Redundancy Parameterization of the ABB YuMi Robot Arm

Alexander J. Elias; John T. Wen

REVIEW 4 major objections 4 minor 10 references

Redundancy Parameterization of the ABB YuMi Robot Arm

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper pins down the ABB YuMi's redundancy parameter: the controller's arm angle is the conventional Shoulder-Elbow-Wrist angle, using the fourth joint axis as the shoulder-elbow direction and adding a quarter-turn offset.

desk verdict A useful, credible reverse-engineering of the YuMi SEW-angle convention, with validation that is suggestive but thinner than the 'complete and validated' claim. read the letter →

arxiv 2505.23111 v1 pith:OY6DYGFX submitted 2025-05-29 cs.RO

Alexander J. Elias , John T. Wen This is my paper

classification cs.RO

keywords redundantmanipulatorSEWanglearmABBYuMiinversekinematicsalgorithmicsingularities7-DOFrobotsingularityanalysis

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to recover the exact redundancy parameterization used by the ABB controller for the 7-DOF YuMi robot arm. It claims that the arm angle displayed in RobotStudio is the conventional Shoulder-Elbow-Wrist (SEW) angle, with the fourth joint axis as the shoulder-elbow direction, the shoulder located on joint axis 1, plus a constant quarter-turn offset. A previously published formula agrees with the displayed angle over much of the workspace but fails in hand-picked configurations near singularities; the paper's formula matches all ten test configurations to the display precision. Because the quarter-turn offset is constant, the known SEW-angle Jacobian, singularity conditions, and inverse-kinematics search apply directly. If correct, this gives anyone planning paths for the YuMi a closed-form way to replicate the controller's redundancy behavior outside the simulator.

What carries the argument

The central object is the SEW (Shoulder-Elbow-Wrist) angle, also called the arm angle: the angle that the elbow direction makes around the shoulder-wrist line. For the YuMi no elbow point is defined; instead the fourth joint axis direction $h_4$ serves as the shoulder-elbow direction, which is equivalent to putting the elbow point infinitely far away along that axis. The load-bearing identity is $\psi_{\mathrm{ABB}}=\psi_{\mathrm{conv}}+\pi/2$, expressing the controller's angle as a constant offset from the conventional angle between the projected reference vector and the projected $h_4$. Because of this identity, the known Jacobian, singularity conditions, and subproblem-based inverse kinematics for the conventional SEW angle apply to the YuMi without modification.

What would settle it

Command a real IRB 14050 through the ten configurations in Table I while recording the controller's reported arm angle, and compare with $\psi_{\mathrm{ABB}}$ computed from the joint values; disagreement beyond the two-decimal display precision, especially in configurations 6 through 10, would refute the formula. A second check would be to command a fixed pose with a fixed SEW angle and read back the joint configuration under joint-level control, since the controller's internal redundancy parameter should reproduce the commanded SEW angle only if the formula is exact.

Watch

Extended reading notes

Core claim

The central claim is that the redundancy parameter used by the ABB controller for the IRB 14050 YuMi is exactly the conventional Shoulder-Elbow-Wrist (SEW) angle defined in the general SEW formulation, with the shoulder-elbow direction chosen as the fourth joint axis, $p_{SE}=R_{03}h_4$, the shoulder fixed at $O_S=O_1$, and a constant quarter-turn offset, $\psi_{\mathrm{ABB}}=\psi_{\mathrm{conv}}+\pi/2$. This puts the measured vector at $-\hat{e}_{y,C}$ rather than $\hat{e}_{x,C}$, and it matches the SEW angle displayed in RobotStudio exactly at the two-decimal display precision for all ten test configurations, including five hand-picked cases where the previously published definition deviates by tens of degrees. Since the offset is constant, the general SEW-angle Jacobian and singularity classification carry over unchanged. The paper also gives the first explicit shoulder location, which makes the formula compatible with any reference vector, and uses a 2D search over $(q_1,q_2)$ to enumerate all inverse-kinematics solutions for a given pose and SEW angle.

Load-bearing premise

RobotStudio's displayed SEW angle is exactly the internal redundancy parameter of the real ABB controller on the IRB 14050, including near singularities and with the 'Limit avoidance distance' parameter active.

