Felis

A cat-inspired robot with an actuated spine.

Zhiyang Dou^*†, Pengfei Ye^*, Yuxiang Ma^*, Ken Suzuki^*, Zeshi Yang^*, Yiming Huang, WeiHsi Chen, Yujie Wang, Minghao Guo, Wenping Wang, Taku Komura, Wojciech Matusik, Cynthia Sung, Lingjie Liu

^*Co-first authors^†Project Lead

Code, Coming soon
Technical report, Coming soon

Teaser video not delivered yet

A cat-inspired legged robot with an actuated universal-joint spine, designed to right itself in midair, walk, turn, jump, and dance with only six motors.

The real Felis robot, three-quarter side view

The real Felis robot, front three-quarter view with its open front end

The robot as built.

Actuation moves from the legs to the spine.

A falling cat lands on its feet by bending and twisting its spine, so that the front and rear halves of its body rotate against each other. Shape change alone turns it over, with no net angular momentum. Most legged robots keep a rigid trunk and put many motors in the legs. We move the actuation into the body instead. Felis joins two body segments with a motor-driven two-axis universal joint at the waist and uses one motor per leg, six in total, half as many as a conventional quadruped. In physics simulation, the spine lets the robot right itself from an upside-down fall before touchdown. On the ground it walks forward and backward, turns in place, jumps and moves in time with music. An actuated spine can take over work usually done by leg motors, which could make legged robots lighter and simpler, with fewer motors.

Felis 6

Conventional quadruped 12

Motor in the spineMotor in a leg

Righting itself in midair.

Released upside down in physics simulation, Felis turns over and lands on its feet.

Video not delivered yet

Slowed down, with the camera circling the robot as it turns.

Five phases of mid-air righting: a real cat in the left column, Felis in the right column — A real cat and Felis, side by side through five phases of the turn. Times are the robot’s, measured from release.Cat photographs: NHPA, from I. Stewart, *Nature* 430, 731 (2004).

One motor per leg.

Forward and backward, turning, and jumping. Each motion plays as a studio render, with the physics simulation in the corner.

Simulation not delivered yet

Render not delivered yet

New parts, same six motors.

Felis takes add-on modules. The first is a longer leg. A connector and a second rod make each leg about half again as long and add no motors. Here it walks forward on the longer legs, in physics simulation.

Felis with its standard legs on the left and the longer legs on the right — Standard legs, 130 mm from hip to foot, and longer legs, 200 mm.

Simulation not delivered yet

Render not delivered yet

Moving in time with music.

Three songs, each staged in its own look. The physics simulation plays in the lower-left corner.

Video not delivered yet

LED show“Bar Bar Bar”, Crayon Pop

Video not delivered yet

Concert stage“I Was Born to Love You”, Freddie Mercury

Video not delivered yet

TV studio“Kiyoku Tadashiku Kabutack”, Takeshi Kusao

Music excerpts are used for non-commercial research demonstration only. All rights belong to their respective owners.

Timeline

2023HKUThe ideaThe idea, and the first simulation environments, built and validated for a quadruped cat, a quadruped dog and an astronaut.With Zeshi Yang (SFU)Advisors: Taku Komura, Wenping Wang
2024–2025HKU & UPennFirst and second robotsThe first two versions of the robot.With Ken Suzuki, WeiHsi Chen and Cynthia SungAdvisors: Lingjie Liu, Cynthia Sung
2025–2026MITThird robotThe third version, the robot shown on this page.With Pengfei Ye and Yuxiang MaAdvisor: Wojciech Matusik

Reading list

Felis builds on more than a century of work on how a falling cat turns over, and on decades of legged robots with articulated bodies and few motors. Robots have turned themselves over in midair by bending their bodies, swinging tails or moving their legs. Spines have helped legged robots run, turn and even walk without leg motors. Robots have also danced to music. This list collects the work we draw on. We want to bring these ideas together in a small robot that is practical to build and use.

The falling cat

10 works

1894
Des mouvements que certains animaux exécutent pour retomber sur leurs pieds, lorsqu'ils sont précipités d'un lieu élevé
É.-J. Marey. Comptes rendus de l'Académie des sciences 119, 714–717.

