Force-aware grasping is an essential capability for most robots in practical applications. Especially for compliant grippers, such as Fin-Ray grippers, it still remains challenging to build a bidirectional mathematical model that mutually maps the shape deformation and contact force. Part I of this article has constructed the force-displacement relationship for design optimization through the co-rotational theory. In Part II, we further devise a displacement-force mathematical model, enabling the compliant gripper to precisely estimate contact force from deformations sensor-free. The presented displacement-force model elaborately investigates contact forces and provides force feedback for a force control system of a gripper, where deformation appears as displacements in contact points. Afterward, simulation experiments are conducted to evaluate the performance of the proposed model through comparisons with the finite-element analysis (FEA) in Ansys. Simulation results reveal that the proposed model accurately estimates contact force, with an average error of around 3% and 4% for single or multiple node cases, respectively, regardless of various design parameters (Part I of this article is released in Arxiv1)

翻译：力觉感知抓取是大多数机器人在实际应用中的关键能力。对于柔性夹爪（如Fin-Ray夹爪）而言，构建能够相互映射形变与接触力的双向数学模型仍具挑战性。本文第一部分通过共旋理论建立了用于设计优化的力-位移关系。在第二部分中，我们进一步提出了一种位移-力数学模型，使柔性夹爪无需传感器即可从形变中精确估计接触力。所提出的位移-力模型细致研究了接触力，并为夹爪的力控制系统提供力反馈，其中形变表现为接触点的位移。随后，通过仿真实验与Ansys中有限元分析（FEA）的对比，评估了所提模型的性能。仿真结果表明，该模型能够精确估计接触力，对于单节点或多节点情况，平均误差分别约为3%和4%，且不受不同设计参数的影响（本文第一部分已发布于Arxiv1）。