A data-driven 2D satellite-robot testbed for PID experimental validation and LQR-based simulation benchmarking

Formation flying in small-satellite missions enables distributed sensing and interferometry; however, many existing ground-based testbeds rely on coupled thruster layouts that complicate control design and obscure the impact of real actuator limitations. This study presents a decoupled-thruster satellite robot implemented on a two-dimensional air-bearing platform with eight electric ducted fan (EDF) thrusters arranged in two independent layers for separate translational and heading control. The platform employs pneumatic levitation, ESP32-based electronics, and vision-based pose tracking with sub-centimeter accuracy. Complete kinematic and dynamic models are developed and augmented with experimentally derived PWM-thrust mappings to capture nonlinear actuation behaviour. PID controllers are implemented on the hardware testbed for waypoint navigation and triangular formation control, while LQR-based simulations are used as model-based benchmarks for systematic gain tuning and performance comparison. Experimental results demonstrate centimeter-level trajectory tracking, smooth heading regulation, and formation spacing errors below 3 cm under identical actuation constraints. By integrating data-driven actuator characterisation with a unified controller evaluation pipeline, this work bridges the gap between idealised control models and experimentally observed actuation limitations, providing a reproducible and practical testbed for multi-agent satellite control and proximity-operations research.