Draft: A Parametric Tool for Robot Design Exploration

David Nguyen; Marcelo Coelho; Sangbae Kim

cs.ROSep 29, 2026

Draft: A Parametric Tool for Robot Design Exploration

Authors: David Nguyen, Marcelo Coelho, Sangbae Kim

Organizations: Department of Mechanical Engineering, Massachusetts Institute of Technology · Department of Architecture, Massachusetts Institute of Technology

Abstract

Robot performance is often limited by the cost of iterating on morphology and control together, since every computer-aided design (CAD) change has to be carried into a simulation-ready model before control work begins. Co-design methods attempt to close this gap, but each uses a model generator written for a single platform or lack the use of real-world data to suggest that designs are plausible. We present Draft, a parametric generation tool whose generalized engine compiles any parametric tree of serial chains into a simulation-ready MJCF model, without CAD. It allows engineers to explore design tradeoffs through easily adjustable models and evaluate how changes influence controller performance. Draft grounds the free parameters of each design using trends fitted to a survey of $114$ actuators and $49$ published robot descriptions, so that a generated robot is anchored to real-world hardware. We validate those trends wholistically by building twins of four off-the-shelf robots, whose masses agree to $1.10\times$ geometric mean fold error. Finally, we demonstrate how Draft exposes design tradeoffs by evaluating three quadrupeds through a two-stage reinforcement learning curriculum.

Figures & tables

Fig. 1: Draft compiles medium-fidelity robot models from a small set of specifications into a simulation-ready MJCF model. One parameter edit propagates through visual, collision, inertial, and actuation properties.

Fig. 2: All generated Draft models are constructed from four main link primitives. The basic link includes a link and motor at its distal end, the sphere link terminates articulated chains with a contact point, the foot link does the same but with a support surface, and the root link holds custom geometry for limbs to extend from.

Fig. 3: An actuator’s parameters are derived from data-informed relations. The inputs are peak torque

\tau

, no-load speed

\omega_{\text{NL}}

, and aspect ratio

a

. Mass

m

is estimated from

\tau

, and gear ratio

N

from

\omega_{\text{NL}}

. Volume

V

is estimated from

\tau

and

N

; together with

a

, it determines radius

r

and length

\ell

. Finally, the rotor inertia

J

is derived from

r

Fig. 4: The four relations that dictate gear ratio, mass, volume, and rotor inertia plotted against the raw data. Panel (a) shows the power-law fit for gear ratio against no-load actuator speed, while (b) shows the fit for actuator mass against peak output torque. Panels (c) and (d) show prediction performance for volume and rotor inertia, respectively. Points are grouped by actuator class (QDD, MidGear, and High GR) and show agreement with the fitted predictions (black lines). The blue bands are

\pm 25\%

in (c) and (d).

Parameter	Fitted value	$n$	$R^{2}$	LOO
Reduction $N$	$327\,\omega_{\text{NL}}^{-1.066}$	$103$	$0.89$	$1.33\times$
Mass $m$	$0.0653\,\tau^{0.666}$	$103$	$0.90$	$1.28\times$
Volume $V$	$\tau^{0.700}N^{-0.167}/23948$	$103$	$0.87$	$1.30\times$
Radius $r$	$(V/2\pi a)^{1/3}$	$103$	—	$1.12\times$
Length $\ell$	$2ar$	$103$	—	$1.14\times$
Inertia $J$	$27.2\,r^{4}$	$88$	$0.84$	$1.56\times$

TABLE I: Fitted trends in pipeline order, with LOO fold error.

Fig. 5: The generation pipeline run end to end against four off-the-shelf robots. The twin takes the vendor’s geometry and declared torque and speed, and derives all other parameters. On the left are renders of the vendor and twin models with the twin’s mass ratio as a percentage above. On the right is the dynamics over $300$ configurations per pair with inertia above and gravity below. The second spread for humanoids only holds the misaligned axes still.

Class	$n$	$c$	$e$	Fold	$n$	$c$	$e$	Fold
	Humanoid				Quadruped
Thigh	$54$	$13.8$	$1.36$	$1.38$	$60$	$28.3$	$2.69$	$1.43$
Shank	$50$	$4.11$	$1.68$	$2.09$	$60$	$9.25$	$2.38$	$1.21$
Hip link	$56$	$2.58$	$1.05$	$3.18$	$72$	$0.60$	$0.51$	$2.88$
Head	$16$	$2.50$	$0.63$	$1.74$	—	—	—	—
Upper arm	$30$	$9.40$	$1.83$	$1.88$	—	—	—	—

TABLE II: Structural mass by segment class, fit as

m=cL^{e}

with

L

in meters, and its in-sample fold error.

