Source-linked AI summary
Draft: A Parametric Tool for Robot Design Exploration
David Nguyen, Marcelo Coelho, Sangbae Kim
TL;DR
Slow CAD-to-simulation iteration and platform-specific, loosely grounded co-design generators limit robot design exploration. Draft compiles parameterized robot specifications into MJCF using hardware-survey trends; its robot twins and quadruped evaluations show mass agreement and design-performance tradeoffs.
Problem
Slow CAD-to-simulation handoffs limit morphology-and-control iteration, while co-design generators can be platform-specific and loosely grounded in hardware constraints.
Source: §I · p. 1Method
Draft compiles parameterized robot specifications into MJCF and uses hardware-survey fits to ground free design parameters.
Source: §I · p. 1, A. Robot Specification · p. 2, §IV · p. 3Results
1.10× geometric mean fold error across four commercial twins, all within ±25% of shipped mass; three quadrupeds differed in speed, step clearance, and push stability.
Source: E. Validation on Commercial Robots · p. 5, C. Results · p. 7, 2) Performance Limiters · p. 7Takeaways & Limitations
The authors conclude that surveyed free parameters make generated designs physically credible, not merely internally consistent.
Source: §VI · p. 8
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
Slow CAD-to-simulation iteration limits joint morphology and control exploration, while existing co-design generators can be platform-specific and loosely grounded in hardware. Draft compiles parameterized robot designs into MJCF and combines data-grounded generation with design evaluation.
I. INTRODUCTION
- Co-design methods jointly optimize design and control,,, but their generators are often platform-specific and use only loose hardware constraints,,.The cited constraints include motor-mass trends fitted to few motors and a single structural density.Source: §I · p. 1
- Draft compiles parameterized designs into simulation-ready MJCF, removing the CAD-to-simulation handoff and enabling rapid generation of variants.The generator can vary gear ratio, link length, and actuator choice in milliseconds.Source: §I · p. 1
- The contribution spans a generalized MJCF generator, trends fitted to 114 actuators and 49 robot descriptions, four commercial-robot twins, and measurable tradeoffs among three quadrupeds.The quadrupeds vary in scale, stance, leg length, and actuator choice under one learning environment.Source: §I · p. 1
A. Co-Design Pipelines
- Draft is a combined generator and evaluator, not a full co-design loop, leaving engineers to perform iteration around their complex design constraints.The authors exclude a design optimizer.Source: A. Co-Design Pipelines · p. 2
B. Actuator and Structural Scaling Laws
Draft uses fitted actuator and structural trends to ground robot parameters, then represents each robot through files that a shared generator compiles across morphologies. Its link primitives and MJCF output support parameterized design iteration.
B. Actuator and Structural Scaling Laws
- Prior scaling laws often omit integrated-module gearboxes or separate motor and transmission models, so Draft fits custom equations for integrated actuators,,,,,.The paper notes that combining separately fitted motor and gearbox models may not yield a viable module.Source: B. Actuator and Structural Scaling Laws · p. 2
- Draft fits structural equations by link type and separates each link’s mass into actuator and structural components, beyond whole-robot biped laws [24].The authors say whole-robot laws limit accuracy outside their fit distribution.Source: B. Actuator and Structural Scaling Laws · p. 2
- Four link primitives serve distinct roles: basic links build chains, sphere and foot links provide contact endings, and root links support custom limb placement.Root geometry is held in a lofted mesh.Source: Figure 2 · p. 2
A. Robot Specification
- A robot specification comprises a parameter file, an expression-based kinematic tree, and a root-body mesh; expressions can link dimensions such as limb radius to motor choice.Using expressions in the tree reduces the number of parameters that must be specified.Source: A. Robot Specification · p. 2
- The generator carries no body plan, so the same code compiles humanoids, quadrupeds, and other articulated morphologies; a 29-joint humanoid takes 202 ms and a 12-joint quadruped 50 ms.The reported compilation produces validated MJCF on a laptop CPU.Source: A. Robot Specification · p. 2
- Draft outputs MJCF rather than URDF because MJCF directly specifies actuator parameters such as armature and gear ratio and automates inertia calculations.Source: A. Robot Specification · p. 2
B. Link Primitives and Actuation
Draft assembles articulated robots from link primitives and derives their inertial and actuator properties from geometry and specified motor parameters. It also fits hardware trends and scores those fits using held-out predictions.
