice de recherche Université de Technologie de Compiègne, Sorbonne Université Examinatrice, - M. Taha BOUKHOBZA Professeur des universités Université de Lorraine Rapporteur, - M. Abdelaziz BENALLEGUE Professeur des universités Université de Versailles Saint-Quentin-en-Yvelines Rapporteur.
Thesis of the team SoftE defended on 02/11/2026
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