The da Vinci Research Kit (dVRK) is widely used for research in robot-assisted surgery, but most modeling and control methods target the first-generation dVRK Classic. The recently introduced dVRK-Si, built from da Vinci Si hardware, features a redesigned Patient Side Manipulator (PSM) with substantially larger gravity loading, which can degrade control if unmodeled. This paper presents the first complete kinematic and dynamic modeling framework for the dVRK-Si PSM. We derive a modified DH kinematic model that captures the closed-chain parallelogram mechanism, formulate dynamics via the Euler-Lagrange method, and express inverse dynamics in a linear-in-parameters regressor form. Dynamic parameters are identified from data collected on a periodic excitation trajectory optimized for numerical conditioning and estimated by convex optimization with physical feasibility constraints. Using the identified model, we implement real-time gravity compensation and computed-torque feedforward in the dVRK control stack. Experiments on a physical dVRK-Si show that the gravity compensation reduces steady-state joint errors by 68-84% and decreases end-effector tip drift during static holds from 4.2 mm to 0.7 mm. Computed-torque feedforward further improves transient and position tracking accuracy. For sinusoidal trajectory tracking, computed-torque feedforward reduces position errors by 35% versus gravity-only feedforward and by 40% versus PID-only. The proposed pipeline supports reliable control, high-fidelity simulation, and learning-based automation on the dVRK-Si.

翻译：达芬奇研究套件（dVRK）被广泛用于机器人辅助手术研究，但现有建模与控制方法主要针对第一代dVRK Classic系统。最新推出的基于达芬奇Si硬件构建的dVRK-Si，其重新设计的患者侧机械臂（PSM）具有显著增大的重力负载，若未建立相应模型将导致控制性能下降。本文首次提出了完整的dVRK-Si PSM运动学与动力学建模框架。我们推导了能够描述闭链平行四边形机构的改进DH运动学模型，通过欧拉-拉格朗日方法建立动力学方程，并将逆动力学表达为线性参数回归形式。基于数值条件优化的周期激励轨迹采集数据，采用带物理可行性约束的凸优化方法进行动态参数辨识。利用辨识模型，我们在dVRK控制架构中实现了实时重力补偿与计算力矩前馈控制。在物理dVRK-Si平台上的实验表明：重力补偿使稳态关节误差降低68-84%，末端执行器静态保持时的漂移从4.2 mm减小至0.7 mm。计算力矩前馈进一步提升了瞬态响应与轨迹跟踪精度：在正弦轨迹跟踪任务中，相比纯重力前馈控制，位置误差减少35%；相比纯PID控制，误差降低40%。所提出的建模流程为dVRK-Si平台实现可靠控制、高保真仿真及基于学习的自动化提供了技术支撑。