Morphology and actuation as inductive biases in robotic hand manipulation

Zalán Tari; Eszter Birtalan; Péter Polcz; Miklós Koller

cs.ROSep 4, 2026

Morphology and actuation as inductive biases in robotic hand manipulation

Authors: Zalán Tari, Eszter Birtalan, Péter Polcz, Miklós Koller

Organizations: Pázmány Péter Catholic University, Faculty of Information Technology and Bionics, Budapest, Hungary

Abstract

Robotic hands vary widely in anatomical fidelity and mechanical complexity, and these structural choices influence the coordination of joint motions and the difficulty of controlling the system. A unified framework is presented in which the kinematic and actuation stages are analysed separately and in composition, through the conditioning of the task Jacobian, the actuation matrix, and their product. It is applied to two hands representing opposing design philosophies, the Shadow Dexterous Hand and the Anatomically Correct, Biomechatronic Hand, along four morphological aspects: joint axis geometry, actuator-to-DOF ratio, coupling architecture, and authority distribution. All parameters are derived from the hands' canonical digital representations. Anatomical fidelity carries no uniform advantage: oblique axes improve thumb conditioning but leave the long fingers worse conditioned than the orthogonal-axis design, while the branching tendon network improves the effective control mapping at every long finger and worsens it significantly at the thumb, where actuator authority is concentrated on thumb opposition. Predictions derived from these metrics are evaluated against reinforcement learning experiments using PPO, DDPG+HER, and TQC+HER, across three different tasks.

Figures & tables

Panel of Figure 1 — Figure 1: Simulation models of the two robotic hands used during analysis [ 7 , 10 ] .

Figure 2: Simplified overview of the analysis pipeline. Each robotic hand is converted from its digital representation to a common structural model $\mathcal{H}=(\mathcal{K},\mathcal{A})$ , from which the task Jacobian $J$ , the actuation matrix $A$ , and the effective control mapping $B=JA$ are constructed.

Panel of Figure 3 — Figure 3: Visualization of the configuration dependence of the kinematic conditioning of the ACBH’s thumb (a) and index finger (b), using overlaid positions. At each position, the velocity ellipsoid of the task Jacobian $J(q)$ is drawn at the fingertip. Ellipsoids are coloured by their isotropy $\sigma_{\min}/\sigma_{\max}$ , from green (well conditioned) towards red (ill-conditioned). The semi-axes of each ellipsoid are proportional to the singular values of the corresponding mapping, so a long axis denotes a direction in which task-space motion is produced most readily. Poor conditioning is indicated not by the ellipsoids’ overall sizes, but by their elongation: a near-spherical ellipsoid denotes a mapping that treats all directions comparably, while an elongated one denotes a large ratio between the most and least accessible directions. The ellipsoids are evaluated at the configurations shown, whereas the metrics reported in Table 2 are evaluated at the mid-range reference configuration $q_{ref}$ . The orientation of the space frame is denoted with the x, y and z axes drawn in red, green and blue, respectively.

Panel of Figure 4 — Figure 4: Visualization of the configuration dependence of the effective control conditioning of the ACBH’s thumb (a) and index finger (b), using overlaid positions. At each position, the velocity ellipsoid of the effective control mapping $B(q)$ is drawn at the fingertip. The semi-axes of each ellipsoid are proportional to the singular values of the corresponding mapping, so a long axis denotes a direction in which task-space motion is produced most readily. Poor conditioning is indicated not by the ellipsoids’ overall sizes, but by their elongation: a near-spherical ellipsoid denotes a mapping that treats all directions comparably, while an elongated one denotes a large ratio between the most and least accessible directions. The ellipsoids are evaluated at the configurations shown, whereas the metrics reported in Table 2 are evaluated at the mid-range reference configuration $q_{ref}$ . The orientation of the space frame is denoted with the x, y and z axes drawn in red, green and blue, respectively.

