A Unified Calibration Framework for Coordinate and Kinematic Parameters in Dual-Arm Robots
Authors: Tianyu Huang, Bohan Yang, Bin Li, Wenpan Li, Haoang Li, Wenlong Li, Yun-Hui Liu
Organizations: Hong Kong Centre for Logistics Robotics and Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China · State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China · Thrust of Robotics and Autonomous Systems, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China
Precise collaboration in vision-based dual-arm robot systems requires accurate system calibration. Recent dual-robot calibration methods have achieved strong performance by simultaneously solving multiple coordinate transformations. However, these methods either treat kinematic errors as implicit noise or handle them through separated error modeling, resulting in non-negligible accumulated errors. In this paper, we present a novel framework for unified calibration of the coordinate transformations and kinematic parameters in both robot arms. Our key idea is to unify all the tightly coupled parameters within a single Lie-algebraic formulation. To this end, we construct a consolidated error model grounded in the product-of-exponentials formula, which naturally integrates the coordinate and kinematic parameters in twist forms. Our model introduces no artificial error separation and thus greatly mitigates the error propagation. In addition, we derive a closed-form analytical Jacobian from this model using Lie derivatives. By exploring the Jacobian rank property, we analyze the identifiability of all calibration parameters and show that our joint optimization is well-posed under mild conditions. This enables off-the-shelf iterative solvers to stably optimize these parameters on the manifold space. Besides, to ensure robust convergence of our joint optimization, we develop a certifiably correct algorithm for initializing the unknown coordinates. Relying on semidefinite relaxation, our algorithm can yield a reliable estimate whose near-global optimality can be verified a posteriori. Extensive experiments validate the superior accuracy of our approach over previous baselines under identical visual measurements. Meanwhile, our certifiable initialization consistently outperforms several coordinate-only baselines, proving its reliability as a starting point for joint optimization.
Figures & tables
Fig. 1: Illustration of a canonical dual-arm robot system. The sensor-side robot is equipped with a camera. The tool-side robot holds a calibration tool (e.g., a chessboard). The closed-loop pose chain in the dual-arm system can be defined by AXB=YCZ .
Fig. 2: Pipeline of the proposed unified calibration algorithm. Given a set of measurements under multiple dual-arm postures, we construct a consolidated Lie-algebraic error model and iteratively refine the coordinate and kinematic parameters on the SE(3) manifold. Before our iterative optimization, the coordinate transforms are initialized by a certifiably correct SDP relaxation solver, while the nominal kinematic parameters directly serve as the initial guess.
Fig. 3: Real-world experiments are conducted on a dual-arm robot system that contains an AUBO-i10 arm equipped with an industrial 3D camera and an AUBO-i10 arm equipped with a calibration tool. The calibration tool consists of a high-precision ChArUco chessboard and a standard ceramic ball.
Kinematic Error Level
Rotation Deviation (deg.)
Translation Deviation (mm)
mean ± std
mean ± std
low ( L )
0.054 ± 0.022
0.417 ± 0.161
medium-low ( ML )
0.103 ± 0.043
1.083 ± 0.412
medium ( M )
0.264 ± 0.089
1.818 ± 0.763
medium-high ( MH )
0.427 ± 0.143
2.861 ± 1.032
high ( H )
0.692 ± 0.278
5.567 ± 0.238
TABLE I: Distribution of robot end-effector pose error caused by different levels of kinematic errors in the simulation analysis (c.f., Section VII-A ).
Measurement Noise Level
Rotation Noise (deg.)
Translation Noise (mm)
mean ± std
mean ± std
low ( L )
0.032 ± 0.013
0.080 ± 0.034
medium-low ( ML )
0.080 ± 0.034
0.160 ± 0.067
medium ( M )
0.128 ± 0.054
0.479 ± 0.202
medium-high ( MH )
0.160 ± 0.067
0.798 ± 0.337
high ( H )
0.239 ± 0.101
1.277 ± 0.539
TABLE II: Distribution of measurement noise at different levels in the simulation analysis (c.f., Section VII-A ).
Fig. 4: Simulated evaluation results on different levels of kinematic errors under (a) medium and (b) high measurement noises (see Section VII-A 1. Each box plot summarizes the error distribution over 40 distinct test samples.
Fig. 5: Simulated evaluation results on different levels of measurement noises under (a) medium-low and (b) medium-high kinematic errors (see Section VII-A 2). Each box plot summarizes the error distribution over 40 distinct test samples.
Fig. 6: Simulated evaluation results on different amounts of calibration samples under (a) medium and (b) high kinematic errors with medium-high measurement noises (see Section VII-A 3). Each box plot summarizes the error distribution over 40 distinct test samples.