Chronophotographs of a cat dropped back-down and turning over in midair.
1936
Das Umdrehen der fallenden Katze in der Luft
G. G. J. Rademaker, J. W. G. ter Braak. Acta Oto-Laryngologica 23(2), 313–343.

Describes how the cat bends and twists its body to turn over.
1969
A dynamical explanation of the falling cat phenomenon
T. R. Kane, M. P. Scher. International Journal of Solids and Structures 5(7), 663–670.

Two bodies that bend but do not twist relative to each other can turn over with zero angular momentum.
1989
Gauge kinematics of deformable bodies
A. Shapere, F. Wilczek. American Journal of Physics 57(6), 514–518.

Rotation produced by a cycle of shape changes, explained as a geometric phase, with the cat as an example.
1993
Gauge theory of the falling cat
R. Montgomery. Fields Institute Communications 1, 193–218.

The two-body falling cat recast in the language of gauge theory.
1998
A distributed control model for the air-righting reflex of a cat
A. Arabyan, D. Tsai. Biological Cybernetics 79(5), 393–401.

A multibody cat model that turns over quickly and then holds its orientation.
2008
Active tails enhance arboreal acrobatics in geckos
A. Jusufi et al. PNAS 105(11), 4215–4219.

Geckos right themselves in midair by swinging their tails.
2012
Tail-assisted pitch control in lizards, robots and dinosaurs
T. Libby et al. Nature 481, 181–184.

Lizards and a lizard-sized robot control their pitch in flight by moving the tail.
2019
Falling Felines and Fundamental Physics
G. J. Gbur. Yale University Press.

A book-length history of the falling-cat problem and the physics around it.
2021
Geometry, Mechanics, and Control in Action for the Falling Cat
T. Iwai. Lecture Notes in Mathematics, Springer.

A monograph on the geometry, mechanics and control of the falling cat.

Robots that right themselves in midair

52 works

1990
Dynamics and optimal control of a legged robot in flight phase
Z. Li, R. Montgomery. IEEE International Conference on Robotics and Automation (ICRA 1990), 1816–1821.

Optimal reorientation of a legged robot in flight by changing its shape, in theory and simulation.
1991
Physical explication and realization of the turning motion of a cat by analysis and experiment using a robot cat
T. Kawamura, K. Yamafuji, T. Kobayashi. Journal of Robotics and Mechatronics 3(5), 437–442.

A robot cat with an actuated backbone turns 180° within 0.6 s after being released upside down.
1992
Elucidation of twisting motion of a falling cat and its realization by a robot
K. Yamafuji, T. Kobayashi, T. Kawamura. Journal of the Robotics Society of Japan 10(5), 648–654 (in Japanese).

A jointed two-column model of the cat's twist, realised on a robot.
1993
A study on the control of the rotational maneuvers of a robot in midair
E. Nakano, M. Tsuchiya. Journal of the Robotics Society of Japan 11(1), 91–99 (in Japanese).

A robot turns over in midair with zero angular momentum by changing its shape, shown in experiments.
1994
Posture detection and landing control of robot thrown in midair
K. Yamafuji, K. Honda, T. Kobayashi. Journal of Robotics and Mechatronics 6(5), 434–439.

Rate gyros estimate a thrown robot's attitude in flight, and its legs are turned toward the ground for landing.
2000
Final-state control of a two-link cat robot by feedforward torque inputs
Z. Weng, H. Nishimura. 6th International Workshop on Advanced Motion Control (AMC 2000), 264–269.

Two rigid bodies joined by two orthogonal waist torques reach a target attitude, in simulation.
2000
3D posture control by using the cat-turn motion
A. Miyajima, K. Yamafuji, T. Tanaka. International Symposium on Adaptive Motion of Animals and Machines (AMAM 2000), Montréal, paper E23.

A "double cat-turn" about two perpendicular axes changes a body's attitude in three dimensions.
2008
Posture control of a free falling robotic cat for soft landing using reinforcement learning
J.-J. Lee, B. G. Shin, J. J. Kim. International Conference on Humanized Systems (ICHS 2008), 83–87.

