Legged Locomotion Lineage

Legged locomotionlegged locomotionLegged locomotion is moving on legs instead of wheels or tracks, re-establishing balance at every discrete, intermittent foothold with no continuous contact patch. Conventional controllers were elaborate state machines triggering motion primitives and reflexes, growing more complex without nearing animal generality. The ETH Zurich line replaced them with simulation-trained reinforcement learning. Lee et al.'s ANYmal controller generalized zero-shot to alpine terrain on proprioception alone, and Miki et al. extended the recipe to perceptive locomotion in the wild. is the control of walking and running robots, and the area where sim-to-real reinforcement learning reached shipping products such as Spot^{Source 12}12 Boston Dynamics 2024, Starting on the Right Foot with Reinforcement Learning. Boston Dynamics, 2024. ETH Zurich's ANYmal line went from simulation-trained policies on hardware in 2019^{Source 1}1 Hwangbo et al. 2019, Learning agile and dynamic motor skills for legged robots. Jemin Hwangbo, Joonho Lee, Alexey Dosovitskiy et al., Science Robotics 4(26), 2019 to a 2.2 km alpine hike in 2022^{Source 3}3 Miki et al. 2022, Learning robust perceptive locomotion for quadrupedal robots in the wild. Takahiro Miki, Joonho Lee, Jemin Hwangbo et al., Science Robotics 7(62), 2022.

Photo: Jonte / Wikimedia Commons. Licence: CC BY-SA 4.0.

The quadruped lineage

Hwangbo and colleagues replaced simulated actuation with a learned network for ANYmal's series-elastic actuators, which predicts joint torque from current and past joint-position errors and velocities; policies trained with ideal or analytical actuator models failed to take a single step without falling. A separate recovery policy flipped ANYmal upright from nine tested configurations, after the authors relaxed joint-velocity constraints following the first hardware attempt^{Source 1}1 Hwangbo et al. 2019, Learning agile and dynamic motor skills for legged robots. Jemin Hwangbo, Joonho Lee, Alexey Dosovitskiy et al., Science Robotics 4(26), 2019.

Lee and colleagues trained a privileged RL teacher to supervise the actions and latent features of a temporal convolutional student, which reads two seconds of proprioceptiveproprioceptionProprioception is sensing the body's own state (joint positions and velocities, orientation, contact), as opposed to exteroception of the outside world through cameras or lidar. It is fast, cheap and never occluded. At ETH Zurich, Lee et al.'s ANYmal controller hiked mud, snow, rubble and vegetation on proprioception alone. Miki et al. kept it as the trusted fallback when the terrain map disagrees with the body. history, plus the command and current state, with no terrain map. Trained on rigid procedural terrain, ANYmal-B and ANYmal-C controllers crossed mud, snow, rubble and vegetation without environment-specific tuning, though a robot commanded off a cliff will walk off it^{Source 2}2 Lee et al. 2020, Learning Quadrupedal Locomotion over Challenging Terrain. Joonho Lee, Jemin Hwangbo, Lorenz Wellhausen et al., Science Robotics 5(47), 2020. RMA, a base policy plus an adaptation module, deployed on the A1 robot without any fine-tuning^{Source 14}14 Kumar et al. 2021, RMA: Rapid Motor Adaptation for Legged Robots. Ashish Kumar, Zipeng Fu, Deepak Pathak et al., RSS 2021; the sim-to-real module covers the distillation mechanics.

Miki and colleagues fed elevation-map height samples and proprioception to a GRU belief encoder whose learned attention gate controls how much exteroception enters; the student imitates a privileged teacher and falls back on proprioception when sensors mislead. The Etzel hike covered 2.2 km and 120 m of climb in 78 minutes against a planner's 76, with no falls but stops to reattach a shoe and swap batteries, and the authors list possible falls at occluded cliffs or stepping stones^{Source 3}3 Miki et al. 2022, Learning robust perceptive locomotion for quadrupedal robots in the wild. Takahiro Miki, Joonho Lee, Jemin Hwangbo et al., Science Robotics 7(62), 2022.

