Series Passive Nonlinear Compliance for Stable Admittance-Controlled Physical Human-Robot Collaboration in Low-Tolerance Assembly

Low-tolerance assembly tasks in physical human-robot interaction (pHRI) often involve intermittent contact with stiff environments, which can induce instability in admittance-controlled manipulators. Increasing virtual damping improves stability but reduces responsiveness and increases operator effort. This paper introduces a series nonlinear compliance mechanism that reshapes interaction dynamics through adjustable stiffness at the robot end-effector. The mechanism provides low stiffness during fine manipulation and higher stiffness at larger displacements to enhance stability during contact-rich assembly. Experimental evaluation in a collaborative peg-in-hole task demonstrates reduced contact forces, improved insertion stability, and faster task completion. In an ultra-low-clearance scenario (0.05 mm), insertion fails under conventional rigid configurations but succeeds consistently with the proposed mechanism. Task completion time is reduced by up to 30% without increasing admittance damping. These results demonstrate that passive nonlinear compliance can improve stability without sacrificing responsiveness in contact-rich pHRI tasks.