Kinematic Synthesis of Flexible Manipulator for Spinal Endoscopic Surgery via Bayesian Optimization with Multi-Physical Constraints

Kinematic synthesis of flexible manipulator for minimally invasive spinal endoscopic surgery faces challenges such as multi-constraint coupling (geometric, performance, environmental) and difficulties in modeling complex flexible deformations. To address these, this paper proposes an integrated kinematic synthesis framework for spinal endoscopic manipulators, which coordinates multi-physical constraints using Bayesian optimization. The framework couples workspace analysis, stiffness modeling, and material limitations to minimize the outer diameter while meeting clinical requirements. A customized Bayesian optimization process is developed for high-dimensional nonlinear design of flexible manipulators, improving optimization efficiency and solution quality. Verification via Monte Carlo simulations and stiffness tests confirms that the optimized design complies with clinical workspace requirements and safe interaction standards. This work provides a robust solution for the design of miniaturized, high-performance spinal endoscopic manipulators.