	Inertia				Gravity
	Swept		Axes Held		Swept		Axes Held
Robot	Med.	Var.	Med.	Var.	Med.	Var.	Med.	Var.
	(%)	(% 2 )	(%)	(% 2 )	(%)	(% 2 )	(%)	(% 2 )
G1	$33.9$	$106$	$28.3$	$72.9$	$25.1$	$173$	$19.5$	$73.6$
H2	$32.6$	$103$	$21.9$	$47.0$	$34.1$	$249$	$14.5$	$48.2$
Go2	$12.8$	$2.4$	—	—	$21.4$	$8.4$	—	—

TABLE III: Twin error in

M(q)

and

g(q)

over

300

poses, median and variance, with misaligned axes held.

Fig. 6: Three quadrupeds from one specification, differing in scale, leg length, and actuators, rendered in one scene at true relative size.

Fig. 7: The same curriculum is used for each of the three robots. A base policy is trained over a small ranges of commanded speeds

v_{\text{cmd}}

, terrain heights

z_{t}

, and pushes

\Delta v

. Next, three task policies train the base policy further, each ramping one of axis. Every policy is trained from ten seeds.

Fig. 8: Four capability axes for the designs of Fig. 6 , in absolute units. Lines are medians over ten training seeds and bands span the seed minimum to maximum; dashed lines are the same policies on the builds carrying the inertia error of Sec. IV-E . (a) Commanded against achieved speed, hollow past each design’s peak. (b) Traversal, ascent and descent pooled. (c) Recovery from a velocity kick. (d) Drivetrain efficiency up to each design’s peak.

Term	Weight	Shaping
Velocity tracking	$1.0$	$\sigma=0.5\sqrt{s}$ m/s
Yaw-rate tracking	$1.0$	$\sigma=0.5/\sqrt{s}$ rad/s
Upright	$1.0$	$\sigma=0.45/\sqrt{s}$
Air time	$0.4$	$t_{\mathrm{max}}=0.35\sqrt{s}$ s
Base height	$0.4$	$h^{*}=0.43s$ , $\sigma=0.11s$ m
Foot clearance	$-2.0\,s^{-3/2}$	$h_{f}^{*}=0.10s$ m

TABLE IV: Stage-one reward terms;

s

enters only where shown.

Design	kg	$L$ (m)	m/s	$\hat{v}$	m	$L$ ’s	m/s	$\hat{v}$	$\eta$
			Speed		Step		Kick
Cheetah	$33$	$0.48$	$3.63$	$\mathbf{1.67}$	$0.12$	$\mathbf{0.26}$	$7.9$	$\mathbf{3.65}$	$0.20$
Bear	$110$	$0.74$	$\mathbf{4.33}$	$1.61$	$0.12$	$0.17$	$\mathbf{8.6}$	$3.20$	$\mathbf{0.47}$
Giraffe	$91$	$1.30$	$2.17$	$0.61$	$\mathbf{0.20}$	$0.15$	$5.3$	$1.48$	$0.41$

TABLE V: Capability, absolute then per leg length

L

;

\hat{v}=v/\sqrt{gL}

. Medians over ten seeds; bold is best.

Design		$\tau$ %	$\omega$ %	$\tau{+}\omega$		$\tau$ %	$\omega$ %	$\tau{+}\omega$		$\tau$ %	$\omega$ %	$\tau{+}\omega$
	Sprint				Kick				Terrain
Cheetah	K	$\mathbf{95}$	$\mathbf{25}$	$\mathbf{1.05}$	H	$69$	$17$	$0.60$	K	$43$	$13$	$0.44$
Bear	K	$\mathbf{77}$	$\mathbf{85}$	$\mathbf{1.04}$	H	$\mathbf{66}$	$\mathbf{59}$	$\mathbf{0.93}$	K	$43$	$50$	$0.55$
Giraffe	H	$\mathbf{96}$	$\mathbf{105}$	$\mathbf{1.08}$	H	$\mathbf{94}$	$\mathbf{99}$	$\mathbf{1.06}$	H	$76$	$71$	$1.00$

TABLE VI: Utilization at the limiting joint, knee (K) or hip pitch (H); bold is actuator limited.

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