Reinforcement learning of the landing posture for a two-segment cat model, in simulation.
2012
Control of a free-falling cat by policy-based reinforcement learning
D. Nakano, S. Maeda, S. Ishii. Artificial Neural Networks and Machine Learning (ICANN 2012), Lecture Notes in Computer Science, 116–123.

Policy-gradient learning of falling-cat control, in simulation.
2013
Falling cat robot lands on its feet
B. Shields et al. Australasian Conference on Robotics and Automation (ACRA 2013), Sydney, 74–82.

A two-body falling-cat robot model with input torques that turn it over from any starting angle, checked in simulation.
2013
Modeling, design and simulation of falling and landing process in a robotic cat
S. M. H. Sadati. MSc thesis, Sharif University of Technology (in Persian).

Models falling-cat robots from two to eight links, optimizes their dimensions and plans a staged landing.
2014
Orienting in mid-air through configuration changes to achieve a rolling landing for reducing impact after a fall
J. T. Bingham et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2014), 3610–3617.

Cat-inspired midair reorientation of jointed robots ahead of a rolling landing.
2014
Understanding of falling cat phenomenon and realization by robot
T. Kawamura. Journal of Robotics and Mechatronics 26(6), 685–690.

A review of the robot-cat line, including a robot with vertebra-like backbones that rights itself.
2016
Research on trajectory planning of a robot inspired by free-falling cat based on modified quasi-Newton algorithm
X. Liang, L. Xu, L. Li. IEEE International Conference on Mechatronics and Automation (ICMA 2016), 552–557.

Plans the turning trajectory of a two-cylinder falling-cat robot model in simulation.
2017
Research on time-optimal falling trajectory of a free-falling cat robot
X. Liang et al. Robot 39(3), 355–362 (in Chinese).

Time-optimal righting trajectories for a two-body cat robot with a waist hinge, tested on a virtual prototype.
2017
Effect of swing legs on turning motion of a free-falling cat robot
J. Zhao, L. Li, B. Feng. IEEE International Conference on Mechatronics and Automation (ICMA 2017), 658–664.

Studies how swinging the legs changes the turning motion of a falling-cat robot model.
2017
Singularity-free planning for a robot cat free-fall with control delay: role of limbs and tail
S. M. H. Sadati, A. Meghdari. International Conference on Mechanical and Aerospace Engineering (ICMAE 2017), 215–221.

Free-fall planning for a cat model with two waist rotations, limbs and a tail, in simulation.
2018
Falling cat robot feedback acquisition and its evaluation
K. Furutachi et al. Robotics Institute Summer Scholars poster, Carnegie Mellon University.

Fast sensing for the CMU Biorobotics Lab's falling-cat robot during a fall of about half a second.
2018
Stickman: towards a human scale acrobatic robot
M. T. Pope et al. IEEE International Conference on Robotics and Automation (ICRA 2018), 2134–2140.

A human-scale acrobatic robot controls its rotation in flight by tucking its body.
2019
SpaceBok: a dynamic legged robot for space exploration
P. Arm et al. International Conference on Robotics and Automation (ICRA 2019), 6288–6294.

A legged robot built for dynamic jumping in low gravity.
2021
Design and experimental validation of reorientation manoeuvres for a free falling robot inspired from the cat righting reflex
X. Garant, C. Gosselin. IEEE Transactions on Robotics 37(2), 482–493.

An articulated robot rolls 180° in free fall through cycles of its internal joints, shown in drop experiments.
2021
Online trajectory optimization for dynamic aerial motions of a quadruped robot
M. Chignoli, S. Kim. IEEE International Conference on Robotics and Automation (ICRA 2021), 7693–7699.

Online trajectory optimization for flips, barrel rolls and spins of a quadruped in the air.
2022
Cat-like jumping and landing of legged robots in low gravity using deep reinforcement learning
N. Rudin et al. IEEE Transactions on Robotics 38(1), 317–328.

Learned leg motions reorient a legged robot in flight so that it lands on its feet in low gravity.
2022
Mini Cheetah, the falling cat: a case study in machine learning and trajectory optimization for robot acrobatics
V. Kurtz et al. IEEE International Conference on Robotics and Automation (ICRA 2022), 4635–4641 (arXiv:2109.04424).

