Estimation of the Caged Object's Posture Under Forces Using Stepwise Geometric Calculations

Abstract

In pin-hole assembly processes, precise alignment or compliance mechanisms are typically required. This paper proposes a method for connecting objects by utilizing caging to constrain their motion, enabling the insertion of a pin into a hole to adjust the allowable relative pose for assembly. This approach eliminates the need for force control, even with low-degree-of-freedom manipulators, and reduces deflection caused by misalignment during connection. Although previous research has extensively studied appropriate finger configurations for caging, the behavior of caged objects under external forces remains insufficiently investigated. Furthermore, when connecting caged objects by contact, pose estimation often requires complex collision computations that account for intricate object geometries, which are computationally expensive and may fail to converge when small gaps are present. To address this issue, we propose a geometric method that approximates pose changes of caged three-dimensional objects under external forces as rotations about contact points. As a representative case, we focus on objects composed of cuboid elements. The estimated results for simple objects, including caged objects with small clearances, were consistent with geometrically derived theoretical solutions, and are obtained within 0.6 seconds, indicating a practical computation time.