Robust Null-Space Controller with Sliding Mode for Hierarchical Task Execution in Multi-Robot Formations: Experimental Validation

This work presents a Robust Null Space (RNS) control strategy for hierarchical task execution in multi-robot formations under reference changes. The controller integrates a task-priority null-space framework with a PI-based Sliding Mode Controller (SMC) to enhance tracking performance during reference changes. The proposed scheme addresses two hierarchical tasks: (i) posture regulation as the primary objective and (ii) shape preservation as the secondary objective. Unlike traditional approaches, the RNS controller employs a PI sliding surface to improve convergence and reduce steady-state errors. A Lyapunovbased analysis guarantees the asymptotic stability of the closed-loop system. Experimental validation with a triangular formation of three Turtlebot3 robots shows that the RNS controller achieves up to 26.10% improvement in IAE and 4.43% in ISE over a traditional Null Space controller, demonstrating its robustness and practical effectiveness. These results not only demonstrate the potential of hierarchical control approaches in multi-robot coordination but also provide relevant tools for real-world applications in logistics, cooperative exploration, and collaborative load transportation, where robustness against disturbances and reference changes is critical.