What Cost of Transport Actually Measures

Cost of transport (COT) is defined as the energy a machine uses to move a unit of its mass over a unit of distance, calculated as power divided by (mass × gravity × velocity), which makes it dimensionless. The formulation traces to biomechanics work summarized by Kuo (2007) in the Journal of the Royal Society Interface and is the same figure legged-robotics groups use to benchmark hardware.

Two conventions are in circulation. Mechanical COT counts only the mechanical work at the joints. Total COT (sometimes written COT_total or "net electrical") counts the wall-plug or battery draw and is the number a buyer should ask for, because it includes controller idle draw, cooling, and drivetrain losses. Seok et al. (IEEE Transactions on Robotics, 2015) lay this out in detail for the MIT Cheetah.

As a rule of thumb, lower is better, values below 1.0 are efficient by robot standards, and any number quoted without stating mass, speed, and whether it is mechanical or total should be treated as marketing rather than a spec.

Why COT Matters More Than Runtime or Battery Size

Runtime numbers on a spec sheet depend on payload, terrain, speed, and how much the robot stands still. COT strips those variables out and lets a buyer compare two machines on the same physics. A quadruped with a smaller battery but half the COT will outlast a heavier rival on the same mission.

For field robotics teams, this is the number that maps directly to mission planning. IEEE Spectrum has covered the point that legged machines have historically been an order of magnitude less efficient than wheels, and closing that gap is why COT is treated as the field's headline efficiency metric.

COT also predicts thermal behavior. A machine at COT 1.5 is dissipating roughly 7.5x the heat per meter of a machine at COT 0.2 at the same mass and speed, which shows up as duty-cycle limits, fan noise, and motor derating on long missions.

How Real Robots and Animals Compare

The table below collects published COT values for well-known legged systems and biological references. Where a robot has been benchmarked in more than one paper the widely cited figure is used; readers building a purchasing case should confirm current numbers with the vendor since firmware and drivetrain revisions move these values. All robot rows are total (electrical) COT unless the source note says otherwise.

Human walking sits near 0.2 and is the reference every legged-robot team is chasing. Cassie is the biped that has come closest to that number in independent testing, while hydraulic Atlas and the earlier Boston Dynamics platforms trade efficiency for peak power.

SystemTypePublished COTSource
Human (walking, preferred speed)Biological biped~0.2 (mechanical)Kuo, J. R. Soc. Interface (2007)
Agility Robotics CassieElectric biped~0.2 (total electrical, best reported)Reher & Ames, IEEE T-RO / arXiv:2011.01807
MIT Cheetah (1st gen)Electric quadruped~0.5 (total electrical)Seok et al., IEEE T-RO (2015)
Unitree Go1Electric quadruped~0.6 (vendor-reported, total electrical, trotting)Unitree Go1 product page (unitree.com)
Boston Dynamics SpotElectric quadruped~1.4 to 1.6 (independent estimates, total electrical)IEEE Spectrum reporting; ~90 min runtime, 32.5 kg, 1.6 m/s max
Boston Dynamics Atlas (hydraulic, retired)Hydraulic humanoidHigher (hydraulic pump idle draw dominates; not published as a clean COT)Boston Dynamics blog (April 2024 retirement post)
Honda ASIMO (walking)Electric humanoid (historical)~3.2 (mechanical, walking)Collins et al., Science (2005)
Cornell Ranger (passive-dynamic biped)Electric biped~0.19 (mechanical)Bhounsule et al., Int. J. Robotics Research (2014)

Where the Numbers Come From and Where They Mislead

The lowest published COT for a walking robot belongs to the Cornell Ranger, a passive-dynamic biped that walked 65 km on a single charge, documented in Bhounsule et al., The International Journal of Robotics Research (2014). That is a research platform tuned to one task, not a general-purpose machine, and buyers should read it as a proof of what is physically possible rather than as a shopping benchmark.

For humanoids, the record on record for a general-purpose biped is Cassie, discussed in Reher and Ames (2020, arXiv:2011.01807), which reports COT in the low 0.2s at walking speeds under specific test conditions. Vendor-quoted numbers for newer humanoids from Agility Robotics, Boston Dynamics (electric Atlas), and Figure often lack a published COT — ask.

Two adjustments matter when reading any COT figure: speed and payload. COT is usually U-shaped versus speed with a minimum near the machine's designed walking pace, so a number quoted at that sweet spot will look better than the number the robot actually experiences on a mixed mission. Adding payload changes the effective mass in the denominator, and vendors sometimes quote COT without payload.

  • Ask whether a quoted COT is mechanical or total electrical.
  • Ask at what speed and payload the measurement was taken.
  • Ask whether the number includes onboard compute and sensor draw.
  • Ask for a runtime figure at the same speed and payload as a cross-check.
  • Treat any COT quoted without units, speed, and mass as unverified.

Using COT in a Buying Decision

For a quadruped tasked with long inspection loops, COT plus battery capacity gives a first-pass runtime estimate that is more honest than the vendor headline number. Dividing total battery energy (in joules) by (COT × mass × gravity) gives the theoretical range in meters at the tested speed.

For a humanoid pilot, COT is a proxy for how much thermal and electrical headroom the platform has for the manipulation work on top of walking. A humanoid with a total-electrical COT above 1.0 will run hot when it also has to lift and place at cycle.

For anyone comparing wheels to legs, the honest reference is that wheeled mobile robots and cars have COTs in the 0.03 to 0.1 range, which is why IEEE Spectrum and every serious legged-robotics paper acknowledge the efficiency gap. Legs are bought for terrain, not for energy.

Bottom Line

Cost of transport is the cleanest one-number comparison for legged robots, but only when the mass, speed, payload, and mechanical-vs-total convention are stated with it. Use it to sanity-check runtime claims, not to replace them.

Before you sign a legged-robot quote, ask the vendor for total electrical COT at your mission speed and payload, and cross-check it against published runtime.

FAQs

What is a good cost of transport for a walking robot?

Below 0.5 is efficient by current standards for an electric legged robot. Human walking sits near 0.2, Cassie has been reported in the low 0.2s, and most commercially available quadrupeds land between 0.5 and 1.6 depending on speed and payload.

Is cost of transport the same as energy efficiency?

It is a specific, dimensionless form of energy efficiency for moving mass. Because it normalizes by mass and distance, it lets you compare a 30 kg quadruped to a 90 kg humanoid without unit conversions, which raw watts per hour cannot.

Why is hydraulic Atlas so much less efficient than electric bipeds?

Hydraulic systems keep a pump running to maintain pressure whether the robot is moving or standing still, so idle electrical draw is high. Electric direct-drive and quasi-direct-drive designs, used in the newer Atlas and in Cassie, only draw current when a joint is doing work.

Do vendors publish cost of transport on spec sheets?

Rarely, and inconsistently. Unitree lists efficiency figures for the Go series; Boston Dynamics, Agility Robotics, and Figure typically publish runtime and speed rather than COT. Buyers should request the number in writing with the test conditions.

How do I estimate runtime from cost of transport?

Divide total battery energy in joules by (COT × mass in kg × 9.81 × speed in m/s) to get seconds of continuous motion at that speed. It is a floor, not a promise — real missions include standing, turning, and compute overhead not captured in COT.

Primary Sources