Editorial extensions

If this is right

A planner operating outside RobotStudio can compute the controller's redundancy parameter directly from forward kinematics, so task-space paths can be planned with the same redundancy behavior as the ABB controller.
The algorithmic singularity structure follows from the conventional SEW-angle classification: augmentation singularities beyond $q_2=0$ and $q_6=0$ exist, and the coordinate singularity occurs when the reference vector is collinear with the shoulder-wrist line.
Using the stereographic SEW angle instead would reduce the coordinate singularity to a half-line, but only if implemented externally by streaming joint commands, since the ABB controller does not support it.
All inverse-kinematics solutions for a given end-effector pose and arm angle can be found by a 2D search, with up to eight solutions inside the joint limits for tested poses.
RobotStudio occasionally reports configurations with the correct pose but an incorrect SEW angle, so a user should check the arm angle separately.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the formula is transferred to the real controller, path planners built on the earlier published SEW definition would silently mis-identify algorithmic singularities; correcting the definition changes which self-motion paths are feasible in exactly the regions where the old formula fails.
The same identification strategy of comparing a closed-form redundancy parameter against the simulator's displayed angle at hand-picked poses near singularities could recover the arm-angle conventions of other 7-DOF arms whose controllers do not document their redundancy parameter.
The nested 1D search, plotting SEW angle versus $q_1$ for a fixed pose, gives a visual read on where IK solutions appear and disappear; it could be used as a quick feasibility check before running a full planner.
The quarter-turn offset suggests ABB chose zero arm angle when the fourth-axis direction aligns with the negative $y$-axis of the SEW frame, a convention that could be adopted in future controller design to match intuitive arm poses.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The new thing here is concrete and usable: a closed-form SEW-angle definition for the ABB YuMi (Eq. 14: ψ_ABB = ψ_conv + π/2, with p_SE = R_03 h_4 and O_S = O_1) that corrects the recent formula from Asgari, Bonev, and Gosselin and matches RobotStudio's displayed SEW angle on the reported test cases. The derivation from the authors' own general SEW framework is clean, the coordinate-free notation is consistent, and the IK demonstrations with the 2D search plus the alternative nested 1D search are a nice practical bonus. The code being public is a real plus. The paper is also honest about one gap: it explicitly says a systematic classification of algorithmic singularities is still needed.

Where it is softer than the abstract suggests: the validation is ten RobotStudio cases, and the random-match statistic reported in Section VII-A is genuinely ambiguous. It says “approximately 40% of randomly chosen poses had matching SEW angles up to 0.01 deg away after rounding” without saying which definitions matched—ψ_ABB, ψ_sign, or all three. The surrounding text implies it is ψ_sign that fails much of the time, but the authors need to say that explicitly and give the agreement rate for ψ_ABB alone. Also, the only ground truth is RobotStudio's on-screen value rounded to two decimals, and the paper itself notes in VII-B that the 'Limit avoidance distance' controller parameter affects solution accuracy. That undercuts the word "exact" in the abstract and in Eq. 14's framing. There is no hardware validation, so the leap from "matches RobotStudio" to "matches the real IRB 14050 controller" is asserted, not shown. These are not fatal—the formula is very plausible and the ten cases include the difficult ones where the prior definition fails—but they are real limitations on the strength of the claim.

Who is this for? Anyone doing offline planning or IK for the YuMi outside RobotStudio, and people studying redundancy parameterization for 7-DOF arms. The value is contained to one robot family and its users, not a new general principle, but for that audience it is genuinely useful.

My recommendation: send it to peer review. The core result is likely correct and worth publishing after revision. The revision should add a broader sweep, clarify the random-match statistic, and soften or justify the "exact" language. I would not desk-reject it.

Referee Report

4 major / 4 minor

Summary. The paper identifies the redundancy parameter used by the ABB YuMi controller as a conventional SEW angle with the shoulder-elbow direction taken along the fourth joint axis, evaluated from the shoulder point O1, plus a quarter-turn offset: Eq. (14), psi_ABB = psi_conv + pi/2. The derivation is placed in the general SEW-angle framework of the authors' prior work [4], with ATAN2 expressions given in Eqs. (17)-(19). The paper then discusses algorithmic singularities, presents an IK solver based on subproblem decomposition with a 2D search, and validates the SEW-angle formula by comparing it with RobotStudio on ten joint configurations. It also shows that the previously published formula of Asgari, Bonev, and Gosselin [2] deviates from RobotStudio in five hand-picked cases.