A quadruped rights itself in midair with its legs, using learning and trajectory optimization.
2022
Planification et réalisation de manœuvres de réorientation de robots en chute libre [Planning and execution of reorientation manoeuvres for free-falling robots]
M. Charlet. MSc thesis, Université Laval (in French).

Fast and multi-axis reorientation of free-falling robots inspired by the cat, with a 180-degree pitch turn on a test platform.
2022
Reorientation of free-falling legged robots
M. Charlet, C. Gosselin. ASME Open Journal of Engineering 1, 011009.

Two manoeuvres inspired by the cat's reflex reorient a free-falling legged robot in roll and pitch.
2022
A review of research on falling cat phenomenon and development of bio-falling cat robot
J. Cao et al. WRC Symposium on Advanced Robotics and Automation (WRC SARA 2022), 160–165.

Reviews research on the falling cat and on robots that imitate it.
2022
On the dynamics and control of a squirrel locking its head/eyes toward a fixed spot for safe landing while its body is tumbling in air
T. Ma, T. Zhang, O. Ma. Frontiers in Robotics and AI 9, 1030601.

A multi-segment model reorients its body by joint motion in the air while the head stays fixed.
2022
Online optimal landing control of the MIT Mini Cheetah
S. H. Jeon, S. Kim, D. Kim. International Conference on Robotics and Automation (ICRA 2022), 178–184.

Online optimal landing control for a quadruped dropped from height.
2023
Reactive landing controller for quadruped robots
F. Roscia et al. IEEE Robotics and Automation Letters 8(11), 7210–7217.

A reactive controller for landing quadruped robots.
2023
Evaluation of legged robot landing capability under aggressive linear and angular velocities
K. Ye, K. Karydis. IEEE International Conference on Robotics and Automation (ICRA 2023), 12184–12190.

Measures how well legged robots can land at high linear and angular velocities.
2023
Integrated attitude and landing control for quadruped robots in asteroid landing mission scenarios using reinforcement learning
J. Qi et al. Acta Astronautica 204, 599–610.

Learned attitude and landing control for quadruped robots landing on asteroids.
2024
Reinforcement learning and sim-to-real transfer of reorientation and landing control for quadruped robots on asteroids
J. Qi et al. IEEE Transactions on Industrial Electronics 71(11), 14392–14400.

Learned reorientation and landing control for quadrupeds in low gravity, transferred from simulation to hardware.
2024
Robust orientation correction control for a falling quadruped with an active spine
V. Parsuram. MS thesis, Worcester Polytechnic Institute.

A real-time controller inspired by the cat's righting reflex reorients a falling quadruped with a two-DoF active spine.
2024
In-flight attitude control of a quadruped using deep reinforcement learning
T. El-Agroudi et al. Conference on Robot Learning (CoRL 2024), PMLR 270, 5014–5029.

A small quadruped controls its attitude during free fall using only its legs, with a learned policy.
2024
Reorientation of a bio-cat falling legged robot driven by pneumatic muscles with energy optimization
X. Zhu et al. WRC Symposium on Advanced Robotics and Automation (WRC SARA 2024), 228–234.

A falling legged robot with a flexible pneumatic-muscle spine reorients itself with minimum energy.
2024
Neural control and learning of a gecko-inspired robot for aerial self-righting
L. Chanfreau, W. Haomachai, P. Manoonpong. Synergetic Cooperation between Robots and Humans (CLAWAR 2023), Lecture Notes in Networks and Systems, 147–158.

Neural control and learning for aerial self-righting of gecko-inspired robot variants.
2024
SpaceHopper: a small-scale legged robot for exploring low-gravity celestial bodies
A. Spiridonov et al. IEEE International Conference on Robotics and Automation (ICRA 2024), 3464–3470.

A small three-legged robot for low gravity that controls its attitude in flight with its legs.
2024
Modeling and in-flight torso attitude stabilization of a jumping quadruped
M. Papadakis et al. arXiv:2409.14567 (preprint).

Stabilizes the torso attitude of a jumping quadruped in flight by moving its legs.
2024
Model predictive attitude control of a jumping-and-flying quadruped for planetary exploration
A. Westre, J. A. Olsen, K. Alexis. IEEE Aerospace Conference (AERO 2024), 1–12.

