Legged Morphologies — Family Index

Tier 3 family index for legged robot bodies. Catalogs platforms by leg count, leg topology, actuation style, and intended duty. Companion to legged-robotics (theory) and motor-families (actuators).

1. At a glance

Coarse classification by leg count:

• 2 legs (biped) — humanoid (anthropomorphic torso, hip-knee-ankle co-linear) and avian / bird-like (counter-knee, no torso, hip well aft of foot). Statically unstable when standing on one foot; require active balance.
• 4 legs (quadruped) — dominant commercial morphology in 2024-25. Statically stable in tripod support phases; dynamically stable at speed via trot / gallop.
• 6 legs (hexapod) — alternating-tripod gait yields permanent static stability. Slower and heavier than quadrupeds for equivalent payload; niche outside research.
• 8 legs (octopod) — rare; spider-bots and a few research platforms.
• >8 (myriapod / centipede) — modular snake-like with leg modules; experimental.

Specialized morphologies orthogonal to leg count:

• Limbed — ≥1 leg can be repurposed as a manipulator (e.g. quadruped with arm-as-fifth-leg).
• Climbing — vertical surface adhesion (gecko, spider).
• Aquatic + legged — amphibious walkers (salamander-bots).
• Wheeled-leg hybrid — wheels at the foot or knee; rolls on flat, walks on rough.

2. Leg topologies

Per-leg kinematic structure (D-H chain from hip to foot):

• RR (2-link planar) — hip-pitch + knee. Cheap, 2 DoF; foot moves on a plane through the hip. Used in toy hexapods and some education platforms.
• RRR (3-link with knee) — hip-roll + hip-pitch + knee-pitch. Standard quadruped leg (Spot, ANYmal, Unitree). 3 DoF gives 3-D foot placement.
• Parallel-Λ leg — thigh and shin actuated by two motors at the hip via a parallelogram or 5-bar linkage. Moves motor mass to body, dramatically reducing leg inertia. Used in MIT Cheetah, ANYmal (offset hip motors via spur gear and parallelogram), Unitree quadrupeds.
• R-P-R (rotary-prismatic-rotary) — hopping legs and SLIP-inspired designs; Raibert one-legged hopper (1986) used pneumatic prismatic shin.
• Stewart-platform foot — 6-DoF parallel mechanism at the foot for fine compliance; redundant, expensive, rare.
• Tail / spine articulation — Cheetah 3 and MIT Mini-Cheetah added articulated spines or tails for pitch authority during flight phase.

Humanoid leg adds ankle (2 DoF — pitch + roll) on top of RRR for a 6-DoF leg per side (hip 3 + knee 1 + ankle 2 = 6). Avian bipeds (Cassie / Digit) compress this to ~5 DoF by omitting hip yaw or constraining ankle.

2a. Leg inertia and reflected inertia

A central design driver across modern legged platforms is distal-limb inertia. Inertia at the foot reflects to the hip motor proportional to leg length squared; for high-bandwidth torque control during foot strike (impulse durations ~10-30 ms) the distal mass dominates achievable closed-loop gains. This is why nearly all post-2018 quadrupeds either (a) use parallel-Λ to keep motor mass at the hip, (b) use cable-driven distal joints, or (c) accept lower bandwidth.

2b. Singularities

The RRR leg has a singularity when the knee is fully extended (Jacobian rank drop along the leg axis). Controllers either enforce a knee-bend offset (~10-15°) or use a redundancy-resolved task-space formulation. Humanoid 6-DoF legs add wrist-style ankle singularities; ZMP controllers avoid these via foot placement constraints.

3. Biped (humanoid + bird-like)

3a. Hydraulic humanoid

• Boston Dynamics Atlas (legacy hydraulic) — DARPA Robotics Challenge platform, 2013-2024. ~150 kg, hydraulic pumps + servo valves at every joint. Famous for parkour and backflip demos. Retired April 2024 in favor of Electric Atlas.