Rudin and colleagues trained flat-terrain walking in under four minutes on one workstation GPU. Their deployment policy used 4,096 ANYmal robots, batches of 98,304 transitions (24 steps per robot) and 1,500 updates in under twenty minutes, with a game-inspired terrain curriculumcurriculum learningCurriculum learning is training on tasks that start easy and grow harder as the agent improves. Rudin et al. adjusted each robot's terrain level by its progress. Their documented curriculum-trained policy for simulation and deployment used 4,096 robots, 98,304 transitions per batch and 1,500 updates in under twenty minutes on an i9-11900k CPU and RTX A6000 GPU. Their separate flat-terrain headline is under four minutes on one workstation GPU. that promotes robots that cross a tile, demotes those that fall short and loops hardest-level solvers back to a random level^{Source 4}4 Rudin et al. 2021, Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning. Nikita Rudin, David Hoeller, Philipp Reist et al., CoRL 2021. The released legged_gym repository (October 2021) is the Isaac Gym environment used to train ANYmal on rough terrain^{Source 5}5 Rudin 2021, Isaac Gym Environments for Legged Robots. Nikita Rudin, 2021.

Photo: ANYbotics / Wikimedia Commons. Licence: CC BY-SA 4.0.

ANYmal Parkour's high-level policy selects walking, jumping, climbing and crouching skills, crossing obstacles at up to two meters per second^{Source 15}15 Hoeller et al. 2023, ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robots. David Hoeller, Nikita Rudin, Dhionis Sako et al., arXiv preprint (Science Robotics 2024), 2023. With a cheap granular-media model in the training loop, Choi and colleagues' Raibo ran on beach sand at 3.03 m/s with feet fully buried^{Source 6}6 Choi et al. 2023, Learning Quadrupedal Locomotion on Deformable Terrain. Suyoung Choi, Gwanghyeon Ji, Jeongsoo Park et al., Science Robotics 8(74), 2023.

A gait is a timing pattern

A gait is a footfall-timing pattern: each leg's phase offset in the stride and its duty factor $\beta$, the fraction of the cycle on the ground. Walk These Ways commands a gait as three timing offsets between foot pairs plus a stepping frequency: (0.5, 0, 0) trots, (0, 0.5, 0) bounds and (0, 0, 0) pronks^{Source 16}16 Margolis et al. 2022, Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior. Gabriel B. Margolis, Pulkit Agrawal, Conference on Robot Learning (CoRL) 2022. Push the dog and the humanoid in the figure below to see why fewer feet on the ground make balance harder.

Why are two legs harder than four?

Every body has a balance point, where its weight is centred. The dot marks it on a robot dog and a humanoid.

BackNext

Four feet give a robot a wide patch to balance over and two feet a tiny one, so a pushed humanoid must step.

How this was made

The steps in words

1. Every body has a balance point, where its weight is centred. The dot marks it on a robot dog and a humanoid.
2. The shaded patch spans the feet on the ground. While the spot straight below the dot stays inside it, the robot stays up.
3. Both robots get the same push, and both balance points move the same distance forward.
4. When walking, only some feet touch the ground. The patch shrinks, the spot often falls outside it, and each new step catches the fall.
5. This patch is called the support polygon. Balance changes fast: one robot dog adjusts its legs 200 times a second to stay up.

Photo: Eadweard Muybridge / Wikimedia Commons. Licence: Public domain.

In the MIT Cheetah 2 design, Park, Wensing and Kim plan stance time from stride length and speed, $T_{st} = L/v_d$, keep swing duration fixed, and modulate duty cycle by vertical impulse scaling. Stride length grows with speed only up to 3 m/s, so this is one controller's schedule. Roll instability ended the 6.4 m/s top-speed treadmill run, and at the highest speeds the robot partly leaned on the side wall. The minimum cost of transport, 0.47, came at 4 m/s^{Source 7}7 Park et al. 2017, High-Speed Bounding with the MIT Cheetah 2: Control Design and Experiments. Hae-Won Park, Patrick M. Wensing, Sangbae Kim, International Journal of Robotics Research 36(2), 2017.

