Macroscopic constraint-based modeling and dynamic simulation for manipulation with a belt-attached hand

This study aims to develop a novel modeling and analysis method based on macroscopic constraints for manipulation with a belt-attached hand. In a mesh-based model where a flexible body is divided into smaller parts and analysis is based on local constraints, the complexity of the model depends on the number of elements and scale of the belt. In contrast, the proposed model has the advantage of allowing dynamic analysis with a small number of unknown variables and constraints because it formulates the adaptive deformation of the belt into the object shape as macroscopic constraints. First, a generalized complementarity condition concerning tautness and adaptive deformation of a cloth-like flexible body and tension is introduced, and the belt-object system is modeled. Subsequently, a dynamic analysis combining algorithms to update the contact state and a mixed nonlinear complementarity problem to satisfy constraints is introduced. Finally, translation involving rolling and slipping, continuous rotation by fingertip vibration, and fixation by grasping the object on the belt are simulated based on the proposed method, and the results are compared with those of a real experiment. We confirmed the efficacy of the proposed method in reproducing the various dynamic behaviors of the belt-object system, including rolling, slipping, and collisions.