Model predictive attitude control of a quadruped during long flights.
2025
Olympus: a jumping quadruped for planetary exploration utilizing reinforcement learning for in-flight attitude control
J. A. Olsen, G. Malczyk, K. Alexis. IEEE International Conference on Robotics and Automation (ICRA 2025), 4366–4372.

A jumping quadruped for low-gravity exploration with learned in-flight attitude control.
2025
A generic continuous multi-joint spinal robotic system for agile and accurate behaviors with GNN-MPC method
Y. Wu et al. Robotics: Science and Systems XXI (RSS 2025).

A continuous multi-joint robotic spine, controlled with learned dynamics and model predictive control, flips itself in free fall.
2025
Global reorientation of a free-fall multibody system using periodical joint motions – theory and motion planning
T. Ma, T. Zhang, O. Ma. Multibody System Dynamics 65(2), 149–171.

Periodic joint motions reorient a free-falling multibody system to any attitude.
2025
Global reorientation of a free-fall robotic system using reconstruction loss-based deep learning method—theory and comparison
T. Ma, O. Ma, T. Zhang. Journal of Intelligent & Robotic Systems 111(2), 62.

A learned method for the global reorientation of a free-falling multibody robot.
2025
High accuracy aerial maneuvers on legged robots using variational integrator discretized trajectory optimization
S. Beck et al. IEEE International Conference on Robotics and Automation (ICRA 2025), 10253–10260.

Whole-body trajectory optimization for precise aerial manoeuvres of legged robots.
2025
Curriculum learning for landing of quadruped robots
S. Karan, S. Borate, M. Vadali. International Conference on Advances in Robotics (AIR 2025), 1–7.

Curriculum reinforcement learning for landing quadruped robots.
2025
Monopedal robot branch-to-branch leaping and landing inspired by squirrel balance control
J. K. Yim et al. Science Robotics 10(100), eadq1949.

A one-legged robot leaps between branches and lands, using balance strategies seen in squirrels.
2025
Conception et validation expérimentale d'un robot mobile robuste pouvant se réorienter en chute libre [Design and experimental validation of a robust mobile robot able to reorient itself in free fall]
C. Gravel. MSc thesis, Université Laval (in French).

Design and experimental validation of a robust mobile robot that reorients itself in free fall.
2026
S-Cheetah: a novel quadrupedal robot with a 3-DOF active spine learning agile locomotion
Z. Li, W. Bai. arXiv:2605.27909 (preprint).

A quadruped with a three-DoF active spine learns agile running and midair righting, in simulation.
2026
Nonlocomotory robotic strategies for dynamic rotation control in terrestrial robots: a review
Y. Liang et al. Advanced Robotics Research, e202500095.

A review of strategies such as tails and reaction wheels for controlling body rotation in terrestrial robots.
2026
Towards low-gravity planetary exploration using reinforcement learning for walking, jumping, and in-flight attitude control
J. A. Olsen, K. Alexis. arXiv:2605.24643 (preprint).

Learned walking, jumping and in-flight attitude control for a quadruped in low gravity.
2026
Residual-learning-based landing control with gravity estimation for quadruped robot in low-gravity scenarios
H. Xiao et al. Astrodynamics.

Learned landing control with gravity estimation for a quadruped in low gravity.

Tails, reaction wheels and other appendages

43 works

2011
A lizard-inspired active tail enables rapid maneuvers and dynamic stabilization in a terrestrial robot
E. Chang-Siu et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011), 1887–1894.

A small robot with a one-DoF active tail stabilizes and reorients itself in midair.
2012
Tail assisted dynamic self righting
A. M. Johnson et al. Adaptive Mobile Robotics (CLAWAR 2012), 611–620.

A measure of how well a tail rights a robot in midair, tested on two robots of very different size.
2012
Tails in biomimetic design: analysis, simulation, and experiment
R. Briggs et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2012), 1473–1480.

Compares tails with reaction wheels for reorienting a body.
2012
Dynamic turning of 13 cm robot comparing tail and differential drive
A. O. Pullin et al. IEEE International Conference on Robotics and Automation (ICRA 2012), 5086–5093.

