Fractional-conformable control for cooperative object transport in multi-robot systems

• A Fractional-Conformable Formation Control law was developed to perform caging using an MRS. • An LQR-drive digital twin was developed to control the MRS during Cooperative Object Transport. • Results prove that the Fractional-Conformable Control and LQR-driven digital twin MRS control improve trajectory tracking performance. This paper proposes a decentralized control framework for cooperative object transport in a multi-robot system (MRS) composed of two omnidirectional robots and one object. The approach integrates Conformable Fractional Functions (CFF) within a fractional-conformable derivative paradigm to govern the stages of cooperation: approach, caging, and transport. A digital twin, regulated by a Linear Quadratic Regulator (LQR), ensures global path tracking, while a CFF-based formation controller maintains inter-robot coordination during motion. We evaluate constant, polynomial, sinusoidal, and logarithmic CFFs in circular and sinusoidal trajectory experiments, using normalized performance indices and error convergence plots. Results show that non-constant CFFs, particularly polynomial and logarithmic, accelerate stabilization and reduce angular error by up to 99% compared with the constant case. The LQR-driven digital twin achieves sub-centimeter positional accuracy and limits orientation deviations to less than 0.15 rad under dynamic conditions. These findings validate the robustness, responsiveness, and real-time feasibility of the proposed controller for cooperative manipulation tasks, demonstrating how fractional-conformable formulations can enhance trajectory tracking and orientation control in decentralized multi-robot coordination with soft robotic grippers.