Multi-Layer Stiffness Optimization Model of a Staggered Continuum Manipulator for Natural Orifice Diagnostic Surgery

Natural orifice diagnostic surgery require manipulators that remain slender yet sufficiently stiff to preserve positioning accuracy under contact. Stiffness performance directly affects the precision and stability. In this paper, a staggered continuum manipulator and a multi-layer stiffness-optimization method is proposed. First, the structure of unit was optimized using topology optimization to maximize performance. Then, a multi-layer stiffness-optimization model with an end-effector accuracy constraint was formulated to jointly optimize local joint and global manipulator parameters across levels. The global layer builds a virtual-joint-model (VJM) stiffness map over the design space, while the local layer refines joint structure to reshape load paths. Finally, prototypes and simulations show that, the optimized manipulator achieves a 66% increase in tip stiffness while reducing mass by 62%, and supports omnidirectional bending up to 170 angle without loss of controllability. In bench tests with externally applied moments and axial tip loads representative of diagnostic maneuvers, the 3D End-Effector position error is 0.72 mm, confirming that stiffness gains translate into reduced load-induced deflection. The results demonstrate that integrating staggered joint layout with multi-layer stiffness optimization provides a practical route to co-optimize flexibility, spatial efficiency, and accuracy for natural-orifice diagnostics.