Significance. If Eq. (14) is correct, the paper closes a genuine gap: ABB manuals do not disclose the SEW-angle definition, and the only prior formula in the literature is shown to disagree with RobotStudio. The derivation is clean and fits into an existing general framework, so the Jacobian and singularity results from [4] carry over directly. The public code repository and the reproducible comparison table are strengths. However, the central claim of an 'exact' match is currently supported only by ten configurations read from a rounded simulator display, not by a comprehensive sweep or hardware validation, so the significance of the empirical contribution is somewhat tempered by the strength of the evidence.

major comments (4)

[VII-A, Table I] The empirical support for Eq. (14) is not yet sufficient for the word 'exact'. Table I reports only ten configurations, all matching RobotStudio to 0.01 degrees, but RobotStudio displays two decimals, so the test cannot distinguish Eq. (14) from any formula that agrees to within 0.005 degrees. The random-pose sentence in Section VII-A ('approximately 40% ... had matching SEW angles') is ambiguous: it appears to count poses where psi_RS, psi_ABB, and psi_sign all agree, and it does not report the agreement rate between psi_ABB and psi_RS alone. If psi_ABB disagreed with RobotStudio on any random pose, the central claim would be falsified. Please report the distribution of psi_ABB - psi_RS over a large random sweep (for example, thousands of poses with both reference vectors), including near-singular poses, and state the maximum residual before rounding.
[VII-B, IV] Section VII-B states that the 'Limit avoidance distance' controller parameter appears to affect solution accuracy in RobotStudio, but the paper does not say whether this parameter was active during the Table I tests or whether the displayed SEW angle is the raw internal parameter. If RobotStudio's display is influenced by the avoidance algorithm, the identification could fit the simulator's display rather than the controller's redundancy coordinate. Please run the validation with this parameter explicitly disabled and, if possible, verify at least a few configurations on the physical IRB 14050.
[Section IV, Eqs. (15)-(16)] The notation e_y in Eqs. (15) and (16) conflicts with the definition in Section II, where e_y is the world y-axis. The minimizer in Eq. (15) and the equality in Eq. (16) are only correct if e_y denotes the C-frame y-axis e_y,C, because R(e_SW, theta)(-e_y) generally has a component along e_SW and cannot equal the purely perpendicular vector -e_SW^{x2} R03 h4. As written, these equations are not valid for a general pose. Please replace e_y by e_y,C (or introduce a distinct symbol) and re-derive the displayed equivalences.
[Abstract and Section V] The abstract promises 'complete numerical conditions for all algorithmic singularities', but Section V does not provide explicit numerical conditions; it lists categories and gives one example of an augmentation singularity, and the Conclusion states that a systematic classification is still needed. Similarly, the paper says the SEW-angle Jacobian expression is obtained, but the explicit expression is not given and is only referenced to [4]. Please either include the promised conditions and Jacobian expression or revise the abstract and wording to match what is actually delivered.

minor comments (4)

[III-B, Eq. (5)] The typesetting of the ATAN2 expression in Eq. (5) is garbled; please check the numerator, which should presumably contain the norm of the cross product term.
[VII-A] The parenthetical about 40% of random poses would be clearer as a separate sentence reporting the sample size, the exact agreement criterion, and the match rate for each definition pair separately.
[VI, Eq. (22)] The half-plane condition e_CE^T R03 h4 > 0 would benefit from an explicit statement that e_CE is a unit vector or from a normalization convention, so the sign convention is unambiguous.
[II] The sentence 'The joint numbering is different in RobotStudio' is important, but a one-line mapping from the product-of-exponentials ordering to the RobotStudio ordering would help readers use the provided code and compare with RobotStudio output.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity found: the SEW-angle formula is an empirical identification validated against RobotStudio as an external benchmark, and the cited prior framework is independently published rather than a self-fulfilling premise.