Morphological aspect	SDH	ACBH	Affects
Joint axis geometry	Orthogonally aligned	Anatomically oblique	$\kappa(J)$
Actuator-to-DOF ratio ( $m/n$ )	$0.82$ (underactuated)	$1.50$ (overactuated)	$r$ , $A$ shape
Coupling architecture	Sparse, explicit	Branching tendon network	$\kappa(B)-\kappa(J)$
Authority distribution	Uniform across joints	Specialized	$\kappa(B)$ outliers

Table 1: Morphological aspects of comparison. Each row defines a structural design aspect along which robotic hands can vary. The rightmost column includes the metrics mainly associated with each aspect.

Hand	Finger	$n$	$m$	$r$	$\kappa(J)$	$\kappa(A)$	$\kappa(B)$
SDH	Index/Middle/Ring	4	3	1	3.84	1.41	4.25
SDH	Little (LF)	5	4	2	4.10	1.41	3.69
SDH	Thumb (TH)	5	5	2	9.45	1.00	9.45
ACBH	Index (F2)	5	7	2	9.55	6.39	6.57
ACBH	Middle (F3)	5	7	2	6.90	6.48	4.85
ACBH	Ring (F4)	5	7	2	6.28	6.52	4.41

Table 2: Per-finger metrics at

q_{\text{ref}}

r=n-k

with

k=3

Hand	Task	$n$	$m$	$r$	$\kappa(J)$	$\kappa(A)$	$\kappa(B)$
ACBH	Pinch (T1 + F2)	11	18	5	9.55	30.74	20.03
SDH	Pinch (TH + FF)	9	8	3	9.45	1.41	9.45
ACBH	Power grasp (5 fingers)	26	39	11	9.55	30.74	20.03
SDH	Power grasp (5 fingers)	22	18	7	9.70	1.41	10.01

Table 3: Task-level structural metrics.

r=n-k

with

k=6

(pinch) or

k=15

(power grasp).

Joint	$\\|R_{m,T1}[:,j]\\|$	Muscles acting
TCMC_Yaw	0.046	11/11
TCMC_Pitch	0.037	11/11
MCP_Roll	0.025	8/11
MCP_Yaw	0.017	8/11
MCP_Pitch	0.0022	7/11
IP_Pitch	0.011	2/11

Table 4: ACBH thumb joint-level actuator authority at

q_{\text{ref}}

, with joints ordered from proximal to distal.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Joint	$a_{i}$ [m]	$\alpha_{i}$ [rad]	$d_{i}$ [m]	$\theta_{i}$
J4 (MCP ab/ad)	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{1}$
J3 (MCP flex)	0.0450	0.0000	0.0000	$\theta_{2}$
J2 (PIP)	0.0250	0.0000	0.0000	$\theta_{3}$

Appendix

List of supptables 1 D-H parameters for the index (FF), middle (MF), and ring (RF) fingers of the SDH.

Joint	$a_{i}$ [m]	$\alpha_{i}$ [rad]	$d_{i}$ [m]	$\theta_{i}$
J5 (metacarpal)	0.0378	$\frac{\pi}{2}$	0.0540	$\theta_{1}$
J4 (MCP ab/ad)	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{2}$
J3 (MCP flex)	0.0450	0.0000	0.0000	$\theta_{3}$
J2 (PIP)	0.0250	0.0000	0.0000	$\theta_{4}$

Appendix

List of supptables 2 D-H parameters for the little finger (LF) of the SDH.

Joint	$a_{i}$ [m]	$\alpha_{i}$ [rad]	$d_{i}$ [m]	$\theta_{i}$
J5 (CMC rot)	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{1}$
J4 (CMC flex)	0.0380	0.0000	0.0000	$\theta_{2}$
J3 (MCP ab/ad)	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{3}$
J2 (MCP flex)	0.0320	0.0000	0.0000	$\theta_{4}$
J1 (IP)	0.0226	0.0000	0.0000	$\theta_{5}$

Appendix

List of supptables 3 D-H parameters for the thumb (TH) of the SDH.