Margolis and colleagues report record agility for the MIT Mini Cheetah with a learned controller, sustaining speeds up to 3.9 m/s^{Source 17}17 Margolis et al. 2022, Rapid Locomotion via Reinforcement Learning. Gabriel B. Margolis, Ge Yang, Kartik Paigwar et al., Robotics: Science and Systems (RSS) 2022, and periodic reward composition yields standing, walking, hopping, running and skipping on Cassie^{Source 18}18 Siekmann et al. 2020, Sim-to-Real Learning of All Common Bipedal Gaits via Periodic Reward Composition. Jonah Siekmann, Yesh Godse, Alan Fern et al., arXiv preprint (ICRA 2021), 2020.

From quadrupeds to humanoids

On Unitree's H1, H2O turns RGB-camera human pose estimates into real-time whole-body teleoperationteleoperationTeleoperation is direct remote control of a robot by a human operator, used in robot learning mostly to record expert demonstrations. In the cheap, precise ALOHA rig, the operator back-drives a leader arm twinning the follower joint for joint, so recordings are in the robot's own action space. Mobile ALOHA extended this leader-follower scheme to a mobile base for whole-body tasks.: it fits and retargetsretargetingRetargeting is mapping motion recorded on one body, usually a human's, onto a robot with different proportions and joint limits, so human demonstrations become references the robot can track. Raw retargeting ignores the robot's physical constraints and can produce morphologically infeasible references. H2O and ASAP therefore add reinforcement learning that restores balance and contact feasibility on the real body. AMASS motions, filters those a privileged imitator cannot track, and trains a tracking policy with domain randomization that outputs 19 joint-position targets to a PD controller. The robot side also uses motion capture for linear velocity^{Source 8}8 He et al. 2024, Learning Human-to-Humanoid Real-Time Whole-Body Teleoperation. Tairan He, Zhengyi Luo, Wenli Xiao et al., IROS 2024.

On the G1 with fixed wrists, ASAP trains an ankle delta-action model from real rollouts, freezes it in simulation for fine-tuning, and deploys the policy without it. Its quantitative hardware comparison against Vanilla covers only kicking and LeBron's "Silencer"^{Source 9}9 He et al. 2025, ASAP: Aligning Simulation and Real-World Physics for Learning Agile Humanoid Whole-Body Skills. Tairan He, Jiawei Gao, Wenli Xiao et al., RSS 2025.

A causal transformer over proprioceptive history gave humanoids a fully learned controller that deployed zero-shot^{Source 19}19 Radosavovic et al. 2023, Real-World Humanoid Locomotion with Reinforcement Learning. Ilija Radosavovic, Tete Xiao, Bike Zhang et al., arXiv preprint (Science Robotics 2024), 2023. Cassie's dual-history controller ran a 400-meter dash^{Source 20}20 Li et al. 2024, Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control. Zhongyu Li, Xue Bin Peng, Pieter Abbeel et al., International Journal of Robotics Research, 2024, a miniature soccer humanoid walked 181% faster and turned 302% faster than a scripted baseline^{Source 21}21 Haarnoja et al. 2023, Learning Agile Soccer Skills for a Bipedal Robot with Deep Reinforcement Learning. Tuomas Haarnoja, Ben Moran, Guy Lever et al., arXiv preprint (Science Robotics 2024), 2023, and Hiking in the Wild maps raw depth and proprioception to joint actions without external state estimation, at up to 2.5 m/s^{Source 22}22 Zhu et al. 2026, Hiking in the Wild: A Scalable Perceptive Parkour Framework for Humanoids. Shaoting Zhu, Ziwen Zhuang, Mengjie Zhao et al., 2026.