B. Link Primitives and Actuation
- Basic links carry distal motors to build serial limbs, sphere and foot links terminate chains with contact points or support surfaces, and lofted root meshes place limbs.Changes to symbolic parameters, such as shoulder width, propagate into the root mesh.Source: B. Link Primitives and Actuation · p. 2
- Primitive-link mass and inertia come from MuJoCo’s inertiafromgeom using geometry and density, while root-link inertia is supplied by trimesh.Link masses, motor classes, and root mesh density are fitted in Section IV.Source: B. Link Primitives and Actuation · p. 2
- Peak torque, no-load speed, and aspect ratio feed fitted actuator relations that derive mass, gear ratio, volume, radius, length, and rotor inertia.Volume is estimated from torque and gear ratio; aspect ratio determines the radius-length distribution.Source: Figure 3 · p. 3
- Each joint uses a DC-motor model with a linear torque-speed curve, specified by peak torque and no-load speed.The reported hand-tuned gains scale with peak torque.Source: B. Link Primitives and Actuation · p. 3
- The link library supports remotely placed actuators with fixed joint types but does not support parallel mechanisms.The quadruped’s hip-mounted knee motor uses two combined modules to create a complex link without added degrees of freedom.Source: B. Link Primitives and Actuation · p. 3
IV. FITTING MODEL PARAMETERS TO HARDWARE
- Because internal consistency alone cannot ensure a plausible design, Draft uses hardware-survey fits as guard rails and scores actuator fits with leave-one-out geometric mean fold error.Each entry is held out in turn, the fit is refit on the rest, and predictions are compared with published values; 1.10× corresponds to a typical 10% miss.Source: §IV · p. 3
A. Actuator Dataset
Draft fits integrated-actuator trends from a catalog of 114 modules, using measured hardware parameters to ground generated designs. Its mass fit indicates sublinear growth with output torque.
A. Actuator Dataset
- The catalog contains 114 integrated rotary actuators, spanning 2.5 to 1180 N·m and 0.19 to 9.3 kg across QDD, MidGear, and High GR classes.The entries cover 33 QDD, 33 MidGear, and 48 High GR modules.Source: A. Actuator Dataset · p. 3
- The actuator catalog excludes high-performance rotor–stator pairs that are not integrated into full actuators, so the fitted equations are a floor rather than a ceiling.The authors describe them as a defensible baseline for custom designs.Source: A. Actuator Dataset · p. 3
B. Actuator Trends
- Actuator parameters are derived from peak torque, no-load speed, and aspect ratio through five characterized relationships.The module trends account for gearbox, housing, and bearings as well as the rotor.Source: B. Actuator Trends · p. 3
1) Mass Relation:
- 0.666 is the fitted exponent relating actuator mass to torque, indicating mass grows slower than torque in this catalog.At fixed output torque, gear ratio barely influences mass, suggesting near-equal contributions from gear ratio and motor mass to torque.Source: 1) Mass Relation · p. 3
2) Gear Ratio Relation:
Draft derives actuator geometry and dynamics parameters from fitted relations, then tests their prediction accuracy on held-out catalog entries. Vendor-level holdout performance remains similar to ordinary held-out performance.
2) Gear Ratio Relation:
- Gear reduction is fitted against no-load speed, so specifying a speed determines the gearbox in the model.The fit is made over the geared actuator catalog.Source: 2) Gear Ratio Relation · p. 3
3) Volume Relation:
- Volume is fitted as torque^0.70 and gear ratio^-0.17, with both exponents left free because a full actuator includes more than the air-gap volume.The fitting choice follows the expectation V ∝ τN^-1 from the motor-torque relation.Source: 3) Volume Relation · p. 3
4) Aspect Ratio Relation:
- 1.12× and 1.14× are the holdout errors for radius and length computed from actuator volume and aspect ratio, versus 1.19× for both when geometry comes from the mass trend.The aspect ratio specifies the relation between actuator radius and length after volume is set.Source: 4) Aspect Ratio Relation · p. 4
5) Rotor Inertia Relation:
- Rotor inertia follows a radius^4 relation; the fitted exponent over 88 modules was 4.02, so the model fixes the exponent at 4 and fits the constant.The reflected rotor inertia is written as N^2J and added by MuJoCo to the joint-space inertia diagonal.Source: 5) Rotor Inertia Relation · p. 4
6) Actuator Fit Accuracy:
- 1.31× is the fold error when holding out entire vendors, similar to the ordinary held-out errors; inertia prediction is looser at 1.56×.Other held-out fold errors are 1.33× for reduction from no-load speed, 1.30× for volume from torque and reduction, and 1.28× for mass from torque.Source: 6) Actuator Fit Accuracy · p. 4
C. Structural Dataset
Draft fits structural mass trends from published humanoid, biped, and quadruped descriptions after estimating and removing actuator mass. Separate body-plan trends predict held-out robot masses better than a median-mass baseline.
