Thesis defence by Rafal Mateusz SOBANSKI

This doctoral thesis is devoted to the development of control algorithms within the framework of the vector field orientation methodology (VFO) for non-holonomic mobile robots and distributed multi-vehicle systems comprising non-holonomic vehicles, which take into account both task execution time constraints and control input constraints. 

This work is based on the concept of fixed-time stability, which assumes that the system’s errors will converge to zero within a finite time, a priori limited by a certain constant value. Furthermore, the value of this upper bound is independent of the specific initial condition and holds for all initial conditions belonging to a certain set of admissible initial conditions. 

In this thesis, given the simultaneous consideration of time constraints and constraints on the control inputs, it is proposed to use a ‘local’ estimate of this upper bound. 

The control algorithms developed are intended for a unicycle-type mobile robot and were designed using a two-stage design approach: we begin by designing a nominal control law, which does not guarantee compliance with the constraints imposed on the control inputs; a scaling procedure is then carried out, which rescales the values of the control signals to ensure compliance with the imposed constraints. 

This thesis presents control laws for two control problems defined for a non-holonomic mobile robot, namely the problem of tracking a non-parametrised reference trajectory and the problem of stabilisation at a given point. Furthermore, two control algorithms for a non-holonomic multi-vehicle system are proposed, which solve the problem of distributed formation. 

The stability of the proposed algorithms has been formally proven, and their performance has been verified using numerical simulations and experimental tests involving physical mobile robots.

• Mr Michaël DEFOORT, University Professor, Hauts-de-France Polytechnic University, Co-supervisor
• Mr Irinel-Constantin MORÃRESCU, University Professor, University of Lorraine, External Examiner
• Mr Ignacy DULĘBA, Professor, Wrocław University of Science and Technology, Rapporteur
• Mr Paweł SKRUCH, Professor, AGH University of Krakow, Rapporteur 
• Ms Rosane USHIROBIRA, Research Director, Inria Lille – Nord Europe, Examiner 
• Ms Taous Meriem LALEG, Research Director, Inria, Paris-Saclay University, Examiner
• Mr Dariusz HORLA, Professor, Poznań University of Technology, Examiner
• Mr Maciej Marcin MICHALEK, Professor, Poznań University of Technology, Co-supervisor
• Mr Kacper PODBUCKI, Poznań University of Technology, Guest

Wheeled mobile robots, Multi-robot system, State and control constraints, Vector field orientation approach, Fixed-time convergence.