Joshua Aurand, Marco Hutter and colleagues at Disney Research Zurich and ETH Zurich (October 2026) built Walk Like This, which sets walking style from a reference clip and speed from a joystick: a diffusion model generates the styled motion and an RL policy tracks it^{Source 31}31 Aurand et al. 2026, Walk Like This: Stylized Locomotion for Physics-Based Characters through Example-Driven Diffusion. Joshua Aurand, Agon Serifi, Sammy Christen et al., 2026. In simulation, a tracker trained on generated motion fell 0.001 times per minute while following the diffusion output, against 1.104 for one trained on the original motion capture, at the cost of larger tracking errors^{Source 31}31 Aurand et al. 2026, Walk Like This: Stylized Locomotion for Physics-Based Characters through Example-Driven Diffusion. Joshua Aurand, Agon Serifi, Sammy Christen et al., 2026. On a Unitree G1 the authors report about 4 hours of zero-shot deployment across styles without a failure^{Source 31}31 Aurand et al. 2026, Walk Like This: Stylized Locomotion for Physics-Based Characters through Example-Driven Diffusion. Joshua Aurand, Agon Serifi, Sammy Christen et al., 2026.

Photo: Oregon State University / Wikimedia Commons. Licence: CC BY-SA 2.0.

Jeon and colleagues compared rewards for a simulated 18-DoF MIT Humanoid running with arms fixed and ten leg joints controlled, holding PPOPPOPPO (proximal policy optimization) is the on-policy reinforcement learning algorithm the locomotion literature standardized on. Schulman and colleagues introduced it as a policy gradient method alternating between sampling environment data and optimizing a surrogate objective by stochastic gradient ascent. The surrogate allows several minibatch epochs per batch where standard policy gradient takes one step. It keeps most of trust region policy optimization's reliability without second-order machinery, and suits massively parallel simulation, whose thousands of robots supply its enormous on-policy batches.-Clip^{Source 23}23 Schulman et al. 2017, Proximal Policy Optimization Algorithms. John Schulman, Filip Wolski, Prafulla Dhariwal et al., 2017 and IsaacGym fixed. Ten runs per case converged to similar performance within 1,000 iterations, potential-based shaping was less sensitive across a 0.1 to 10 times weight sweep, and the practical variant set the shaping discount to 1 against PPO's 0.99, which the authors say sacrifices policy invariance^{Source 10}10 Jeon et al. 2023, Benchmarking Potential Based Rewards for Learning Humanoid Locomotion. Se Hwan Jeon, Steve Heim, Charles Khazoom et al., ICRA 2023.

Industrial adoption

Boston Dynamics says Spot's earlier controller evaluated dozens of MPCmodel predictive controlModel predictive control is constant re-planning against an explicit dynamics model: each step it optimizes a short action sequence, executes only the first action and re-solves from the measured state. Per-step feedback corrects model error instead of freezing it into policy weights, so MPC shows less frozen-policy sim-to-real failure; a wrong model still costs closed-loop performance. Long assumed too slow for full robot dynamics, whole-body MPC now runs in real time on quadruped and humanoid hardware with Zhang and colleagues' MuJoCo-based iLQR controller. Posted in 2025, it was revised in 2026 to appear at ICRA 2026. horizons with distinct step-trajectory references in under a millisecond and picked the highest-scoring output. Its 2024 account adds a learned policy, keeps the model-based controller for what it does well and drops the parallel MPC instances. Spot now falls less, the company reports, including on extremely slick or irregular surfaces, without a numerical fall rate, and a separate research architecture climbs boxes over 70 cm^{Source 12}12 Boston Dynamics 2024, Starting on the Right Foot with Reinforcement Learning. Boston Dynamics, 2024.

Boston Dynamics benchmarks policies in simulation, then on an internal Spot robustness fleet running 24/7 for over 2,000 cumulative hours a week; falls reproducible in simulation are recreated for training or evaluation^{Source 12}12 Boston Dynamics 2024, Starting on the Right Foot with Reinforcement Learning. Boston Dynamics, 2024.

On 19 March 2025 the RAI Institute described an Atlas policy that tracks retargeted human motion, each maneuver built from about 150 million simulator runs and transferred zero-shot^{Source 11}11 RAI Institute 2025, Reinforcement Learning Accelerates Humanoid Behavior Production. Robotics and AI Institute, 2025. Boston Dynamics later said Atlas practiced "for millions of hours in simulations in parallel", with only rotary actuators that are easier to represent in simulation^{Source 24}24 Rodriguez et al. 2026, Training a Humanoid Robot for Hard Work. Alberto Rodriguez, Shane Rozen-Levy, Vinay Kamidi, Boston Dynamics blog, 2026.