Joint	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$v_{1}$ [m]	$v_{2}$ [m]	$v_{3}$ [m]
Index / Middle / Ring fingers
J4 (MCP ab/ad)	0.000	$-$ 1.000	0.000	0.0950	0.0000	$-$ 0.0330
J3 (MCP flex)	1.000	0.000	0.000	0.0000	0.0950	0.0000
J2 (PIP)	1.000	0.000	0.000	0.0000	0.1400	0.0000
J1 (DIP)	1.000	0.000	0.000	0.0000	0.1650	0.0000
Little finger

Appendix

List of supptables 4 SDH PoE screw axes

\hat{\xi}_{i}=[\omega_{i};\,p_{i}\times\omega_{i}]

in the palm-fixed space frame at zero configuration, derived from the official URDF.

Joint	$a_{i}$ [m]	$\alpha_{i}$ [rad]	$d_{i}$ [m]	$\theta_{i}$
MCP_Yaw	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{1}$
MCP_Roll	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{2}$
MCP_Pitch	0.0500	0.0174	0.0000	$\theta_{3}$
PIP_Pitch	0.0300	0.0000	0.0000	$\theta_{4}$

Appendix

List of supptables 5 D-H parameters for the index finger (F2) of the ACBH.

Joint	$a_{i}$ [m]	$\alpha_{i}$ [rad]	$d_{i}$ [m]	$\theta_{i}$
MCP_Yaw	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{1}$
MCP_Roll	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{2}$
MCP_Pitch	0.0520	0.0174	0.0000	$\theta_{3}$
PIP_Pitch	0.0310	0.0000	0.0000	$\theta_{4}$

Appendix

List of supptables 6 D-H parameters for the middle finger (F3) of the ACBH.

Joint	$a_{i}$ [m]	$\alpha_{i}$ [rad]	$d_{i}$ [m]	$\theta_{i}$
MCP_Yaw	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{1}$
MCP_Roll	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{2}$
MCP_Pitch	0.0510	0.0349	0.0000	$\theta_{3}$
PIP_Pitch	0.0290	0.0000	0.0000	$\theta_{4}$

Appendix

List of supptables 7 D-H parameters for the ring finger (F4) of the ACBH.

Joint	$a_{i}$ [m]	$\alpha_{i}$ [rad]	$d_{i}$ [m]	$\theta_{i}$
MCP_Yaw	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{1}$
MCP_Roll	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{2}$
MCP_Pitch	0.0460	0.0174	0.0000	$\theta_{3}$
PIP_Pitch	0.0260	0.0000	0.0000	$\theta_{4}$

Appendix

List of supptables 8 D-H parameters for the little finger (F5) of the ACBH.

Joint	$a_{i}$ [m]	$\alpha_{i}$ [rad]	$d_{i}$ [m]	$\theta_{i}$
TCMC_Yaw	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{1}$
TCMC_Pitch	0.0500	1.5202	0.0000	$\theta_{2}$
MCP_Yaw	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{3}$
MCP_Roll	0.0000	$\frac{\pi}{2}$	0.0000	$\theta_{4}$
MCP_Pitch	0.0400	0.0000	0.0000	$\theta_{5}$

Appendix

List of supptables 9 D-H parameters for the thumb (T1) of the ACBH.

Joint	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$v_{1}$ [m]	$v_{2}$ [m]	$v_{3}$ [m]
MCP_Yaw	0.035	0.914	0.405	$-$ 0.074	$-$ 0.007	0.022
MCP_Roll	$-$ 0.015	$-$ 0.405	0.914	0.030	$-$ 0.023	$-$ 0.010
MCP_Pitch	0.999	$-$ 0.038	$-$ 0.001	0.003	0.080	0.002
PIP_Pitch	0.999	$-$ 0.054	$-$ 0.008	0.007	0.125	0.022
DIP_Pitch	0.999	$-$ 0.054	$-$ 0.008	0.008	0.145	0.044

Appendix

List of supptables 10 ACBH PoE screw axes for the index finger (F2).

