Towards Dynamic Model Identification and Gravity Compensation for the dVRK-Si Patient Side Manipulator

Abstract

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.

Figures (9)

• Figure 1: Patient Side Manipulator (PSM): dVRK Classic (left), dVRK-Si (right).
• Figure 2: An overview of the workflow for the proposed dVRK-Si PSM modeling, dynamic parameter identification, and deployment. Free-space dynamic model identification proceeds from symbolic robot modeling to optimized periodic excitation-trajectory generation, hardware execution, and physically consistent parameter estimation via convex optimization to obtain the full dynamic model. The identified model is then deployed through three control implementations: (1) a simplified statics-only gravity-compensation variant fitted from static torque measurements (neglecting friction and spring effects) and integrated into the dVRK software, (2) real-time open-loop gravity compensation implemented, and (2) real-time computed-torque feedforward, where joint accelerations are obtained by numerical differentiation and inverse-dynamics torques are added as a feedforward term to a baseline PID loop.
• Figure 3: Modeling of the motion of the PSM gripper.
• Figure 4: The planar view of the frame definition for the dVRK-Si PSM. The units of the link lengths are mm. All frames are left-hand frames.
• Figure 5: Experimental setup: dVRK-Si PSM is mounted at a zero-degree inclination relative to the table.