3b. Electric humanoid

Active commercial / pre-production platforms as of 2024-25:

• Boston Dynamics Atlas (Electric, 2024+) — hydraulic-era geometry but all-electric joints; new range-of-motion exceeds human (rotates head and joints continuously). Targeting Hyundai factory deployment.
• Tesla Optimus Gen 2 (2023) / Gen 3 (2024-25) — Tesla in-house actuators; targeted at Tesla factory tasks, then mass-market home.
• Figure 02 (2024) — Figure AI; deployment trial at BMW Spartanburg, partnership with OpenAI for vision-language.
• Apptronik Apollo — collaborative humanoid, instrumented force/torque ankle, GXO and Mercedes-Benz pilots.
• Sanctuary AI Phoenix — Canadian humanoid, hydraulic-electric hybrid, focus on dexterous teleop.
• 1X NEO — soft-shell home humanoid, tendon-driven, OpenAI investment.
• Unitree H1 / G1 — H1 first sub-100 kg sub-USD-100k humanoid (2023); G1 smaller (2024) at ~USD 16k.
• Fourier Intelligence GR-1 — Chinese humanoid, rehabilitation lineage.
• Xiaomi CyberOne — Xiaomi’s announcement (2022); limited public demos.
• NimbRo / NimbRo-OP3 — University of Bonn research bipeds, RoboCup Adult and Kid leagues.
• HRP-2 / HRP-3 / HRP-4 / HRP-5 / Kaleido — AIST (Japan) long-running humanoid lineage; HRP-5P (2018) demoed drywall installation.
• HUBO (KAIST) — DRC-era Korean humanoid.
• Robonaut 2 (NASA, legacy) — torso-only humanoid on ISS 2011-2018, legs added 2014.
• ASIMO (Honda) — retired 2018; long-running development from 1986 to 2018.
• iCub (IIT) — child-sized open research humanoid since 2008.

3c. Bird-like biped (avian)

Counter-knee, no humanoid torso, hip well aft of foot — analogous to ostrich kinematics. Generally lower mass and more energy-efficient than humanoids per unit distance:

• Cassie (Agility Robotics, 2017) — research-grade bipedal walker, no torso, no arms; ETH / Oregon State Hurst lab lineage.
• Digit (Agility Robotics, 2019-2024+) — Cassie geometry + torso + arms (4 DoF each, dual-purpose for balance and pick); commercial warehouse trial at Amazon AR Sandbox 2023, Ford 2020 trial, GXO Logistics 2024 deployment.
• SCHAFT — Japanese biped acquired by Google 2013, dissolved 2018.
• ALR Andes (UCLA) — academic ostrich-style biped.
• Ostrich Bot (Caltech) — Caltech AMBER lab series.

3c-i. Why avian over humanoid?

Avian bipeds typically achieve 2-3× the energy efficiency of equivalently-sized humanoids and longer battery runtime (Cassie / Digit 4-6 h vs Atlas Electric ~60 min). Reasons: counter-knee places the hip-knee linkage in tension (efficient bone-tendon analogue), no arms or torso mass to balance, and the foot is closer to the body’s CoM. Trade-off: no upper-body manipulation. Digit added 4-DoF arms specifically to bridge this gap for warehouse pick-place.

3d. Humanoid balance fundamentals

Bipedal balance is conventionally analyzed via the Zero-Moment Point (ZMP) — the ground point where the net ground reaction torque has no horizontal component. Walking is stable when ZMP remains inside the support polygon. ZMP-based controllers (Honda ASIMO, HRP series) emphasize flat-foot walking with conservative speeds. Modern controllers add the Capture Point (CP) — where the robot must step to come to rest — and Centroidal Momentum formulations (Orin, Goswami). MIT, IHMC, and Boston Dynamics push beyond ZMP via whole-body MPC; Cassie / Digit use reinforcement-learned policies trained in simulation.

