Whole-Body Elasto-Geometrical Calibration of Wheeled Humanoid Robots Using a Shared-Waist Dual-Chain Model

Pengxin Zha; Yi Lu; Haojun Ma; Jun Zhu; Minghao Qiu; Xiaoyan Wang; Wei Shan; Maoqing Yao

cs.RONov 5, 2026

Whole-Body Elasto-Geometrical Calibration of Wheeled Humanoid Robots Using a Shared-Waist Dual-Chain Model

Authors: Pengxin Zha, Yi Lu, Haojun Ma, Jun Zhu, Minghao Qiu, Xiaoyan Wang, Wei Shan, Maoqing Yao

Organizations: The authors are with AgiBot, China.

Abstract

Wheeled humanoid robots carry both arms on one actuated waist, usually without torque sensors, so the accuracy of both end-effectors depends on a single waist model. After a first stage that estimates the tracker and target extrinsics, we identify the waist and both arms in one problem from the target positions on both flanges, measured by an optical tracker. The kinematic model is complete, with waist-base, parallel-axis, and branch parameters; arm compliances are driven by measured torques and waist compliances by gravity torques of the robot's mass model; and Gaussian priors with evidence-maximizing scales stabilize the estimate. Independent and sequential single-chain calibration are restrictions of this problem, and its waist information is the sum of the single-chain Schur complements. On two robots with different waists, each without and with a payload, calibration reduces the mean errors on held-out poses from 11.3-31.1 mm to 0.50-1.11 mm. For every training-set size from 20 poses to all, the method has 17-63% lower mean errors than adaptations of two published whole-body calibration methods, mainly through the waist compliance. Independent calibration yields two waist models; using either for both arms raises the other arm's error to up to 3.21 mm.

Figures & tables

Fig. 1: MDH frames of the two robots at zero joint positions (front view), computed from the nominal model of the robot description. Arrows are the axes $x_{i}$ and $z_{i}$ in the drawing plane; a circle with a dot (a cross) is an axis pointing towards (away from) the viewer; colors alternate between consecutive frames. The symbols mark the link lengths $a_{i-1}$ and offsets $d_{i}$ visible in this view. (a) G2: joints 1–5 form the shared waist (frames 3 and 4 coincide), joints 6–12 belong to each arm. (b) G2max: the revolute pitch joint forms the waist (frames 0 and 1 coincide); joints 2–8 belong to each arm.

Fig. 2: Overall calibration workflow and its implementation in GKCS. (a) Steps of the procedure (Sections III and IV ); circled numbers: GKCS layers of (b) that run the step. (b) Layered architecture of GKCS with the functions of each layer. (c) GKCS main window after the whole-body calibration of G2 without load: calibration data, errors before and after calibration on the training and validation poses, nominal MDH parameters and identified deviations, and the identification log.

Panel of Figure 3 — Fig. 3: Compared formulations. Colors mark the least-squares problem in which a part of the model is estimated and the target data it uses; gray dashed lines are the extrinsics, fixed from Stage I. The waist (W) includes the waist-base parameters and the waist compliances. (a) IND identifies each chain alone and returns two waist models. (b) SEQ L→R identifies the waist with the left arm and then the right arm with the waist fixed. (c) DUAL identifies the waist and both arms in one problem; the adaptations BON and NGU have the same structure with other body models. (d) One-stage estimation of the extrinsics with the body parameters, as in the original procedures of [ 2 , 3 ] .

Fig. 4: Experimental setup. (a) G2 and (b) G2max without payload: the optical tracker in front of the robot measures the targets on both flanges, and GKCS runs on the laptop. (c) 5 kg payload and target on a G2 flange; (d) 10 kg payload and target on a G2max flange.

Dataset	Waist	Payload	Poses	Used	Train/val	$\|\boldsymbol{\tau}_{1}\|$ L/R
		(kg/arm)				(N $\cdot$ m)
G2, no load	5R	0	95	95	70/25	15.3/14.8
G2, loaded	5R	5	95	95	70/25	36.7/35.9
G2max, no load	1R	0	81	71	54/17	33.1/47.2
G2max, loaded	1R	10	72	60	46/14	90.0/87.9

TABLE I: Datasets. Waist: Joints of the Waist Model (R: Revolute); Poses: Executed Calibration Poses; Used: After Cleaning;

|\tau_{1}|

: Mean Absolute Torque of Arm Joint 1.

