Asymmetric Force Feedback Caging for Symmetry Preservation in Cooperative Multi-Robot Object Transport

Cooperative object transport requires accurate trajectory tracking, formation regulation, and reliable interaction between mobile robots and a payload. This paper integrates a force-feedback reactive caging law into a polynomial conformable fractional function (CFF) formation controller. The caging distance decreases when either instrumented gripper finger reports force below a threshold and increases more gradually when both measurements exceed the threshold. Four contraction-to-release ratios, ρA∈{1,2,5,10}, are evaluated in 80 trials using circular and sinusoidal trajectories with a repeatable reference disturbance. Experiments use two omnidirectional robots equipped with soft grippers, single-finger force sensors, and Vicon motion capture, coordinated through ROS2 and an LQR-regulated digital twin. Relative to the polynomial CFF controller, the force-feedback extension reduces normalized orientation IAE from 0.1457 to 0.1210 for the circular trajectory and from 0.0017 to 0.0015 for the sinusoidal trajectory. Increasing ρA reduces the fraction of time with subthreshold measured force, from 0.4495 to 0.1274 for the circular path and from 0.4395 to 0.3481 for the sinusoidal path. However, spatial symmetry is trajectory dependent, and larger asymmetry increases mean symmetry error on the sinusoidal path. These results identify a trade-off between formation centering and sensor-referenced force persistence, without establishing mechanical grasp stability.