A small legged robot turns quickly with a tail, compared with differential drive.
2013
A nonlinear feedback controller for aerial self-righting by a tailed robot
E. Chang-Siu et al. IEEE International Conference on Robotics and Automation (ICRA 2013), 32–39.

Nonlinear feedback control lets a tailed robot right itself in the air.
2013
Precise dynamic turning of a 10 cm legged robot on a low friction surface using a tail
N. J. Kohut et al. IEEE International Conference on Robotics and Automation (ICRA 2013), 3299–3306.

A tail gives a small legged robot precise turns on a slippery surface.
2013
Rapid turning at high-speed: inspirations from the cheetah's tail
A. Patel, M. Braae. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2013), 5506–5511.

A cheetah-inspired tail for rapid turning at high speed.
2013
Controlling aerial maneuvering of a miniature jumping robot using its tail
J. Zhao et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2013).

A tail controls the attitude of a miniature jumping robot in the air.
2014
Rapid acceleration and braking: inspirations from the cheetah's tail
A. Patel, M. Braae. IEEE International Conference on Robotics and Automation (ICRA 2014), 793–799.

A cheetah-inspired tail for rapid acceleration and braking.
2014
A bio-inspired hopping kangaroo robot with an active tail
G.-H. Liu et al. Journal of Bionic Engineering 11(4), 541–555.

A hopping kangaroo robot with an actively controlled tail.
2015
On the conical motion of a two-degree-of-freedom tail inspired by the cheetah
A. Patel, E. Boje. IEEE Transactions on Robotics 31(6), 1555–1560.

Conical motion of a two-degree-of-freedom tail for body reorientation.
2015
MSU Tailbot: controlling aerial maneuver of a miniature-tailed jumping robot
J. Zhao et al. IEEE/ASME Transactions on Mechatronics 20(6), 2903–2914.

A miniature jumping robot controls its aerial manoeuvres with a tail.
2015
Parallel composition of templates for tail-energized planar hopping
A. De, D. E. Koditschek. IEEE International Conference on Robotics and Automation (ICRA 2015), 4562–4569.

A tail energizes and stabilizes planar hopping.
2015
Tail-assisted rigid and compliant legged leaping
A. L. Brill et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2015), 6304–6311.

A tail assists leaping with rigid and with compliant legs.
2016
Robotic vertical jumping agility via series-elastic power modulation
D. W. Haldane et al. Science Robotics 1(1), eaag2048.

The jumping robot Salto controls its pitch in flight with an inertial tail.
2016
Comparative design, scaling, and control of appendages for inertial reorientation
T. Libby et al. IEEE Transactions on Robotics 32(6), 1380–1398 (arXiv:1511.05958).

Compares tails, reaction wheels and moving body segments, including an actuated body joint, for reorienting in flight.
2016
Frontal plane stabilization and hopping with a 2DOF tail
G. Wenger, A. De, D. E. Koditschek. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2016), 567–573.

A two-degree-of-freedom tail stabilizes a hopping robot in the frontal plane.
2016
On designing an active tail for legged robots: simplifying control via decoupling of control objectives
S. W. Heim et al. Industrial Robot 43(3), 338–346.

Designs an active tail for legged robots with decoupled control objectives.
2017
Repetitive extreme-acceleration (14-g) spatial jumping with Salto-1P
D. W. Haldane, J. K. Yim, R. S. Fearing. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2017), 3345–3351.

Repeated jumping in three dimensions, with a tail for pitch and thrusters for roll and yaw.
2018
Modeling and control of an articulated tail for maneuvering a reduced degree of freedom legged robot
W. Saab, J. Yang, P. Ben-Tzvi. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2018), 2695–2700.

A tail steers and balances a quadruped whose legs only propel it.
2018
Steering of an underactuated legged robot through terrain contact with an active tail
C. S. Casarez, R. S. Fearing. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2018), 2739–2746.

A tail steers an underactuated legged robot by touching the ground.
2018
Precision jumping limits from flight-phase control in Salto-1P
J. K. Yim, R. S. Fearing. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2018), 2229–2236.

How flight-phase control with a tail limits the precision of jumping.
2019
Towards jumping locomotion for quadruped robots on the moon
H. Kolvenbach et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2019), 5459–5466.