	G2, no load			G2, 5 kg/arm			G2max, no load			G2max, 10 kg/arm
Method	L	R	Rel.	L	R	Rel.	L	R	Rel.	L	R	Rel.
Nominal	13.92	24.60	21.50	17.21	31.14	22.60	22.16	11.31	25.01	25.11	16.35	27.99
IND-G	0.84	1.10	0.89	1.50	1.62	1.82	1.11	0.78	1.21	2.04	1.54	2.20
IND-GC	0.82	0.82	0.80	0.99 -	1.05 +	1.19	0.55	0.45	0.60	0.65	0.59	0.82
SEQ L→R -G	0.84	1.20 +	0.98	1.50	1.91 +	2.08 +	1.11	0.86	1.34	2.04	2.55 +	2.55 +
SEQ L→R -GC	0.82	0.88 +	0.80	0.99 -	1.21 +	1.39 +	0.55	0.67 +	0.83 +	0.65	1.52 +	1.56 +

TABLE II: Mean Position Errors on the Validation Poses (mm). L, R: Left and Right Target; Rel.: Dual-Arm Relative Error. Bold: Lowest Calibrated Value per Column. + / - : Larger/Smaller than DUAL of the Same Variant (BON: DUAL-GC; NGU: DUAL-G), Paired 95% CI Excluding Zero. IND, SEQ, and DUAL Use the Proposed Model; BON-GC w : BON-GC with the Waist Compliances of the Proposed Model. All Methods Use the Stage-I Extrinsics and a Complete Waist Base.

		Waist					Arm
	Parameters	Joint 1	Joint 2	Joint 3	Joint 4	Joint 5	Joint 6	Joint 7	Joint 8	Joint 9	Joint 10	Joint 11	Joint 12
Nominal	$a_{i-1}$ (mm)	144	360	380	0	0	0	0	0	10.5	10.5	0	0
	$\alpha_{i-1}$ (rad)	$\pi$ /2	0	0	$-\pi$ /2	$-\pi$ /2	$-\pi$ /2	$\pi$ /2	$\pi$ /2	$\pi$ /2	$\pi$ /2	$\pi$ /2	$\pi$ /2
	$d_{i}$ (mm)	0	0	0	0	457.5	243.5	0	332	0	278	0	0
	$\theta_{i}$ (rad)	0	0	0	$-\pi$ /2	$-\pi$ /2	0	$-\pi$	$-\pi$	$-\pi$	$-\pi$	$\pi$ /2	0
	$\beta_{i-1}$ (mrad)	–	0	0	–	–	–	–	–	–	–	–	–

TABLE III: MDH Parameters of G2: Nominal (Robot Description, Zero Joint Positions) and Identified by DUAL-GC on the Dataset Without Load.

c_{i}

: Compliance About the Joint Axis,

c_{t,i}

: Tilt Compliance of a Waist Joint, Both in

10^{-4}

rad/(N

\cdot

m);

\beta_{i-1}

Only for Axes Parallel to the Previous One (–: Not in the Model); : Not Identifiable and Kept at the Nominal Value;

(\gamma_{l},b_{l})

: Branch Parameters of the Left Arm (Those of the Right Arm Are Redundant). The Right Arm Shares the Waist of the Left Chain; Its Nominal Parameters Differ Only in

\alpha_{5}

\pi

		Waist	Arm
	Parameters	Joint 1	Joint 2	Joint 3	Joint 4	Joint 5	Joint 6	Joint 7	Joint 8
Nominal	$a_{i-1}$ (mm)	0	680	0	0	25	25	0	95
	$\alpha_{i-1}$ (rad)	0	0	$\pi$ /2	$\pi$ /2	$\pi$ /2	$\pi$ /2	$\pi$ /2	$-\pi$ /2
	$d_{i}$ (mm)	0	276	0	450	0	267	0	0
	$\theta_{i}$ (rad)	0	$-\pi$	$\pi$ /2	$-\pi$	$-\pi$	$-\pi$	$\pi$ /2	0
	$\beta_{i-1}$ (mrad)	–	0	–	–	–	–	–	–