Joint	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$v_{1}$ [m]	$v_{2}$ [m]	$v_{3}$ [m]
MCP_Yaw	0.000	0.866	0.500	$-$ 0.071	0.000	0.000
MCP_Roll	0.000	$-$ 0.500	0.866	0.041	0.000	0.000
MCP_Pitch	1.000	0.000	0.000	0.000	0.082	0.000
PIP_Pitch	1.000	0.015	0.009	$-$ 0.002	0.127	0.026
DIP_Pitch	1.000	0.015	0.009	$-$ 0.003	0.143	0.053

Appendix

List of supptables 11 ACBH PoE screw axes for the middle finger (F3).

Joint	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$v_{1}$ [m]	$v_{2}$ [m]	$v_{3}$ [m]
MCP_Yaw	$-$ 0.056	0.905	0.422	$-$ 0.069	0.005	$-$ 0.019
MCP_Roll	0.045	$-$ 0.419	0.907	0.032	0.023	0.009
MCP_Pitch	0.997	0.070	$-$ 0.018	$-$ 0.005	0.075	$-$ 0.001
PIP_Pitch	0.995	0.101	$-$ 0.003	$-$ 0.012	0.121	0.020
DIP_Pitch	0.995	0.101	$-$ 0.003	$-$ 0.014	0.137	0.044

Appendix

List of supptables 12 ACBH PoE screw axes for the ring finger (F4).

Joint	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$v_{1}$ [m]	$v_{2}$ [m]	$v_{3}$ [m]
MCP_Yaw	$-$ 0.144	0.882	0.448	$-$ 0.061	0.010	$-$ 0.039
MCP_Roll	0.033	$-$ 0.448	0.893	0.027	0.041	0.020
MCP_Pitch	0.989	0.144	0.036	$-$ 0.010	0.068	$-$ 0.003
PIP_Pitch	0.986	0.159	0.044	$-$ 0.018	0.108	0.017
DIP_Pitch	0.986	0.159	0.044	$-$ 0.021	0.121	0.040

Appendix

List of supptables 13 ACBH PoE screw axes for the little finger (F5).

Joint	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$v_{1}$ [m]	$v_{2}$ [m]	$v_{3}$ [m]
TCMC_Yaw	0.850	0.396	$-$ 0.346	0.004	0.007	0.019
TCMC_Pitch	0.142	$-$ 0.807	$-$ 0.574	0.000	0.018	$-$ 0.025
MCP_Yaw	0.991	0.132	$-$ 0.029	$-$ 0.003	0.034	0.036
MCP_Roll	0.098	$-$ 0.554	0.827	$-$ 0.006	$-$ 0.044	$-$ 0.029
MCP_Pitch	0.094	$-$ 0.822	$-$ 0.562	0.043	0.035	$-$ 0.044
IP_Pitch	0.094	$-$ 0.822	$-$ 0.562	0.082	0.041	$-$ 0.046

Appendix

List of supptables 14 ACBH PoE screw axes for the thumb (T1).

List of suppfigures 1 Success rates of the SDH and ACBH over time in the Reach task environment, trained with PPO. The smoothed values are computed using an exponential moving average with weight $\alpha=0.6$ .

List of suppfigures 2 Success rates of the SDH and ACBH over time in the BlockRotateZ task environment, trained with DDPG+HER. The smoothed values are computed using an exponential moving average with weight $\alpha=0.6$ .

List of suppfigures 3 Success rates of the SDH and ACBH over time in the BlockRotateXYZ task environment, trained with DDPG+HER. The smoothed values are computed using an exponential moving average with weight $\alpha=0.6$ .

List of suppfigures 4 Success rates of the SDH and ACBH over time in the BlockRotateXYZ task environment (with rotation_threshold set to 0.4 radians), trained with TQC+HER. The smoothed values are computed using an exponential moving average with weight $\alpha=0.6$ .

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