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Stanford Doggo: An Open-Source, Quasi-Direct-Drive Quadruped

Nathan Kau, Aaron Schultz, Natalie Ferrante, Patrick Slade

arXiv:1905.04254v1cs.RO

TL;DR

Many legged-robot platforms are expensive and take years to develop, and some designs cannot sustain continuous agility. Stanford Doggo uses a quasi-direct-drive quadruped design; it matches the galago’s vertical jumping agility and improves 22% over the previous best robot. Its open-source design is intended to lower access barriers.

  • Problem

    Many legged-robot platforms take years to develop and are expensive, while some energy-storing designs cannot sustain continuous agility.

    Source: §I · p. 1

  • Method

    The paper presents Stanford Doggo, a quasi-direct-drive quadruped with a belt-drive design informed by transmission scaling principles.

    Source: §I · p. 1, B. Transmission Principles · p. 3

  • Results

    22% improvement over the previous best robot in vertical jumping agility; Stanford Doggo matches the galago and meets or exceeds common state-of-the-art legged-robot metrics.

    Source: §I · p. 1

  • Takeaways & Limitations

    The open-source design costs less than $3000 and requires only hand tools for assembly, supporting the stated aim of lowering access barriers to legged-robot research and education.

    Source: §V · p. 6

    Open-loop foot-position tracking limited steady velocity; the authors expect higher peak velocity may be possible with closed-loop control.

    Source: §IV · p. 5

Abstract

from arXiv · show

This paper presents Stanford Doggo, a quasi-direct-drive quadruped capable of dynamic locomotion. This robot matches or exceeds common performance metrics of state-of-the-art legged robots. In terms of vertical jumping agility, a measure of average vertical speed, Stanford Doggo matches the best performing animal and surpasses the previous best robot by 22%. An overall design architecture is presented with focus on our quasi-direct-drive design methodology. The hardware and software to replicate this robot is open-source, requires only hand tools for manufacturing and assembly, and costs less than $3000.

I. INTRODUCTION

Stanford Doggo is a quasi-direct-drive quadruped designed to combine dynamic locomotion with strong vertical jumping agility. It matches the galago’s agility and improves 22% over the previous best robot, while the paper emphasizes open, lower-cost replication.

I. INTRODUCTION

  • Many legged-robot platforms take years to develop and are expensive, while some energy-storing designs cannot sustain the continuous agility needed for many tasks.The paper considers robots that carry their own power supply and can repeatedly jump or locomote.Source: §I · p. 1
  • Vertical jumping agility measures how quickly an animal changes energetic state, approximating vertical climbing speed through repeated jumps; greater jump distance can help robots overcome obstacles.The paper links this metric to improved path-planning capabilities.Source: §I · p. 1
  • A quasi-direct-drive transmission uses a single reduction stage below 10:1, trading some control bandwidth for higher torque while retaining backdrivability for motor-current force sensing.Direct-drive systems omit speed reduction and support tunable compliance at kHz timescales.Source: §I · p. 1
  • 22% improvement over the previous best robot in vertical jumping agility; Stanford Doggo also matches the galago, the animal with the best reported agility.The paper also reports that it matches or exceeds common performance metrics of state-of-the-art legged robots.Source: §I · p. 1

A. Design

Stanford Doggo’s design combines a compact coaxial belt-drive leg, accessible open-source hardware, and open-loop sinusoidal gait control. The controller turns virtual-leg commands into motor torques using PD control.