TABLE IV: MDH Parameters of G2max: Nominal and Identified by DUAL-GC on the Dataset Without Load (Notation of Table III ). The Nominal Right Arm Differs Only in

\alpha_{1}

\pi

Fig. 5: Mean validation error of both targets against the number of training poses (

N

; 20 random subsets per size, the full training set once), for DUAL-GC and IND-GC with the proposed model and for the adaptations of [ 2 , 3 ] ; BON-GC w adds the waist compliances of the proposed model to BON-GC. Logarithmic scale.

Fig. 6: Standard deviation of each identifiable waist parameter in DUAL relative to the better single chain, from ( 8 ) at the DUAL-GC solution; the waist block also contains

\boldsymbol{x}_{\mathrm{wb}}

and the waist compliances. The dashed line marks

1/\sqrt{2}

, the ratio for two chains with equal information.

	G2		G2 5 kg		G2max		G2max 10 kg
Model	L	R	L	R	L	R	L	R
Proposed	0.83	0.79	1.11	0.97	0.61	0.50	0.72	0.64
Least squares	0.78 -	0.82	1.09	0.95	0.60	0.48	0.71	0.66
No tilt compl.	0.83	0.84 +	1.15	1.05 +	0.79 +	0.58	1.22 +	0.78 +
No waist compl.	0.96 +	0.96 +	1.43 +	1.34 +	0.87 +	0.62	1.40 +	1.37 +
No branch	0.85 +	0.78	1.15 +	0.96	0.60	0.57	0.89 +	0.69

TABLE V: Validation Errors (mm) of DUAL-GC with Parts of the Proposed Model Removed, All Training Poses. Compl.: Compliance; + / - : Larger/Smaller than the Proposed Model, Paired 95% CI Excluding Zero. Last Three Rows: Arm Compliances Only and Least Squares, with Complete Kinematics, Without

\beta

and Branch, and Also Without Waist Base.

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OmniCalib: Target-Free, Task-Structured Self-Calibration for Humanoid Robots

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Robotics Camera Calibration Humanoid Robotics

Open paper AskPDF arXiv

Assembly, wear, and component replacement perturb the sensor extrinsics and joint zeros encoded by a humanoid CAD model. Existing procedures calibrate one sensor pair or require external fiducials. Using only robot-native motion and onboard sensing, we present OmniCalib, a target-free workflow that calibrates the full upper limbs---all 14 arm joint zeros and the extrinsics of both wrist and chest cameras---as well as lower limbs and the multi-camera head rig. Each module matches a robot-native task to a parameter block, checks observability, and writes only supported corrections to the CAD model. Our depth ICP method recovers all 14 arm joint zeros and calibrates all RGB-D camera extrinsics without any calibration target. Relative to CAD, the estimated extrinsic corrections are 10.56 mm and 1.74 degrees for the left wrist, 6.33 mm and 1.25 degrees for the right wrist, and 9.81 mm and 0.929 degrees for the chest RGB-D camera. ICP point-to-plane residual is 2.09 mm. On the same injected offsets, ICP and ArUco recover all 14 joint zeros below the 0.1-degree encoder-resolution reference. On an AGIBOT A3 Ultra humanoid, four static double-support stances recover all 12 lower-limb joint-zero offsets injected with an RMS error of 0.063 degrees. The head module combines multi-camera visual odometry with legged odometry and dynamic compensation through the live ROS transform tree. Using only planar walking, it attains a mean SO(3) error of 1.061 degrees across three sequences. The best sequence reaches 0.775 degrees, competitive with iKalibr at 0.902 degrees from rich 6-DOF excitation. Rig-relative angles repeat within 0.140 degrees. Injection recovery and held-out tests validate each observable block.

Abstract

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