Fig. 7: Simulated ablation study regarding our initialization (i.e., SDP-Ini ) on different levels of kinematic errors under (a) medium and (b) high measurement noises (see Section VII-A 4). The curves report the mean deviations over 40 distinct test samples and the iterations to convergence of the unified optimizer with different initializations.
Fig. 8: Data acquisition in real-world experiments. (a) We synchronically adjust the attitudes of both robot arms, ensuring that distinct measurements are obtained. (b) Example images captured at different arm postures, where the calibration pattern is detected to estimate the tool pose in the sensor frame.
Method
Number of Calibration Samples
20
40
60
80
100
120
eR (deg.)
et (mm)
eR (deg.)
et (mm)
eR (deg.)
et (mm)
eR (deg.)
et (mm)
eR (deg.)
et (mm)
eR (deg.)
et (mm)
Wu [ 10 ]
1.3904
6.3091
1.1626
4.2898
1.0959
4.0361
1.0566
3.6754
0.9863
3.9177
0.9769
3.6729
Wang [ 13 ]
1.5661
6.2315
1.2790
4.2283
1.1347
4.0292
1.0737
3.6786
0.9798
4.3918
0.9568
4.1135
Jiang [ 12 ]
1.4773
6.2637
1.2465
4.3564
1.1920
4.1233
1.1049
3.8480
1.0134
4.3927
1.0101
4.0489
SDP-Ini (Ours)
1.1608
4.8550
0.8881
3.3454
0.7879
3.1204
0.7246
2.9885
0.7281
3.0956
0.7191
2.8456
TABLE III: Real-world evaluation results on different amount of calibration samples (see Section VII-B 1). Mean rotation/translation derivations of each method evaluated on 30 distinct test samples are reported. The best results are boldfaced .
Fig. 9: Real-world evaluation results on different amount of calibration samples (see Section VII-B 1). Here we use box plots to show the error distributions of each method over 30 distinct test samples.
Fig. 10: Real-world ablation study regarding our initialization (i.e., SDP-Ini ) on different amount of calibration samples (see Section VII-B 1). The curves report the mean deviations over 30 distinct test samples and the iterations to convergence of the unified optimizer with different initializations.
Fig. 11: The cooperative-measuring evaluation results (see Section VII-B 2). Below each method are the corresponding aligned point clouds obtained from multiple dual-arm postures, with each transformed point cloud visualized in a different color. The red-grid sphere denotes the minimum enclosing ball (MEB) computed from the centers of the spheres fitted to all transformed point clouds, while the blue points indicate the fitted sphere centers. The number reported below is the MEB radius rMEB , where a smaller value indicates higher cooperative-measuring accuracy.
Fig. 12: The standard ball is rigidly attached to the tool-side end-effector and thus remains static in frame {E2} throughout the experiment. For each dual-arm posture, we can transform the ball point cloud measured in {L1} to the common frame {E2} via ( 54 ). As a result, the dual-arm system is now equivalent to a multi-view measuring setup.
This article proposes a general optimization framework for solving hand-eye calibration problem. Unlike traditional methods, an iterative algorithm based on Lie algebra that achieves approximately global optimal solutions is developed. During the optimization process, the method strictly preserves the structural constraints of the calibration parameters and enables synchronized updates between calibration parameters. Recognizing that data used in real-word hand-eye calibration often contain uncertainty, especially in over-loading and large workspace industrial robot scenarios, which can significantly degrade accuracy, and accurately modeling such uncertainty is inherently difficult, this article avoids explicit uncertainty modeling. Instead, an uncertainty metric to evaluate the relative uncertainty between data sources is introduced and used to dynamically refine the iterative process. To further enhance convergence efficiency, an effective initial solution generation method that improves overall stability and accuracy is designed. Numerical simulations and real-world experiments validate the effectiveness of the proposed approach, and in synthetic datasets, the proposed approach improves the estimation accuracy by at least 67% under high-uncertainty conditions compared with the existing methods.
Yanjia Chen, Xiangfei Li, Huan Zhao +4
State Key Laboratory of Intelligent Manufacturing Equipment and Technology and the School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China.
We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a bi-level optimization approach for the dual-arm problem, where we derived the analytical solution to the lower-level convex sub-problem and solved the high-level nonconvex problem using a primal-dual approach. However, the gradient-based nature leads to a large computation overhead, and it prohibits directly imposing an L∞ Cartesian error constraint along the joint trajectory due to the sparsity of the gradient. In this work, we propose a diffusion-based framework that relies on probabilistic sampling to tackle the aforementioned challenges in the nonconvex high-level problem, leading to a 35x reduction in the runtime and 34% less Cartesian error compared to our prior work.
Jushan Chen, Jonathan Fried, Santiago Paternain
Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, 110 8th St, Troy, NY 12180, USA
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.