Integrated ADRC and Consensus Control for Anti-Disturbance Formation Tracking Control of Multiple Biomimetic Underwater Spherical Robots

To facilitate the practical deployment and engineering implementation of multi-robot coordination for biomimetic underwater spherical robots (BUSRs), it is imperative to develop a formation tracking control method with a simple structure, a small number of tunable parameters, convenient parameter tuning and strong anti-disturbance capability. This study proposes a formation controller integrating virtual structure (VS), consensus protocol, and parallel output-velocity-type active disturbance rejection control (POV-ADRC), denoted as VS-C-POV-ADRC. A rotating global (RG) coordinate system is established to decouple robot positions from heading angles, which makes the parameter tuning more convenient. A double-loop control architecture is constructed, where the outer consensus control loop generates the desired velocity for each robot based on virtual-structure reference positions, and the inner POV-ADRC loop achieves high-precision velocity tracking. The proposed controller features a compact structure with only five adjustable parameters per motion direction, realizing easy engineering implementation and adaptation to the limited computing capacity of BUSRs. The simulation and experiment results demonstrate that the proposed algorithm enables robots to maintain a stable formation and achieve trajectory tracking accuracy within one body length, while exhibiting superior disturbance rejection. The proposed method provides a feasible and practical solution for BUSR formation control.