A quadruped built for lunar gravity controls its pitch in flight with a reaction wheel.
2020
Dynamics and aerial attitude control for rapid emergency deployment of the agile ground robot AGRO
D. J. Gonzalez et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2020), 2577–2584.

A cat-inspired ground robot uses its wheels as reaction wheels to control its attitude when dropped.
2021
Dynamic modeling, analysis, and design synthesis of a reduced complexity quadruped with a serpentine robotic tail
Y. Liu, P. Ben-Tzvi. Integrative and Comparative Biology 61(2), 464–477.

A quadruped with single-DoF legs and a serpentine tail for righting and maneuvering, in simulation.
2021
Dynamic modeling, analysis, and comparative study of a quadruped with bio-inspired robotic tails
Y. Liu, P. Ben-Tzvi. Multibody System Dynamics 51(2), 195–219.

Compares a quadruped model with different bio-inspired robotic tails.
2021
Real-time planning and nonlinear control for quadrupedal locomotion with articulated tails
R. T. Fawcett et al. Journal of Dynamic Systems, Measurement, and Control 143(7), 071004.

Real-time planning and control for quadruped locomotion with articulated tails.
2021
Enabling dynamic behaviors with aerodynamic drag in lightweight tails
J. Norby et al. IEEE Transactions on Robotics 37(4), 1144–1153.

Lightweight tails that use aerodynamic drag enable dynamic behaviours, including reorientation in the air.
2021
Tails stabilize landing of gliding geckos crashing head-first into tree trunks
R. Siddall et al. Communications Biology 4, 1020.

Tails stabilize the head-first landing of gliding geckos, tested with a soft robot model.
2022
Design and experimental validation of a monopod robot with 3-DoF morphable inertial tail for somersault
J. An et al. IEEE/ASME Transactions on Mechatronics 27(6), 5072–5083.

A one-legged robot with a three-degree-of-freedom morphable inertial tail performs somersaults.
2023
Towards safe landing of falling quadruped robots using a 3-DoF morphable inertial tail
Y. Tang et al. IEEE International Conference on Robotics and Automation (ICRA 2023), 1141–1147.

A three-DoF tail mounted on a quadruped reorients it during falls for a safe landing.
2023
Combining tail and reaction wheel for underactuated spatial reorientation in robot falling with quadratic programming
X. Chu et al. IEEE Robotics and Automation Letters 8(11), 7783–7790.

A tail and a reaction wheel together reorient a falling robot in three dimensions.
2023
Enhanced balance for legged robots using reaction wheels
C.-Y. Lee et al. IEEE International Conference on Robotics and Automation (ICRA 2023), 9980–9987.

Pitch and roll reaction wheels improve the balance of a quadruped.
2023
Orientation control system: enhancing aerial maneuvers for quadruped robots
F. Roscia et al. Sensors 23(3), 1234.

Two reaction wheels control a quadruped's roll and pitch during aerial manoeuvres.
2023
Proprioception and tail control enable extreme terrain traversal by quadruped robots
Y. Yang et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2023), 735–742.

Proprioception and tail control let a quadruped cross extreme terrain.
2024
Enhanced aerial reorientation performance using a 3-DoF morphable inertial tail inspired by kangaroo rats
J. An et al. IEEE Robotics and Automation Letters 9(11), 9470–9477.

A kangaroo-rat-inspired morphable tail improves reorientation in the air.
2024
Manipulator as a tail: promoting dynamic stability for legged locomotion
H. Huang et al. IEEE International Conference on Robotics and Automation (ICRA 2024), 9712–9719.

A manipulator arm used as a tail improves the dynamic stability of a legged robot.
2024
Learning rapid turning, aerial reorientation, and balancing using manipulator as a tail
I. Yang, J. Hwangbo. arXiv:2407.10420 (preprint).

A quadruped learns to turn, reorient in the air and balance with an arm used as a tail.
2025
Jointed tails enhance control of three-dimensional body rotation
X. Fu et al. Journal of the Royal Society Interface 22(223), 20240355.

Jointed tails improve control of body rotation in three dimensions.
2025
Tethered variable inertial attitude control mechanisms through a modular jumping limbed robot
Y. Tanaka, A. Zhu, D. Hong. IEEE Aerospace Conference (AERO 2025), 1–11.

