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

Haoying Zhou; Hao Yang; Brendan Burkhart; Anton Deguet; Zhonghao Zhang; Loris Fichera; Gregory S. Fischer; Jie Ying Wu

cs.ROMar 12, 2026

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

Authors: Haoying Zhou, Hao Yang, Brendan Burkhart, Anton Deguet, Zhonghao Zhang, Loris Fichera, Gregory S. Fischer, Jie Ying Wu,

Organizations: Department of Robotics Engineering, Worcester Polytechnic Institute, MA 01609, USA. · Laboratory for Computational Sensing and Robotics, Johns Hopkins University, MD 21218, USA. · Department of Computer Science, Vanderbilt University, TN 37212, USA. · Department of Computer Science, Johns Hopkins University, MD 21218, USA.

Abstract

The da Vinci Research Kit (dVRK) has been widely used for research in robot-assisted surgery over the past decade, and its latest generation, the dVRK-Si was made publicly available in 2025. This manuscript presents the first complete kinematic and dynamic modeling framework for the dVRK-Si Patient-Side Manipulator (PSM), whose redesigned mechanism differs substantially from that of the first-generation dVRK and therefore requires a new formulation to accurately capture gravitational effects and improve overall control performance. We first develop a modified DH kinematic model that represents the dVRK-Si PSM's redesigned mechanism. The equations of motion are then derived using the Euler-Lagrange formulation, and the inverse dynamics are expressed in a linear-in-parameters regressor form. The dynamic parameters are identified from data collected along a periodic excitation trajectory optimized for numerical conditioning and estimated by convex optimization subject to the physical feasibility constraints. The identified model is integrated into the dVRK control stack to enable real-time gravity compensation and computed-torque feedforward control. Experiments on a physical dVRK-Si demonstrate that the gravity compensation reduces steady-state joint errors by up to 84% and decreases end-effector tip drift during static holds from 4.2 mm to 0.7 mm. Computed-torque feedforward control further improves transient and trajectory-tracking accuracy. During sinusoidal trajectory tracking, computed-torque feedforward reduces position errors by 35% versus gravity-only feedforward and by 40% versus PID-only. The proposed pipeline could support reliable control, high-fidelity simulation, and learning-based automation on the dVRK-Si.

Figures & tables

Panel of Figure 1 — Fig. 1: Patient Side Manipulator (PSM): dVRK Classic (left), dVRK-Si (right).

Fig. 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 implementation, and (3) 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.

Fig. 3: Overview of the joint coordinates provided by dVRK software (n=7), extended for dynamics estimation (n=13), and for complete model (n=20).

Fig. 4: Modeling of the motion of the PSM gripper.

Fig. 5: 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.

$i$	Ref	$a_{i-1}$	$\alpha_{i-1}$	$d_{i}$	$\theta_{i}$	$\delta_{Li}$	$I_{mi}$	$F_{i}$	$K_{si}$
1	0	0	$\frac{\pi}{2}$	0	$q_{1}+\frac{\pi}{2}$	$\checkmark$	$\times$	$\checkmark$	$\times$
1’	1	$-l_{1H}$	$-\frac{\pi}{2}$	0	$\frac{\pi}{2}$	$\times$	$\times$	$\times$	$\times$
2	1’	$l_{1L}$	0	0	$q_{2}-\frac{\pi}{2}$	$\checkmark$	$\times$	$\checkmark$	$\times$
2’	2	$l_{2L0}$	$\frac{\pi}{2}$	$l_{2H0}$	0	$\times$	$\times$	$\times$	$\times$
2”	2’	0	$-\frac{\pi}{2}$	0	$-q_{2}+\frac{\pi}{2}$	$\checkmark$	$\times$	$\checkmark$	$\times$
2”’	2”	$l_{2L1}$	$\frac{\pi}{2}$	$l_{2H1}$	0	$\times$	$\times$	$\times$	$\times$

TABLE I: dVRK-Si PSM Model Description Parameters

Fig. 6: Experimental setup: dVRK-Si PSM is mounted at a zero-degree inclination relative to the table.

Placement	J1	J2	J3	J4	J5	J6	J7
0 ∘ Horizontal (JHU)	7.43	10.57	21.91	36.28	45.29	45.49	87.56
0 ∘ Horizontal (VU)	10.72	7.60	14.55	48.90	31.99	37.89	87.04
45 ∘ Downward (VU)	9.45	7.92	20.51	62.14	40.01	64.49	68.47

TABLE II: NRMSE Results for All Joints under 0 ∘ Horizontal Placement and 45 ∘ Downward-Tilted Surgical Scene Placement

Fig. 7: Measured and model-predicted joint torques/forces over a representative segment of an excitation trajectory.

Item	Pose Idx	PD Pos Err	GC Pos Err	PD $\mathbf{\tau}$	GC $\mathbf{\tau}$	Non- Drift LB $\mathbf{\tau}$	Non- Drift UB $\mathbf{\tau}$
Joint1 (deg or N $\cdot$ m)	1	0.14	0.04	-1.42	-1.07	-0.11	-1.76
	2	0.06	0.04	0.60	1.25	0.43	2.17
	3	0.85	0.16	8.87	7.67	6.06	9.75
	4	0.50	0.11	-5.25	-6.39	-4.66	-7.99
	5	0.27	0.05	-2.81	-3.61	-2.48	-4.51
Joint2 (deg or N $\cdot$ m)	1	0.50	0.13	5.29	4.32	2.98	5.75

TABLE III: Drift Test Results

Fig. 8: Sinusoidal trajectory tracking using PID controller only (top), PID controller with dVRK software gravity compensation (middle), and PID controller with computed torque feedforward (bottom). Left panels compare desired and measured joint positions and report the position tracking error

\bm{q}_{err}=\bm{q}_{des}-\bm{q}_{meas}

. Right panels show the corresponding torque/force, including the desired joint efforts, measured joint efforts, and the errors between the measured and desired joint efforts

\bm{\tau}_{err}=\bm{\tau}_{des}-\bm{\tau}_{meas}

over a 10 s trial.

Item	Joint Idx	Mean	STD	RMSE	Max
Joint Position Errors (deg or mm)
PID with Torque Feedforward	1	0.46	0.24	0.52	0.94
	2	0.44	0.22	0.49	1.07
	3	0.78	0.40	0.88	1.57
PID with dVRK Software Gravity Compensation	1	0.68	0.30	0.74	1.13
	2	0.66	0.30	0.73	1.14

TABLE IV: Tracking Error Statistics

Fig. 9: Residual PID feedback joint torque/force comparison; contributions due to gravity compensation and computed-torque feedforward are excluded.

Fig. 10: Comparison of two gravity-compensation implementations (from Section III-I1 and Section III-J ) and the full computed-torque term over a sinusoidal trajectory.

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