4. Quadruped

4a. Mainstream commercial

• Boston Dynamics Spot — since 2019, SDK available, payload bay with mounting rail and PoE, supports arm option (Spot Arm). 32.5 kg, 14 kg payload, IP54, 90 min runtime.
• ANYbotics ANYmal C / D / X — ETH spinoff, industrial inspection focus, IP67, ANYmal X (2024) ATEX / IECEx EX-rated for Zone 1 hazardous (oil & gas, chemical plants).
• Unitree A1 / Aliengo / Go1 / Go2 / B1 / B2 — mass-market 2022-2025; Go2 EDU at ~USD 2.8k brought research-grade quadrupeds to undergraduates; B2 industrial-class 6 m/s peak demo.
• Ghost Robotics Vision-60 / Spirit-40 / Q-UGV — US military / security; deployed at USAF bases, Tyndall AFB perimeter patrol.
• DEEP Robotics X20 / X30 / Lynx — Chinese industrial inspection quadrupeds.
• Xiaomi CyberDog 1 / 2 — consumer / hobbyist; open-source firmware.
• MAB Robotics Honey Badger — Polish quadruped, sewer / underground inspection focus.

4a-i. Quadruped form factor segmentation

The commercial quadruped market segments by mass and payload class:

• Compact / education (5-20 kg) — Unitree Go2, A1, MIT Mini-Cheetah derivatives. USD 2-10k. Indoor research, education, hobbyist.
• Mid-class industrial (25-50 kg) — Spot (32.5 kg), ANYmal C (~50 kg), Unitree Aliengo. Commercial inspection, payload 10-15 kg. USD 75-150k.
• Heavy industrial (60-80 kg) — Unitree B2, ANYmal D / X. 20-50 kg payload, outdoor / hazardous use.
• Military / payload (80-120 kg) — Ghost Robotics Q-UGV, DEEP Robotics X30. Tens-of-kg payload, multi-hour outdoor missions.

Mass scales with the cube of leg length (for fixed slenderness); payload scales with motor torque density. The ~50 kg sweet spot dominates because it balances payload (10-14 kg) with safe human-proximity operation.

4b. Research

• MIT Cheetah 1 / 2 / 3 / Mini-Cheetah — Sangbae Kim lab; Cheetah 3 (2018) demoed backflips and stair climb without vision. Mini-Cheetah open-source-ish; many derivatives.
• ETH StarlETH (legacy) — precursor to ANYmal.
• HyQ / HyQ2Max (IIT) — hydraulic quadrupeds, Caldwell lab; highest torque density of any quadruped lineage.
• ANYmal (ETH 2016) — research platform that spun out to ANYbotics.

5. Multi-leg (hexapod and more)

• RHex (Boston Dynamics, 2001-2010) — six C-shaped compliant legs, single-DoF rotary per leg, alternating tripod. Famous for terrain robustness with mechanical simplicity. Variants: X-RHex, EduBot.
• Lauron V (Schunk / FZI, legacy) — six-legged research hexapod, insect-inspired.
• PhantomX (Trossen Robotics) — hobbyist hexapod kit.
• Hexapod-2 (Honda) — internal Honda research hexapod.

Rhex-derivative C-leg topology trades fine foot placement for robustness; alternating tripod is the default gait.

5a. Hexapod vs quadruped trade-off

Hexapods give permanent static stability (3-point contact in alternating tripod) at the cost of 50% more actuators, mass, and energy per unit payload. The market has decisively moved to quadrupeds for nearly all commercial duty because closed-loop balance control on a quadruped is now a solved problem (since ~2018, via MPC + RL). Hexapods retain niche advantage where loss-of-power must leave the platform standing (some inspection in seismically active areas, some space concepts).

6. Specialty and climbing

• Stickybot (Stanford, 2006-2008) — gecko-inspired directional adhesive pads; vertical glass climbing.
• RiSE (CMU) — vertical climbing hexapod with microspine feet for rough vertical surfaces.
• Spider (CSAIL) — research climbing platforms with electroadhesion.
• Modsnake (CMU, Howie Choset, 2013+) — modular hyper-redundant snake; one of the few non-legged continuum platforms in this taxonomy.

6a. Climbing locomotion modes

• Dry adhesion (gecko-inspired) — directional fibrillar pads (Stickybot); shear-engaged, peel-released. Effective on smooth glass.
• Microspine — arrays of small hooks engaging surface asperities (RiSE, SpinybotII). Works on rough concrete and stone.
• Electroadhesion — applied voltage induces image-charge attraction; payload-limited but works on most materials.
• Suction — vacuum pads; bandwidth-limited by pump speed.
• Magnetic — ferromagnetic surfaces only; common for ship-hull inspection legged platforms.