full rationale

The paper's central claim, Eq. (14), states that the ABB SEW angle is the conventional SEW angle plus a quarter-turn offset, with the shoulder-elbow direction taken as the fourth joint axis. This is not derived by assuming the conclusion; it is a closed-form candidate definition whose support is the direct comparison to RobotStudio readings in Table I. RobotStudio is an external artifact whose displayed SEW angle is not constructed from the paper's own equations, so agreement with it is genuine, independent evidence rather than a self-referential fit. The authors explicitly write out the defining equations (Eqs. (10)-(19)) in terms of the general SEW framework from their prior work [4], rather than treating that framework as an unexamined black box. The self-citations to [4] and [8] supply general mathematical machinery (SEW-angle definitions, Jacobian/singularity classification, subproblem decomposition) that was published independently and does not assume the YuMi result. No parameter is fitted to RobotStudio and then relabeled as a prediction: the offset and axis choices are stated analytically and then tested on joint configurations, including hand-picked cases where the competing definition fails. The paper's admitted limitations, such as the unclear effect of the 'Limit avoidance distance' parameter and the unsupported assertion that the controller matches the real robot, are correctness risks rather than circularity: they do not make Eq. (14) equivalent to its inputs by construction. For these reasons, the derivation chain is not circular and warrants a score of 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim depends on the identified SEW-angle parameters (offset, shoulder, shoulder-elbow direction) that are fitted to RobotStudio observations, plus standard kinematic modeling assumptions. No new physical entities are introduced.

free parameters (3)

SEW angle quarter-turn offset = pi/2 rad
The ABB SEW angle equals the conventional SEW angle plus pi/2 (Eq. 14). This offset is not derived from first principles; it is identified from RobotStudio data.
Shoulder position O_S = O_1 (point on axis 1 closest to joint axis 2)
The SEW-angle frame origin is placed at O_1. The paper states this differs from ABB's manual description and is inferred to make the definition match RobotStudio for all reference vectors.
Shoulder-elbow direction p_SE = R_03 h_4 (joint 4 axis direction)
The shoulder-elbow direction used in the SEW angle is chosen as the joint 4 axis, a modeling choice based on observed RobotStudio behavior (Sec. IV).

assumptions (4)

domain assumption RobotStudio's displayed SEW angle equals the ABB controller's internal redundancy parameterization, including on the real robot.
The paper validates against the simulator and states the controller matches the real robot without direct hardware evidence (Introduction, Sec. VII).
domain assumption The PoE kinematic parameters in Eq. (4) correctly describe the YuMi's geometry.
All SEW angle and IK computations use these link vectors and joint axes read from ABB data.
standard math The general SEW-angle framework, Jacobian, and singularity categories from [4] are correct.
The paper transfers results from the authors' prior published framework; no independent re-derivation is given.
domain assumption ABB allows reference vectors h1, world z, and world y.
The SEW definition includes the reference vector choice; the set is taken from ABB manuals.

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Cite this review

Pith. "Pith review of Redundancy Parameterization of the ABB YuMi Robot Arm." pith.science (2026). https://pith.science/paper/OY6DYGFX

@misc{pith2026250523111,
  author       = {Pith},
  title        = {Pith review of: Redundancy Parameterization of the ABB YuMi Robot Arm},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OY6DYGFX}},
  note         = {Machine review of arXiv:2505.23111}
}

read the original abstract

The ABB YuMi is a 7-DOF collaborative robot arm with a complex, redundant kinematic structure. Path planning for the YuMi is challenging, especially with joint limits considered. The redundant degree of freedom is parameterized by the Shoulder-Elbow-Wrist (SEW) angle, called the arm angle by ABB, but the exact definition must be known for path planning outside the RobotStudio simulator. We provide the first complete and validated definition of the SEW angle used for the YuMi. It follows the conventional SEW angle formulation with the shoulder-elbow direction chosen to be the direction of the fourth joint axis. Our definition also specifies the shoulder location, making it compatible with any choice of reference vector. A previous attempt to define the SEW angle exists in the literature, but it is incomplete and deviates from the behavior observed in RobotStudio. Because our formulation fits within the general SEW angle framework, we also obtain the expression for the SEW angle Jacobian and complete numerical conditions for all algorithmic singularities. Finally, we demonstrate using IK-Geo, our inverse kinematics (IK) solver based on subproblem decomposition, to find all IK solutions using 2D search. Code examples are available in a publicly accessible repository.

Figures

Figures reproduced from arXiv: 2505.23111 by the authors.

