Surrogate-Assisted Coordinated Optimization of Mechanism Parameters and Motion Trajectories for a Variable-Link-Length Robotic Manipulator

Fixed-link manipulators have limited adaptability to changes in task locations and obstacle layouts, while sequential mechanism design and trajectory planning restrict their coordinated performance. This study proposes a surrogate-assisted bilevel optimization method for a four-degree-of-freedom PRRR variable-link-length manipulator. The three link lengths are treated as outer-layer mechanism variables, whereas B-spline control points and trajectory duration are optimized in the inner layer subject to joint, motion, endpoint, and collision constraints. An objective-decoupled surrogate predicts trajectory duration, path length, jerk cost, and minimum clearance, and is embedded in an adaptive reference vector-guided multi-operator multi-objective beluga whale optimization algorithm. The framework combines inverse-kinematics prescreening, surrogate evaluation, high-fidelity trajectory re-optimization, dense constraint verification, and preference-based decision-making. Blind-test, ablation, and high-fidelity verification results show that the method efficiently identifies high-quality, physically feasible mechanism–trajectory candidates. Factorial analysis of an obstacle-constrained handling task indicates that trajectory optimization primarily improves smoothness and clearance, whereas mechanism adaptation redistributes joint motion and further enhances overall trajectory quality. Physical experiments demonstrate the executability of the selected mechanism–trajectory solutions without observed cylinder collision or joint-limit activation in the tested trials. These results demonstrate that the proposed framework provides an effective approach to task-adaptive mechanism–trajectory co-optimization in constrained environments.