Task-Oriented Co-Design and Optimization of Geared Actuators for Robotic Applications

Xuanyu Huang; Jianqiang Dong; Hang Zhao

cs.ROSep 19, 2026

Task-Oriented Co-Design and Optimization of Geared Actuators for Robotic Applications

Authors: Xuanyu Huang, Jianqiang Dong, Hang Zhao

Organizations: The authors are with the Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China

Abstract

Different tasks performed by legged robots impose distinct torque and speed requirements on actuators. Existing robotic actuators are generally optimized at the component level for metrics such as torque or power density, without explicit task guidance. System-level optimization across components such as motors, gearboxes, and sensors is challenging because of the high computational cost and coupling among mechanical, electrical, and electromagnetic behaviors. Consequently, improvements in individual components may not translate into better robot performance in a specific task. To this end, we present a systematic optimization framework for task-oriented co-design of actuator hardware and control. First, surrogate models are employed to accelerate motor evaluation and support global exploration of the coupled design space. Then, a hierarchical mixed-variable optimization strategy is adopted, combining discrete enumeration with continuous search over dimensions and real-valued indices. These indices are rounded to select admissible values for the remaining discrete choices before each evaluation. Within this search, rated output torque density and task performance are jointly optimized, with Bezier-parameterized joint torque profiles determined for each hardware candidate. Finally, the effectiveness of the proposed framework is validated through actuator fabrication and experiments on a two-degree-of-freedom jumping leg. Based on its measured mass, the fabricated prototype achieves a nominal rated output torque density of 35.7 N m/kg, approximately 60% higher than that of a widely used commercial geared joint actuator, while being 18.6% lighter. Under matched bench conditions, it achieves 12.0% greater jump height at twice-rated torque. Together, these results demonstrate a systematic route from task requirements to actuator design and control.

Figures & tables

Fig. 1: Overview of the task-oriented motor–gearbox and control co-design framework and its experimental validation.

Panel of Figure 2 — Fig. 2: Representative MuJoCo frames for Unitree G1 fast walking, stair ascent, and jumping.

Fig. 4: Reduced-order jumping-task representation: (a) the two-DOF vertical-guide leg and (b) representative fifth-order Bézier profiles with six control coefficients for each joint.

Fig. 5: Hierarchical mixed-variable optimization for task-oriented motor–gearbox co-design and constrained Pareto selection.

Group	Symbols	Range or options	Feasibility constraints
Motor: slot–pole	$(S,P)$	$18\mathrm{S}/\{16,20,22\}\mathrm{P}$ ; $24\mathrm{S}/\{22,26,28\}\mathrm{P}$ ; $27\mathrm{S}/30\mathrm{P}$	winding factor: $k_{w,1}>0.9$
Motor: radial	$D_{\mathrm{so}},D_{\mathrm{b}}$ ; $w_{t},h_{s}$	$D_{\mathrm{so}}:60$ – $96\,\mathrm{mm}$ ; $D_{\mathrm{b}}:36.1$ – $75\,\mathrm{mm}$ ; $w_{t}:2$ – $5\,\mathrm{mm}$ ; $h_{s}:1$ – $19.15\,\mathrm{mm}$	valid stator and slot geometry
Motor: slot/magnet	$h_{\mathrm{tt}},w_{\mathrm{so}}$ ; $t_{\mathrm{mag}},\alpha_{\mathrm{mag}}$	$h_{\mathrm{tt}},w_{\mathrm{so}}:0.5$ – $2\,\mathrm{mm}$ ; $t_{\mathrm{mag}}:1$ – $3\,\mathrm{mm}$ ; $\alpha_{\mathrm{mag}}:120$ – $180^{\circ}$ elec.	positive clearances; manufacturable geometry
Motor: axial/winding	$l_{m},d_{w},b$	$l_{m}:1$ – $30\,\mathrm{mm}$ ; standard wire index; symmetry divisors	realizable winding; current/voltage limits
Reducer: selection	$\mathcal{T},i_{t}$	$\mathcal{T}\in\{\mathrm{NGW,NW,3K}\}$ ; $i_{t}:1$ – $50$ in $0.5$ steps	assembly and ratio feasibility
Reducer: geometry	$\mathbf{z},r_{a}$ ; $\mathbf{m},\mathbf{x}_{p}$	topology-dependent integers; bounded continuous values	geometry and tooth-root strength constraints

TABLE I: Motor–Gearbox Design Variables and Constraints

Fig. 6: Coupled motor–gearbox design space: (a) motor geometric design variables and (b) planetary gearbox topologies considered, including NGW, NW, and 3K configurations.