7. Hybrid wheel-leg

• Boston Dynamics Handle (2017-2019, legacy) — two-leg + wheel biped, 100 kg payload demo. Retired in favor of Stretch.
• Ascento (ETH) — balanced wheel + spring-loaded leg; ballbot lineage.
• Skywalker AGV — wheel-leg hybrid AMR variants.
• Ghost Robotics Vision-60 wheeled variant — research swap of feet for wheels.
• ANYmal Wheels (ETH testbed) — ANYmal with wheels at the foot for hybrid roll-walk.

8. Leg actuation styles

Cross-cutting taxonomy of how the joints are driven. See motor-families for motor-level detail.

• Hydraulic — historical: Atlas (legacy), HyQ, BigDog. Highest torque density of any actuation style but heavy pumps, leaky valves, audible. Largely abandoned for new platforms after ~2020.
• Quasi-direct-drive (QDD) electric — low-K_v BLDC + 6:1 to 9:1 single-stage planetary; motor torque directly felt through the gear. Backdrivable. MIT Mini-Cheetah, ODRI Solo 8 / 12, Unitree Go / Aliengo / B1. Best torque-control bandwidth; current de-facto standard for quadrupeds.
• Series-Elastic Actuator (SEA) — Pratt-Williamson 1995; intentional spring in series between motor and joint, force = spring deflection × K. Cassie / Digit, Atlas Spring Flamingo (legacy), most NASA / DLR platforms.
• Cable-driven / tendon — antagonistic tendons via remote motors. 1X NEO. Routing complexity offset by very low distal limb mass.
• Hybrid (parallel-Λ + offset motor) — most modern quadrupeds offset motors to body via parallelogram or 5-bar to reduce leg inertia while keeping QDD characteristics. ANYmal C/D, Unitree B-series.
• Harmonic-drive geared — high reduction (50:1 to 160:1), zero backlash, low backdrivability. Used in legacy humanoid hips and knees (HRP-2/3/4, ASIMO) and many surgical / industrial arms. Falling out of favor for new humanoids due to impedance limitations.
• Cycloidal-drive geared — similar reduction range to harmonic, higher torque density and shock tolerance, slightly more backlash. Used in some industrial humanoid joints and collaborative arms.

8a. Torque density and bandwidth trade-offs

QDD electric peaks at ~10-15 Nm/kg motor + gearbox; SEA delivers similar peak torque but with bandwidth limited by spring stiffness (typically 30-80 Hz force bandwidth); hydraulic exceeds 30 Nm/kg at the actuator but with system-level penalties (pump mass, hose mass, fluid mass). For dynamic gaits requiring ~200-500 Hz torque-control bandwidth (foot-strike rejection), QDD is the dominant choice.

8b. Backdrivability and impedance

Backdrivability — the ability for an external load to drive the motor in reverse without large parasitic torque — is essential for compliant impact and impedance control. QDD with single-stage planetary achieves it at the cost of low gear reduction (so higher peak current). SEA achieves it via the series spring. Harmonic-drive geared actuators (used in many humanoid joints pre-2018) are not backdrivable and require torque sensing at the joint output to emulate compliance.

9. Gait taxonomy

Bipedal gaits

• Walk — single-support phases overlap with double-support (both feet on ground briefly).
• Run — flight phase: no foot on ground for part of cycle.
• Hop — single-leg cyclic compression; Raibert hoppers.
• No biped trot or gallop.

Quadrupedal gaits

• Walk — 4-3 support pattern, one foot lifts at a time; statically stable.
• Trot — diagonal pair (left-front + right-rear, then opposite). Dynamic; most common at moderate speed.
• Pace — lateral pair (both left, then both right). Camels, some horses.
• Bound — front pair then back pair (rabbit-like).
• Gallop — asymmetric four-beat; horse and cheetah top speed.
• Pronk — all four feet leave and land simultaneously. Gazelle alarm gait; demoed on Mini-Cheetah.
• Crawl — sub-walk variant with very long support phases; useful on slippery or compliant terrain.

