A Compact 6D Suction Cup Model for Robotic Manipulation via Symmetry Reduction

Active suction cups are widely adopted in industrial and logistics automation. Despite that, validated dynamic models describing their 6D force/torque interaction with objects are rare. This work aims at filling this gap by showing that it is possible to employ a compact model for suction cups, providing good accuracy also for large deformations. Its potential use is for advanced manipulation, planning, and control. We model the interconnected object-suction cup system as a lumped 6D mass-spring-damper systems, employing a potential energy function on $\text {SE}(3)$, parametrized by a $6\times 6$ stiffness matrix. By exploiting geometric symmetries of the suction cup, we reduce the parameter identification problem, from $6(6+1) / 2 = 21$ to only $\boldsymbol {5}$ independent parameters, greatly simplifying the parameter identification procedure, that is otherwise ill-conditioned. Experimental validation is provided and data is shared openly to further stimulate research. As an indication of the achievable pose prediction in steady state, for an object of about $\boldsymbol {1.75}$ kg, we obtain a pose error in the order of $\boldsymbol {5}$ mm and $\boldsymbol {3}$ deg, with a gripper inclination of $\boldsymbol {60}$ deg.