MSc Thesis Defense: Omar Sabra Kaek, Deformable Formation Control for Multi-Robot Systems in Dynamic Environments Using Elliptic Fourier Descriptors and Dynamic Parabolic CBF, Date & Time: 30 June 2026 – 4:00 PM, Place: FENS G035

Deformable Formation Control for Multi-Robot Systems in Dynamic Environments Using Elliptic Fourier Descriptors and Dynamic Parabolic CBF

Omar Sabra Kaek
Mechatronics Engineering, MSc Thesis, 2026

Thesis Jury

     Prof. Mustafa Ünel (Thesis Advisor)

  Assoc. Prof. Kemalettin Erbatur

  Assoc. Prof. Hüseyin Üvet

Date & Time: June 30th, 2026 – 4:00 PM

Place: FENS G035

 

Keywords : Multi-Robot Systems, Formation Control, Elliptic Fourier Descriptors, Control Barrier Functions, Dynamic Obstacle Avoidance

Abstract

One of the challenges with autonomous multi-robot systems is to navigate in dynamic environments when the passages are stationary and narrow, and obstacles are moving. The traditional formation control methods based on rigid geometry cannot work in confined spaces, and conservative collision avoidance may lead to system freezing or deadlock. This thesis introduces a new hybrid formation control approach combining geometric shape adaptation and safety critical filtering. The framework uses Elliptic Fourier Descriptors (EFD) and Implicit Polynomials (IP) to dynamically deform the spatial boundary of the swarm using real-time Sequential Quadratic Programming (SQP) optimization so that nonholonomic robots can squeeze through non-dynamic bottlenecks. At the same time, a Dynamic Parabolic Control Barrier Function (DPCBF) layer is a minimally intrusive velocity filter, generating provably safe control inputs, to proactively avoid moving obstacles while maintaining operational flexibility. Comprehensive hardware-in-the-loop simulations have been performed on the MovingAI benchmark topology with ROS 2 and Gazebo. The proposed architecture demonstrated low steady state tracking errors (0.15–0.19 m RMSE) and guaranteed zero collision for up to seven followers and eight dynamic guards, in stress testing scenarios. Extensive ablation tests show that disabling either the geometric adaptation or safety filter leads to system failure.