Duty factor β (fraction of cycle a given foot is on the ground) classifies gaits: walk β > 0.5 (overlapping support), run / trot β = 0.5 (instant double-support), gallop β < 0.5 (flight phase). Symmetry — whether contralateral feet are 180° out of phase — distinguishes trot / pace from gallop / bound.

Hexapod gaits

• Alternating tripod — alternate sets of 3 legs (front-left + middle-right + rear-left, then opposite). Always 3-point contact; permanent static stability.
• Ripple — phase offset between legs, smoother but slower.
• Wave — one leg at a time; slowest, most stable.

Gait selection

Gait is usually chosen by Froude number Fr = v² / (g·L) where L is leg length. Walk→trot transitions in quadrupeds occur near Fr ≈ 0.5; trot→gallop near Fr ≈ 2-3. Most commercial quadrupeds (Spot, ANYmal) stay in trot during operational use; gallop and bound are reserved for research demos. Modern MPC-based controllers (MIT Cheetah, ANYmal-RL via Hwangbo et al.) treat contact schedule as part of the optimization rather than hand-tuning gait, blurring the classical taxonomy.

10. Performance specs (typical)

Platform	Top speed	Notes
Atlas (Electric)	~1.5-2.5 m/s	New range-of-motion exceeds human
Atlas (legacy hydraulic)	~4 m/s (9 mph demo)	Parkour, backflip
Cassie / Digit	1.5 m/s comfortable, ~3.0 m/s peak	Cassie set 100 m record in 24.7 s at OSU
Spot	1.6 m/s	Stable for indoor inspection
ANYmal C / D	~1.0 m/s	Conservative for inspection use
Unitree B2	6 m/s peak demo	Industrial-class quadruped
MIT Mini-Cheetah	~3.5 m/s	Research benchmark
Cheetah 3	Backflip + stair climb	No vision used in stair demo

11. Payload, battery, runtime

Platform	Payload	Runtime
Atlas (Electric)	~10 kg	~60 min
Spot	14 kg	90 min
ANYmal C/D/X	10 kg	2-4 h
Unitree Go2 EDU	12 kg	1-2 h
Cassie / Digit	16 kg	4-6 h

Runtime scales with locomotion duty cycle; figures assume continuous walking at nominal speed.

11a. Energy economy

Cost of Transport CoT = P / (m·g·v) is the standard non-dimensional efficiency metric.

• Human walker: CoT ≈ 0.2
• Cassie / Digit: CoT ≈ 0.5-0.8
• ANYmal: CoT ≈ 0.9-1.2
• Spot: CoT ≈ 1.5-2.0
• Atlas (Electric): CoT ≈ 2-3
• Atlas (legacy hydraulic): CoT ≈ 4-5 (penalized heavily by always-on hydraulic pumps)
• BigDog (legacy gas-engine-hydraulic): CoT ≈ 15 (military-grade noisy, energy-intensive)

Counter-knee avian bipeds are the most efficient electric legged morphology to date.

12. Ingress and ratings

• Spot — IP54 (dust, splash).
• ANYmal X — IP67 + ATEX / IECEx Zone 1 EX-rated (only commercial quadruped with explosive-atmosphere certification as of 2024).
• ANYmal C / D — IP67.
• Atlas (Electric) — IP54-class industrial.
• Unitree Go2 — IP66.
• Cassie / Digit — IP54.

Ingress determines indoor vs outdoor vs hazardous-area deployment. Refrigerated warehouse and food / pharma usually require IP65+.

13. Application taxonomy

• Industrial inspection (oil & gas, power, chemical) — Spot, ANYmal C/D/X. EX-rated → ANYmal X.
• Military / security perimeter — Ghost Robotics Vision-60, Q-UGV.
• Warehouse logistics (biped pick-place) — Digit (Agility, Amazon AR Sandbox, GXO).
• Research biped — Cassie, Atlas Electric, HRP-5.
• Humanoid mass-market home (early) — Tesla Optimus, 1X NEO.
• EOD / bomb disposal — historically tracked (PackBot, TALON); some quadruped trials.
• Rough-terrain mapping / SAR — quadruped + LIDAR (Spot + Velodyne / Ouster, ANYmal + Hesai).
• Entertainment — Boston Dynamics demos, Unitree H1 dance routines, Spot music videos.
• Education biped — Unitree H1 / G1.
• Education quadruped — Unitree Go2 EDU, MIT Mini-Cheetah derivatives.
• Humanoid HRC retail / hospitality — Apptronik Apollo, Figure 02.
• Teleop humanoid — 1X NEO.