A. Design

  • The open-source replication package includes CAD, a bill of materials, assembly instructions, wiring schematics, and software; estimated build cost is $3000, including outsourced machining beyond hand-tool work.Components and quoted machining services are available online.Source: A. Design · p. 2
  • Coaxial drive assemblies let the legs rotate continuously in either direction and outside the body, avoiding Minitaur’s workspace restriction; each assembly uses two nested 3:1 belt drives.The nested shafts save space and weight.Source: A. Design · p. 2
  • The belt drive was chosen over gears to reduce weight, cost, and reflected inertia; distributed tooth loads permit lightweight plastic pulleys that are easily 3D-printed.Lower pulley inertia improves transparency, while printing lowers manufacturing cost.Source: A. Design · p. 2
  • A Teensy 3.5 computes leg trajectories and sends position commands at 100Hz; ODrive controllers apply 10kHz field-oriented commutation to the motors, with a relay-based emergency stop.The electrical system also includes four leg subsystems, a power distribution board, and wireless groundstation communication.Source: A. Design · p. 2
  • Piecewise sinusoidal open-loop trajectories produce walking, trotting, bounding, and pronking by shaping flight and stance phases.Trajectory parameters become desired leg angle and link separation; PD control adds virtual stiffness and damping before generalized torques are converted to motor torques through the leg Jacobian.Source: A. Design · pp. 2–3

B. Transmission Principles

The transmission principles compare quasi-direct-drive gearing with a larger direct-drive motor using actuator scaling laws. They set a mass threshold for the transmission and identify performance trade-offs that depend on the application.

B. Transmission Principles

  • For an N:1 reduction, QDD output torque scales with N; matching it with a direct-drive motor requires an N-fold radius increase, with motor mass scaling as r and torque as r^2.Reflected inertia scales as r^3, and the larger-motor comparison implies an N-fold motor-mass increase.Source: B. Transmission Principles · p. 3
  • A QDD transmission should weigh less than (N−1)m, where m is motor mass, to save mass against a larger direct-drive motor producing the same torque.The threshold follows from comparing transmission mass with the added mass of the larger motor.Source: B. Transmission Principles · p. 3
  • Meeting the mass threshold may reduce control bandwidth, efficiency, and reliability; transparency also worsens as reduction N increases because of transmission dynamics.The passage notes reflected inertia is invariant between QDD and direct drive, while transmission dynamics still affect transparency.Source: B. Transmission Principles · p. 3

C. Performance Metrics

The section defines the robot-performance measures and describes how actuator, force-transparency, and bandwidth characteristics are measured. It also specifies the robot properties compared across designs.

C. Performance Metrics

  • Maximum continuous torque is measured as motor current rises until a 125°C steady-state temperature; peak torque uses peak force over one second.Reflected inertia is estimated from the motor rotor’s CAD model and scaled by the square of the speed reduction ratio; torque density is peak motor torque divided by motor mass.Source: C. Performance Metrics · pp. 3–4
  • Leg transparency is assessed by comparing estimated foot force, derived from motor torques through the leg Jacobian, with load-cell force under steady-state conditions.Motor torques are estimated from motor currents and the torque constant; virtual compliance varies vertical foot force while keeping the load cell in tension.Source: C. Performance Metrics · p. 4
  • Control bandwidth is approximated from the crossover frequency while tracking 4–12 Nm sinusoidal torque trajectories across 5–400 Hz.The torque range was selected to emulate walking, and steady-state response amplitude and phase were recorded.Source: C. Performance Metrics · p. 4
  • Robot comparisons include leg count, total degrees of freedom, leg length, mass, motor share of total mass, and speed reduction ratio.Source: C. Performance Metrics · p. 4
  • Steady velocity is the maximum forward-running speed, measured over 0.7 meters; cost of transport uses mean voltage and current during steady running with robot mass.Cost of transport is included to inform the efficiency of fast forward locomotion.Source: C. Performance Metrics · p. 4
  • Vertical jumping agility is peak jump height divided by stance time plus time to apogee; jump height runs from the crouched center of gravity to the apex.Stance runs from actuation onset until the feet leave the ground; time to apogee runs from liftoff until vertical velocity reaches zero.Source: C. Performance Metrics · p. 4

III. RESULTS

Stanford Doggo reports the highest vertical jumping agility among the compared robots, matching the galago, and a jump more than twice that of other quadrupeds. Results also compare its actuator and physical properties with other robots.