**Figure 2.** SEW angle calculation. The 4th joint axis direction [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Singularity regions using the conventional and stereographic SEW [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Finding all IK solutions using 2D search. The error function is multi [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Finding all IK solutions using nested 1D search. For each [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

[4]

Asgari, I

M. Asgari, I. A. Bonev, and C. Gosselin, ``Singularity analysis of Kinova’s Link 6 robot arm via Grassmann line geometry,'' in Proc. IEEE Int. Conf. Robot. Autom. (ICRA) , pp. 8814--8820, IEEE, 2024

work page 2024
[2]

Kreutz-Delgado, M

K. Kreutz-Delgado, M. Long, and H. Seraji, ``Kinematic analysis of 7- DOF manipulators,'' Int. J. Robot. Res. , vol. 11, no. 5, pp. 469--481, 1992

work page 1992
[1]

11em plus .33em minus .07em @technote 4000 4000 100 4000 4000 500 `\.=1000 = #1 #1 #1 0pt [0pt][0pt] #1 * \| ** #1 \@IEEEauthorblockNstyle \@IEEEauthorblockAstyle \@IEEEauthordefaulttextstyle \@IEEEauthorblockconfadjspace -0.25em \@IEEEauthorblockNtopspace 0.0ex \@IEEEauthorblockAtopspace 0.0ex \@IEEEauthorblockNinterlinespace 2.6ex \@IEEEauthorblockAinte...

work page
[3]

Asgari, I

M. Asgari, I. A. Bonev, and C. Gosselin, ``Singularities of ABB ’s YuMi 7- DOF robot arm,'' Mech. Mach. Theory , vol. 205, p. 105884, 2025

work page 2025
[5]

A. J. Elias and J. T. Wen, ``Redundancy parameterization and inverse kinematics of 7- DOF revolute manipulators,'' Mech. Mach. Theory , vol. 204, p. 105824, 2024

work page 2024
[6]

ABB, Technical reference manual - System parameters RW7 , 2024

work page 2024
[7]

ABB, Operating manual - IRB 14000 , 2022

work page 2022
[8]

ABB, Technical reference manual - RAPID overview RW7 , 2024

work page 2024

Show all 10 references

[9]

A. J. Elias and J. T. Wen, `` IK-Geo : Unified robot inverse kinematics using subproblem decomposition,'' Mech. Mach. Theory , 2025

2025
[10]

A. J. Elias and J. T. Wen, ``Path planning and optimization for cuspidal 6R manipulators,'' arXiv preprint arXiv:2501.18505 , 2025

2025 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [4]

Asgari, I

M. Asgari, I. A. Bonev, and C. Gosselin, ``Singularity analysis of Kinova’s Link 6 robot arm via Grassmann line geometry,'' in Proc. IEEE Int. Conf. Robot. Autom. (ICRA) , pp. 8814--8820, IEEE, 2024

work page 2024

[2] [2]

Kreutz-Delgado, M

K. Kreutz-Delgado, M. Long, and H. Seraji, ``Kinematic analysis of 7- DOF manipulators,'' Int. J. Robot. Res. , vol. 11, no. 5, pp. 469--481, 1992

work page 1992

[3] [1]

11em plus .33em minus .07em @technote 4000 4000 100 4000 4000 500 `\.=1000 = #1 #1 #1 0pt [0pt][0pt] #1 * \| ** #1 \@IEEEauthorblockNstyle \@IEEEauthorblockAstyle \@IEEEauthordefaulttextstyle \@IEEEauthorblockconfadjspace -0.25em \@IEEEauthorblockNtopspace 0.0ex \@IEEEauthorblockAtopspace 0.0ex \@IEEEauthorblockNinterlinespace 2.6ex \@IEEEauthorblockAinte...

work page

[4] [3]

Asgari, I

M. Asgari, I. A. Bonev, and C. Gosselin, ``Singularities of ABB ’s YuMi 7- DOF robot arm,'' Mech. Mach. Theory , vol. 205, p. 105884, 2025

work page 2025

[5] [5]

A. J. Elias and J. T. Wen, ``Redundancy parameterization and inverse kinematics of 7- DOF revolute manipulators,'' Mech. Mach. Theory , vol. 204, p. 105824, 2024

work page 2024

[6] [6]

ABB, Technical reference manual - System parameters RW7 , 2024

work page 2024

[7] [7]

ABB, Operating manual - IRB 14000 , 2022

work page 2022

[8] [8]

ABB, Technical reference manual - RAPID overview RW7 , 2024

work page 2024