13a. Sensor stack patterns

Across applications a common sensor stack has emerged:

• IMU — body-mounted 9-DoF (gyro + accel + mag), 200-1000 Hz, used for orientation and body-frame velocity (Spot, ANYmal, all).
• Joint encoders — absolute at output + incremental at motor for backlash compensation.
• Joint torque — direct via SEA spring deflection, or via motor current (QDD).
• Foot contact — limit switch (cheap), force sensor at sole, or contact estimation from joint torque residual (most modern QDD platforms).
• Vision — RGB-D (Realsense D435 / D455 on Spot, Unitree), stereo (Atlas), or LIDAR (Velodyne / Ouster / Hesai on inspection quadrupeds).
• GPS / RTK — outdoor inspection only.
• Tactile / skin — emerging for humanoid HRC: capacitive or resistive arrays on torso and arms. Sanctuary, Apollo prototypes have it; not yet widespread.

13b. Connectivity and fleet

Commercial fleets (Spot, ANYmal, Digit) ship with cloud telematics: Boston Dynamics Orbit, ANYbotics Astra, Agility Arc. These provide mission scheduling, log aggregation, OTA firmware, and remote teleop. Open-source quadruped stacks (Champ, Pupper, Solo) rely on local ROS 2 + custom dashboards. Fleet software is becoming a bigger differentiator than the hardware itself.

14. Foot designs

• Point foot — sphere or hemisphere (Cassie, MIT Cheetah). Simple contact model; one contact point per leg.
• Rubber pad foot — flat compliant pad (Spot, ANYmal). Larger friction patch, less sensitive to small obstacles.
• Curved compliant foot — RHex C-leg or rounded toe; rolls support point as leg sweeps.
• Grouser / track foot — rare on legged robots; common on tracked vehicles.
• Humanoid rigid sole — flat plate ankle, simplest IK and ZMP control.
• Humanoid articulated toe — Atlas, Sanctuary Phoenix; passive or actuated toe joint extends step length and improves push-off.
• Instrumented foot (F/T at ankle) — Optimus, Apollo, HRP-5; 6-axis F/T sensor at ankle for ground-reaction estimation and impedance control.

14a. Contact estimation

Without an F/T sensor at the foot (most quadrupeds), ground contact is estimated from joint torque residual: predicted torque from inverse dynamics minus measured torque exceeds threshold → foot is loaded. This requires accurate model parameters (CoM, inertia tensors) and is sensitive to friction and impact transients. Modern controllers (Bloesch, Hutter et al. 2013) fuse this with IMU and proprioception in a probabilistic filter.

15. Selection heuristics

• Outdoor inspection, oil & gas, hazardous area → ANYmal X (EX-rated).
• Indoor / outdoor inspection, general industrial → Spot or ANYmal C/D.
• Warehouse pick-place, 16 kg payload, totes → Digit + arms.
• Research-grade humanoid (full-body manipulation, balance) → Atlas Electric or HRP-5.
• Education biped → Unitree H1 (full-size) or G1 (compact).
• Education quadruped → Unitree Go2 EDU; MIT Mini-Cheetah for SEA / QDD research.
• Military / payload-bearing quadruped → Ghost Robotics Vision-60 or Q-UGV.
• Search-and-rescue rubble → quadruped + tracked manipulator hybrid.
• Teleop bipedal home / retail → 1X NEO.
• Humanoid HRC retail / light manufacturing → Apptronik Apollo, Figure 02.
• Legged drone fail-over → not a standard category; experimental hybrids only.