Fig. 7: Validation of the 18S/20P motor surrogate using 200 independent cases: parity plots for

K_{t}

K_{e}

, and efficiency, and

R^{2}

values for eight predicted outputs.

Fig. 8: Pareto-front analysis across slot–pole combinations after per-candidate dual-joint Bézier-policy optimization. Colored markers denote feasible nondominated candidates. The star and cross show the fabricated actuator and DM8009 reference, respectively.

Metric	DM8009	Optimized
Estimated mass [kg]	0.896	0.689
Gear ratio	9.00	32.63
Rated output torque [N m]	20.0	25.8
Rated torque density [N m/kg]	22.3	37.4
Peak torque [N m]	40.0	51.5
Maximum speed [rpm]	320	250

TABLE II: Model Comparison with the DM8009

Fig. 9: Mechanical design and fabricated prototype of the optimized actuator: (a) CAD sectional view and (b) fully assembled prototype.

Fig. 10: Fabricated key components of the optimized actuator: (a) wound stator, (b) rotor, and (c) planetary gearbox.

Fig. 11: Single-motor bench characterization hardware: (a) fabricated motor test module and (b) assembled setup with the load device and torque sensor.

Parameter	Model	Measured
$K_{t}$ [N m/ $A_{\mathrm{line,pk}}$ ]	0.04780	0.04453
$K_{e}$ [ $V_{\mathrm{ll,pk}}$ /(rad/s)]	0.05618	0.06391
$\omega_{0}$ [rad/s]	898.7	790

TABLE III: Motor Model and Bench Measurements

Fig. 12: Representative jumping sequences at twice-rated output torque under the common $5.5\,\mathrm{kg}$ bench load and $48\,\mathrm{V}$ DC bus: (a) DM8009 at $40\,\mathrm{N\,m}$ and (b) optimized actuator at $52\,\mathrm{N\,m}$ .

Fig. 13: Twice-rated (

52\,\mathrm{N\,m}

) push-phase comparison between measured optimized-actuator feedback and the design-stage vertical-guide model prediction. Colors distinguish the knee and hip joints; solid and dashed lines denote experiment and model, respectively.

Command level	DM8009	Optimized
$0.75\times$ rated	No jump	0.490 m
$1.00\times$ rated	0.490 m	0.580 m
$1.50\times$ rated	0.615 m	0.745 m
$2.00\times$ rated	0.750 m	0.840 m

TABLE IV: Normalized Torque-Sweep Experimental Results

Fig. 14: Measured hip and knee responses at twice-rated output-torque commands:

40\,\mathrm{N\,m}

for the DM8009 and

52\,\mathrm{N\,m}

for the optimized actuator. Solid and dashed curves denote knee and hip quantities, respectively.

Case	Slider rise [m]	Cum. loss [%]
Design-stage model	1.008	0.0
Measured motor parameters	0.898	10.9
$+$ measured actuator mass	0.893	11.3
Experiment	0.840	16.6

TABLE V: Twice-Rated Prediction–Experiment Error Decomposition

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ρ(q)

enters the design explicitly. For a counterweight moment

p=m_c r_c

with gravity torque

-gpφ(q)

, the weighted mean-square residual gravity torque has the closed-form minimizer

p^*=E_ρ[τ_gφ]/(gE_ρ[φ^2])

. If payload gravity torque is affine in payload mass, the optimum is also affine:

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. For fixed static moment, added counterweight inertia is

I_c=pr_c

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m_c=p/r_c

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r_c=0.20

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College of Engineering and Information Technology, University of Dubai Dubai, United Arab Emirates

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Abstract

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