An Empirical Study of Wrist-Target Construction and Joint-Angle Limits in Humanoid Arm Retargeting

MinJun Chang

cs.ROOct 27, 2026

An Empirical Study of Wrist-Target Construction and Joint-Angle Limits in Humanoid Arm Retargeting

Authors: MinJun Chang

Organizations: Georgia Institute of Technology

Abstract

Motion retargeting maps a demonstrated human movement onto a robot to compute its joint motion. This study examines how the construction of the desired wrist position affects whether computed arm joint angles reach their permitted limits on a Unitree H1-2. A reconstructed target is formed from demonstrated arm directions and robot segment lengths, so its shoulder-to-wrist distance depends on the demonstrated angle between the segments even when no posture-matching preference is applied. A reach-normalized target retains that direction while rescaling the distance, using the same processed demonstrations and the same joint-angle method. Across a forward-reach sweep the reconstructed target places a joint angle at a bound in 10 of 20 repetitions and the reach-normalized target in none. Across 25 recordings from one participant the corresponding counts are 8 and 6 on the reaching arm and 14 and 5 on the supporting arm, and a second participant repeats the bricklaying and lifting comparison. In hardware replay a joint is commanded to a bound in 12 of 16 direction-matching arm-records and in none of the 16 normalized records, and within the eligible records both tracking error and executed torque at those frames exceed their values elsewhere in the same run. Cross-body reach and arm-to-arm clearance identify limits of radial adjustment. The findings support treating target construction and posture matching as separate retargeting decisions, and evaluating both alongside the wrist positions and clearance that manipulation requires.

Figures & tables

Fig. 1: Reconstructed and reach-normalized wrist targets share a shoulder-to-wrist direction but differ in distance. The reconstructed distance depends on the demonstrated angle between the arm segments in ( 1 ) and ( 2 ). Normalization rescales that distance along the same direction and applies the selected cap.

Joint	Right range	Left range	Effort	Velocity
	(rad)	(rad)	(N m)	(rad/s)
Shoulder pitch	$[-3.14,\ 1.57]$	$[-3.14,\ 1.57]$	40	0 9
Shoulder roll	$[-3.40,\ 0.38]$	$[-0.38,\ 3.40]$	40	0 9
Shoulder yaw	$[-3.01,\ 2.66]$	$[-2.66,\ 3.01]$	18	20
Elbow	$[-0.95,\ 3.18]$	$[-0.95,\ 3.18]$	18	20

TABLE I: Limits of the four active joints per arm. Effort and velocity are model parameters, not constraints on the offline solve.

Fig. 2: Saturated reaching-arm recordings across four forward-reach settings. Each setting has five repetitions. Reconstructed and reach-normalized targets use the same joint-angle method. Direction matching is an additional comparison. Lines connect the evaluated settings rather than identify a precise onset threshold.

Competing centering weight $w_{c}$	$g=1$	$g=0.001$
$0$	23/25 (15/25)	10/25 (15/25)
$0.05$	16/25 (15/25)	0 7/25 (12/25)
$0.20$	0 6/25 ( 0 9/25)	0 5/25 ( 0 8/25)
$0.50$	0 0/25 ( 0 0/25)	0 0/25 ( 0 0/25)

TABLE III: Saturated recordings under competing posture and centering weights. Reaching arm, supporting arm in parentheses.

Arm	Posture gain $g$	$w_{c}=0.20$	$w_{c}=0.50$
Right	$1$	40.37	149.88
Right	$0.001$	39.00	153.38
Left	$1$	35.03	173.33
Left	$0.001$	36.04	177.93

TABLE IV: Wrist-target error in millimeters at the two largest competing centering weights.

Fig. 3: Replayed arm motion sampled at equal intervals under the two hardware conditions of Section V-C . (a) Regularized direction matching, in which the right arm extends away from the torso and approaches full extension. (b) The reach-normalized target, in which both elbows remain flexed and the wrists stay nearer the torso. Frames are spaced $8$ s apart across $24$ s of replay in both rows, with $t$ set independently for each sequence. The two rows come from separate replay sessions and are not aligned to a common motion phase, and they differ in the requested motion and in the joint-angle method rather than in the wrist target alone. The operator’s face is blurred.

Statistic	Tracking	Torque
Maximum ratio	1.891	2.067
Correlation with saturated fraction	0.850	0.845
Correlation after the paired-record omission	0.457	0.602

TABLE V: Within-run tracking and torque associations across the 12 eligible direction-matching arm-records.

Fig. 4: Left-arm bricklaying replay under regularized direction matching at speed scale $0.2$ . Shading marks 497 saturated frames of shoulder roll in seven episodes. The measured angle remains within the model bound. The bottom panel averages absolute executed torque across four arm joints. This recording supplies the influential pair in Table V .

Fig. 5: Maximum radial deficit across both arms after one common horizontal base translation per recording. Deficits are measured relative to the capped reach radius. The 8 cm reference is an exploratory threshold rather than a validated grasp or placement tolerance.

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Abstract

Motion Retargeting

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