In August 2025, Boston Dynamics and Toyota Research Institute reported Large Behavior Models on Atlas: a 450M-parameter diffusion transformer trained with flow matchingflow matchingFlow matching is a generative modeling recipe that learns a time-dependent vector field carrying noise to data, by regressing against the conditional flow instead of estimating a score. In pi0, which brought it to robot control, an action expert trained this way denoises continuous action chunks. Integrating the field as an ODE for a handful of steps is fast enough for high-frequency control and keeps diffusion policies' multimodality. on curated teleoperated demonstrations from hardware and simulation. It controls the full robot at 30 Hz, predicting 48 actions (1.6 seconds) per inference and most often executing 24 (0.8 seconds at 1x speed), and the neural policies share its control interface with an MPC-based teleoperation system^{Source 13}13 Cousineau et al. 2025, Large Behavior Models and Atlas Find New Footing. Eric Cousineau, Scott Kuindersma, Lucas Manuelli et al., 2025. Boston Dynamics unveiled the product version of Atlas at CES on 5 January 2026 and committed its 2026 fleets to Hyundai and Google DeepMind^{Source 30}30 Boston Dynamics 2026, Boston Dynamics Unveils New Atlas Robot to Revolutionize Industry. Boston Dynamics, 2026.

Agility reports that Digit's whole-body control model, an LSTM with fewer than one million parameters, trains in Isaac Sim for decades of simulated time over three or four days and transfers zero-shot^{Source 25}25 Agility Robotics 2025, Training a Whole-Body Control Foundation Model. Agility Robotics, Agility Robotics blog, 2025. Figure reports that its S0 whole-body policy, now conditioned on camera perception, traverses real-world stairs^{Source 26}26 Figure AI 2026, Ramping Figure 03 Production. Figure AI, Figure AI news, 2026.

Limits of the lineage

Contact-rich manipulation is harder to simulate: Acosta and colleagues call dynamic contact the computational bottleneck for most simulations^{Source 27}27 Acosta et al. 2021, Validating Robotics Simulators on Real-World Impacts. Brian Acosta, William Yang, Michael Posa, arXiv preprint (IEEE RA-L / IROS 2022), 2021, and the locomotion-manipulation comparison explains why. Eureka's LLM-written rewards beat human experts on 83% of 29 environments^{Source 28}28 Ma et al. 2024, Eureka: Human-Level Reward Design via Coding Large Language Models. Yecheng Jason Ma, William Liang, Guanzhi Wang et al., ICLR 2024, and DrEureka writes both reward functions and domain-randomization distributions, getting a quadruped to walk atop a yoga ball^{Source 29}29 Ma et al. 2024, DrEureka: Language Model Guided Sim-To-Real Transfer. Yecheng Jason Ma, William Liang, Hung-Ju Wang et al., RSS 2024.

Lukas Amiet, Marco Hutter, Cesar Cadena and colleagues at ETH Zurich (October 2026) had an ANYmal D quadruped solve a Rubik's Cube with its feet; the cube is 0.4 m on a side and weighs 4.6 kg, and the robot flips it or pins it with one foot while the other pushes a layer round^{Source 32}32 Amiet et al. 2026, Solving a Giant Rubik's Cube with a Quadruped Robot. Lukas Amiet, Gabriel Sánchez-Blanco Repgen, Mayank Mittal et al., 2026. Skills trained with privileged RL and distilled into policies that read onboard depth and proprioception completed all three attempted hardware solves without intervention, each about 30 steps over 8 to 9 minutes^{Source 32}32 Amiet et al. 2026, Solving a Giant Rubik's Cube with a Quadruped Robot. Lukas Amiet, Gabriel Sánchez-Blanco Repgen, Mayank Mittal et al., 2026. In separate skill trials both flips succeeded 15 of 15 times, while the counterclockwise layer turn succeeded 13 of 15 times and the clockwise turn 10 of 15^{Source 32}32 Amiet et al. 2026, Solving a Giant Rubik's Cube with a Quadruped Robot. Lukas Amiet, Gabriel Sánchez-Blanco Repgen, Mayank Mittal et al., 2026.