15a. Total-cost-of-ownership notes

Acquisition price is only part of TCO. Spot at ~USD 75-100k (2024) carries USD 1500-3000/yr in service; ANYmal X is 2-3× higher acquisition but rated for 24/7 unattended duty in hazardous areas, displacing two FTE human inspectors. Humanoid pricing as of 2024-25 is in flux: Unitree H1 at ~USD 90k undercuts Boston Dynamics by 5-10×, but with substantially smaller R&D / support ecosystem. Total cost over a 5-year deployment generally favors the platform with the strongest software / SDK / fleet management (currently Spot and ANYmal).

16. Cross-references

• legged-robotics — theory and dynamics
• humanoid-balance — ZMP, capture point, MPC for humanoids
• dynamic-locomotion — SLIP, hopping, gait optimization
• mobile-bases — wheeled and tracked alternatives
• motor-families — QDD vs SEA vs hydraulic motor selection
• mpc-for-robots — model predictive control for legged systems
• end-effectors-zoo — companion grippers and arm-as-fifth-leg

16a. Open questions and active research (2024-25)

• Sim-to-real RL for humanoids — Cassie / Digit policies trained in Isaac Gym / MuJoCo Playground and deployed zero-shot are now standard; humanoid equivalents (Unitree H1, Atlas Electric) are catching up with massive-parallel domain randomization.
• Whole-body manipulation — using legs as supports while one limb manipulates; arm-as-fifth-leg quadrupeds (Spot Arm extreme reach mode).
• Long-duration energy — batteries cap most platforms at <6 h continuous; tethered (Atlas legacy DRC) or hydrogen-fuel-cell variants are experimental.
• Failure resilience — what does a humanoid do when a foot slips on ice? Modern controllers fall and self-right rather than rigidly resisting; Atlas Electric demos include trip-recovery.
• Force-closed manipulation by legs — using two legs as a parallel manipulator while the other two support; not yet productized.

17. Citations

• Raibert, M. H., “Legged Robots That Balance,” MIT Press, 1986.
• Wensing, P. M., Kim, S., et al., “Proprioceptive Actuator Design in the MIT Cheetah,” IEEE Trans. Robotics, 2017.
• Hutter, M., et al., “ANYmal — A Highly Mobile and Dynamic Quadrupedal Robot,” IROS 2016.
• Hyun, D. J., Seok, S., Lee, J., Kim, S., “High Speed Trot-Running: Implementation of a Hierarchical Controller Using Proprioceptive Impedance Control on the MIT Cheetah,” IJRR 2014.
• Boston Dynamics Atlas technical briefs and IROS / ICRA papers, 2013-2024.
• Agility Robotics Cassie and Digit technical briefs, 2018-present.
• Pratt, G., Williamson, M., “Series Elastic Actuators,” IROS 1995.
• Saranli, U., Buehler, M., Koditschek, D. E., “RHex: A Simple and Highly Mobile Hexapod Robot,” IJRR 2001.
• Park, H.-W., Wensing, P. M., Kim, S., “High-speed bounding with the MIT Cheetah 2: Control design and experiments,” IJRR 2017.
• Bloesch, M., Hutter, M., et al., “State estimation for legged robots — consistent fusion of leg kinematics and IMU,” RSS 2012.
• Hwangbo, J., Lee, J., Dosovitskiy, A., et al., “Learning agile and dynamic motor skills for legged robots,” Science Robotics 2019.
• Kuindersma, S., Tedrake, R., et al., “Optimization-based locomotion planning, estimation, and control design for the Atlas humanoid robot,” Autonomous Robots 2016.
• Pratt, J., Carff, J., Drakunov, S., Goswami, A., “Capture Point: A step toward humanoid push recovery,” Humanoids 2006.
• Vukobratovic, M., Borovac, B., “Zero-Moment Point — thirty five years of its life,” Int. J. Humanoid Robotics 2004.
• Orin, D., Goswami, A., Lee, S.-H., “Centroidal dynamics of a humanoid robot,” Autonomous Robots 2013.
• Saranli, U., Buehler, M., Koditschek, D. E., “RHex: A simple and highly mobile hexapod robot,” IJRR 2001.
• Seok, S., Wang, A., Chuah, M. Y., et al., “Design principles for energy-efficient legged locomotion and implementation on the MIT Cheetah robot,” IEEE/ASME Trans. Mechatronics 2015.