C. Structural Dataset
- The structural dataset retains 29 humanoids and 20 quadrupeds from 118 parsed descriptions, covering 8.8–85.0 kg and 1037 segments.Models departing substantially from the tool’s tree structure and morphology are excluded.Source: C. Structural Dataset · p. 4
- Actuator mass is estimated from each joint’s torque and speed limits and subtracted from link mass before fitting; entries with negative adjusted mass are excluded.The assumed actuator-to-link attribution follows the humanoid model convention, while quadruped knee actuators are accounted for as often remotized to the hip.Source: C. Structural Dataset · p. 4
1) Structural Mass Trends:
- Structural mass is fitted separately for humanoids and quadrupeds as m = cL^e, with e floored at zero; torso mass uses volumetric density instead of length.The fitted torso densities are 716 kg/m^3 for humanoids and 654 kg/m^3 for quadrupeds.Source: 1) Structural Mass Trends · pp. 4–5
2) Structure Fit Accuracy:
- 1.22× and 1.18× are the held-out total-mass fold errors for humanoids and quadrupeds, compared with 1.42× and 1.77× for the median-mass baseline.Applying humanoid trends to quadrupeds yields 1.38× fold error, supporting separate fits by body plan.Source: 2) Structure Fit Accuracy · p. 5
- Link-relation errors are wider because actuator attribution assumptions, design and material diversity, and actuator-mass errors affect the structural fits.The authors report that this residual does not influence the high-level trends the tool is intended to identify.Source: 2) Structure Fit Accuracy · p. 5
D. Design Filter
The design filter flags generated models that fall outside surveyed actuator and structural ranges. Commercial-robot twins match shipped mass closely, while dynamics comparisons reveal the importance of joint-axis alignment.
D. Design Filter
- The filter warns for aspect ratios outside [0.28, 1.69], links over twice their class’s structural density, and high actuator mass fractions.Median actuator mass fractions are 54% for humanoids and 45% for quadrupeds; actuators beyond family or catalog extremes are refused.Source: D. Design Filter · p. 5
E. Validation on Commercial Robots
- All four commercial-robot twins fall within ±25% of shipped mass, with a 1.10× geometric mean fold error.The reported mass ratios are 111% (G1), 91% (H2), 101% (Go2), and 84% (B2).Source: E. Validation on Commercial Robots · p. 5
- Twin validation compares joint-space mass matrices and gravity vectors across 300 configurations, with rotor terms disabled because only G1 publishes per-joint armature.Go2 has the lowest reported errors, at 12.8% and 21%.Source: E. Validation on Commercial Robots · p. 5, Table III · p. 5
- Joint-axis mismatch contributes to higher humanoid dynamics errors: G1 has six misaligned joints up to 16°, and H2 has four up to 30°.Holding those joints fixed lowers medians by 6–19% and variance by 32–200%; remaining disagreement is attributed partly to compounding error from more degrees of freedom.Source: E. Validation on Commercial Robots · pp. 5–6
V. EVALUATING DESIGNS WITH REINFORCEMENT LEARNING
Draft evaluates three feasible quadruped designs under a shared two-stage reinforcement-learning curriculum. The setup scales rewards with robot size and trains a base locomotion policy before task-specific curricula.