III. RESULTS

  • Compared with Minitaur, Stanford Doggo’s actuator has 37% higher peak force and 76% higher continuous torque, with an 8% increase in total mass.The passage also reports a three times increase in inertia and lower total actuator cost than Minitaur.Source: §III · p. 4
  • Force-trajectory mean absolute percent errors were 2.8% for step functions and 5.3% for 2 rad/s sine waves; walking-like torque control bandwidth was estimated at 150 Hz.Source: §III · p. 4, Figure 6 · p. 5
  • Stanford Doggo’s motor mass share is 35%, comparable to Minitaur and Jerboa, and 46% higher than MIT Cheetah 2’s.The passage says a larger proportion of Doggo’s mass is committed to torque production rather than structure or electronics.Source: §III · p. 5, Table II · p. 5
  • Stanford Doggo reported the highest vertical jumping agility among robots, matching the galago, and its jump was more than twice that of other quadrupeds.The Salto-1P jump was only 0.11 m higher, despite Salto-1P being a specialized monopod.Source: §III · p. 5, Table III · p. 5
  • MIT Cheetah 3 produces significantly larger force per weight than MIT Cheetah 2, but few performance details have been published.Source: §III · p. 5

IV. DISCUSSION

Stanford Doggo combines leading vertical jumping agility with a lightweight, high-torque actuator design, while open-loop control constrains steady velocity and contributes to higher cost of transport.

IV. DISCUSSION

  • 150 Hz estimated control bandwidth exceeds MIT Cheetah 2’s reported 104 Hz motor-to-foot-force bandwidth; QDD yields 3× output torque and 770 g mass reduction, or 16% of robot mass.Compared with Minitaur, Doggo’s actuator has 2.7 times its reflected inertia but 1.8 times its continuous torque at similar mass.Source: §IV · p. 5
  • Steady velocity was limited by unstable open-loop foot-position tracking, and the robot used a trotting gait for stability at high speeds.The authors expect significantly higher peak velocity to be possible with closed-loop control because motor performance was not limiting [29].Source: §IV · p. 5
  • Cost of transport is higher than Minitaur’s, which the authors attribute to inefficient open-loop control trajectories.The authors expect better control to improve it [29].Source: §IV · p. 5
  • More than doubling quadruped robots’ jump height, Stanford Doggo’s maximum vertical jump height can be accurately evaluated using open-loop control.The paper attributes this jump-height gain to increased torque and the lightweight belt drive.Source: §IV · pp. 5–6
  • Stanford Doggo’s vertical jumping agility outperforms all legged robots, highlighting increased peak torque compared with the Minitaur actuator.The paper identifies shorter legs, a lightweight belt transmission, and a parallel linkage as factors in its advantage over MIT Cheetah 2.Source: §IV · p. 6
  • Shorter legs increase end-linkage force; the lightweight belt drive reduces mass versus MIT Cheetah 2, while parallel-link joint torques sum to raise foot force over a similarly sized serial linkage.The paper notes that MIT Cheetah 2 reported higher torque density, but not higher vertical jumping agility.Source: §IV · p. 6

V. CONCLUSION

Stanford Doggo combines quadruped dexterity and inherent stability with exceptional vertical jumping agility, while meeting or exceeding state-of-the-art performance on common metrics. Its low-cost, open-source design is intended to make legged-robot research and education more accessible.

V. CONCLUSION

  • Stanford Doggo combines quadruped dexterity and inherent stability with vertical jumping agility greater than specialized monopods and matching the galago, the highest-performing animal.Source: §V · p. 6
  • The robot meets or exceeds state-of-the-art legged robotic systems on a number of common performance metrics.Source: §V · p. 6
  • The complete design is open-source, costs less than $3000, and requires only hand tools for assembly, with the aim of lowering barriers to legged-robotics research and education.Source: §V · p. 6
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