This study presents an integrated framework for enhancing the safety and operational efficiency of robotic arms in laparoscopic surgery by addressing minimum distance estimation between multi-arm manipulators and the associated collision-aware warning. By combining analytical modeling, real time simulation, and machine learning, the framework offers a robust solution for ensuring safe robotic operations. An analytical model was developed to estimate the minimum distances between robotic arms based on their joint configurations, offering theoretical calculations that serve as both a validation tool and a benchmark. To complement this, a 3D simulation environment was created to model two 7 DOF Kinova robotic arms (Kinova inc., Boisbriand, QC, Canada), generating a diverse dataset of configurations for distance estimation and collision warning. Using these insights, a deep residual neural network model was trained with joint configurations as inputs. On the held out validation set, the model achieves R2 = 0.940, RMSE = 42.0 mm, MAE = 28.7 mm, and a near zero mean bias, demonstrating strong predictive accuracy and consistent generalization across the workspace. The framework is intended as an early collision warning layer, where a warning is triggered when the predicted inter-arm distance falls below a 0.2 m threshold, which corresponds to a surface to surface clearance of approximately 50 mm given the Kinova Gen3 (Kinova inc., Boisbriand, QC, Canada) cross sectional radius. This work demonstrates the effectiveness of combining analytical modeling with machine learning to enhance the precision and reliability of multi-arm robotic systems.

翻译：本研究提出了一种集成框架，通过解决多臂机械臂间最小距离估计及相关碰撞感知预警问题，提升腹腔镜手术中机械臂的操作安全性与效率。该框架融合解析建模、实时仿真与机器学习，为保障机器人安全操作提供了稳健解决方案。基于机械臂关节构型，建立了解析模型以估算臂间最小距离，其理论计算结果可作为验证工具与基准参照。为补充该模型，创建了三维仿真环境，模拟两台七自由度Kinova机械臂（加拿大Kinova公司，博瓦布里扬市），生成了用于距离估计与碰撞预警的多样化构型数据集。基于上述分析，以关节构型为输入训练了深度残差神经网络模型。在留出验证集上，该模型实现了R²=0.940、RMSE=42.0 mm、MAE=28.7 mm及近乎零的平均偏差，展现出强劲的预测精度与跨工作空间的一致泛化能力。该框架旨在作为早期碰撞预警层：当预估臂间距离低于0.2米阈值时触发预警（考虑Kinova Gen3机械臂横截面半径，该阈值对应约50毫米的表面间间隙）。本研究证明了将解析建模与机器学习相结合以提升多臂机器人系统精度与可靠性的有效性。