A. Quadruped Designs
- Cheetah, Bear, and Giraffe vary in scale, stance, leg length, and motor choice, and all pass the design filter.Cheetah is light with 6:1 QDD units; Bear is heavy with 20:1 mid-gear units and over six times Cheetah’s joint torque; Giraffe has legs more than twice Cheetah’s length and 80:1 actuators.Source: A. Quadruped Designs · p. 6
B. Training Setup
- Each design is trained with PPO from ten independent seeds, using generated MJCF models and DC-motor torque–speed curves.The curriculum has two stages: base locomotion training followed by task-specific training.Source: B. Training Setup · p. 6, Figure 7 · p. 6
1) Base Policy Training:
- Rewards scale with quadruped size using Froude similarity, with scale s = L/0.48 m and speed and time scaled by √L.This addresses the different stride lengths of short- and long-legged robots.Source: B. Training Setup · p. 6, 1) Base Policy Training · p. 6, Table IV · p. 6
- Stage one trains a velocity-tracking policy on gently uneven terrain with intermittent pushes, rewarding posture, foot air time, and base height while penalizing undesirable motion and contact.The base policy spans commanded speed, terrain height, and pushes; each later task curriculum ramps one axis.Source: 1) Base Policy Training · p. 6, Figure 7 · p. 6
2) Task-Based Curricula:
The shared task curricula expose distinct capability profiles rather than a single dominant quadruped. In absolute units, Bear leads speed and push rejection, while Giraffe leads stair height and efficiency leadership changes with speed.
2) Task-Based Curricula:
- Each task curriculum ramps one variable—commanded velocity, terrain height, or push magnitude—while keeping the others at base-policy values across designs.This holds the training environment consistent so the robots, rather than differing curricula, are compared.Source: 2) Task-Based Curricula · p. 6
C. Results
- Capabilities are evaluated as maximum base velocity, stair-step height, maximum push, and drivetrain efficiency based on mechanical output power and theoretical copper loss.Figure 8 reports medians over ten seeds, with bands spanning the seed minimum to maximum.Source: C. Results · pp. 6–7, Figure 8 · p. 7
- Bear is fastest and rejects the largest kick, while Giraffe clears the tallest step; Giraffe leads efficiency at low speeds, but Bear surpasses it around 2 m/s.Cheetah trails Bear only slightly in top speed and push stability despite its smaller frame, but has substantially worse efficiency than the other designs.Source: C. Results · p. 7
1) Normalizing by Scale:
Normalizing capability by leg length shifts several comparisons toward Cheetah. Performance limiters differ by task: learned speed is robot-limited, while push stability and terrain behavior show different actuator and policy constraints.
1) Normalizing by Scale:
- After scaling by leg length, Cheetah leads terrain performance at 26% of its leg length, while Bear and Giraffe climb 15–17%.Cheetah also leads normalized push stability, and its adjusted speed barely exceeds Bear’s; Giraffe’s relative performance drops.Source: 1) Normalizing by Scale · p. 7, Table VI · p. 7
2) Performance Limiters:
- The velocity task is robot-limited for all three designs, although the limiting actuator differs across robots.Cheetah’s knee is torque-limited but not speed-limited; Giraffe’s hip-pitch motor is limited by both, while Bear operates near the torque–speed curve boundary.Source: 2) Performance Limiters · p. 7, Table VI · p. 7
- Push stability is actuator-limited for Giraffe and Bear, but not for Cheetah.The text suggests Cheetah’s smaller scale could make its dynamics too fast for a 50 Hz policy to recover from pushes.Source: 2) Performance Limiters · p. 7
- The terrain curriculum produces the lowest actuator utilization because termination rewards standing over attempting and failing to climb.The reported terrain limits therefore reflect the policy’s learned refusal to climb, not simply actuator saturation.Source: 2) Performance Limiters · p. 7
3) Seed Variance:
The reported capability trends survive both reseeding and adjusted link masses that reproduce vendor-to-twin residuals. The conclusion identifies broader co-design, subsystem, and design-space extensions for Draft.
3) Seed Variance:
- Reseeding shifts top speed and kick by up to about a quarter of their median and efficiency by a few percent, while trends persist.Each Tab. V number is a median over ten seeds, each a median over 256 robot rollouts.Source: 3) Seed Variance · p. 7
4) Sensitivity to Inertia Error:
- No capability trend changes when link masses are adjusted to reproduce Go2 and B2 vendor-to-twin residuals, without retraining policies.The test assesses generation and evaluation pipeline validity, not the training environment.Source: 4) Sensitivity to Inertia Error · pp. 7–8
VI. CONCLUSION AND FUTURE WORK
- Future directions include a co-design loop, additional subsystems such as dexterous hands, and denser legged-design sweeps extended to humanoids.The denser sweep would extend tradeoffs from three quadrupeds into a surface identifying optima; additional subsystems would need a more extensive actuator catalog.Source: §VI · p. 8