Attitude control by changing inertia on a modular jumping limbed robot.
2026
Enhanced quadruped locomotion via reaction wheels in low-gravity environments
C. Zhou et al. Acta Astronautica 247, 302–314.

Reaction wheels improve quadruped locomotion in low gravity.
2026
Underactuated multimodal jumping robot for extraterrestrial exploration
N. R. Wagner, J. K. Yim. arXiv:2603.06525 (preprint).

An underactuated jumping robot with reaction wheels for exploring other worlds.
2026
Dynamic modeling and attitude control of a reaction-wheel-based low-gravity bipedal hopper
S. Hari, M. V. S. Nikhil, R. P. Kumar. arXiv:2603.10670 (preprint).

A bipedal hopper controls its attitude with a reaction wheel in low gravity.

Spines and body joints in legged robots

62 works

1995
Control of vertebrate backbone system by using artificial rubber muscles (control of two-degree-of-freedom system by using three artificial rubber muscles)
T. Kawamura, H. Kawahara, M. Nakazawa. Journal of Robotics and Mechatronics 7(6), 483–487.

A vertebra-like backbone with a two-degree-of-freedom bending joint driven by three artificial rubber muscles.
1999
Mechanical construction and computer architecture of the four-legged walking machine BISAM
K. Berns et al. IEEE/ASME Transactions on Mechatronics 4(1), 32–38.

A four-legged walking machine with an active body joint.
2005
Development of biomimetic quadruped walking robot with 2-DOF waist joint
K.-H. Kim, S.-H. Park, Y.-J. Lee. Proceedings of SPIE 6042, 60423H.

A walking quadruped with a two-DoF waist joint.
2005
Discontinuous spinning gait of a quadruped walking robot with waist-joint
S.-H. Park, D.-S. Kim, Y.-J. Lee. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), 2744–2749.

A quadruped turns in place by using its waist joint.
2007
From swimming to walking with a salamander robot driven by a spinal cord model
A. J. Ijspeert et al. Science 315(5817), 1416–1420.

A salamander robot with an actuated spine and four single-motor legs swims and walks.
2007
Discontinuous zigzag gait planning of a quadruped walking robot with a waist-joint
S.-H. Park, Y.-J. Lee. Advanced Robotics 21(1–2), 143–164.

A waist joint shifts the body sideways to keep a walking quadruped stable.
2010
Hysteresis in gait transition induced by changing waist joint stiffness of a quadruped robot driven by nonlinear oscillators with phase resetting
S. Aoi et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2010), 1915–1920.

Changing the waist joint's stiffness changes a quadruped's gait transitions.
2010
Facilitating multi-modal locomotion in a quadruped robot utilizing passive oscillation of the spine structure
T. Takuma, M. Ikeda, T. Masuda. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2010), 4940–4945.

Passive oscillation of the spine lets a quadruped switch between gaits.
2010
Learning approach to study effect of flexible spine on running behavior of a quadruped robot
H. J. Bidgoly et al. Emerging Trends in Mobile Robotics (CLAWAR 2010), 1195–1201.

A learning approach to study how a flexible spine affects quadruped running.
2011
Effect of flexible spine on stability of a passive quadruped robot: experimental results
M. H. H. Kani et al. IEEE International Conference on Robotics and Biomimetics (ROBIO 2011), 2793–2798.

Experiments on how a flexible spine affects the stability of a passive quadruped.
2011
A study on trunk stiffness and gait stability in quadrupedal locomotion using musculoskeletal robot
K. Tsujita, K. Miki. International Conference on Advanced Robotics (ICAR 2011), 316–321.

Trunk stiffness and gait stability in a musculoskeletal quadruped modelled on the cat.
2011
Additional DOFs and sensors for bio-inspired locomotion: towards active spine, ankle joints, and feet for a quadruped robot
D. Kuehn et al. IEEE International Conference on Robotics and Biomimetics (ROBIO 2011), 2780–2786.

Adds an active spine, ankle joints and feet to a quadruped robot.
2012
Embodiment enables the spinal engine in quadruped robot locomotion
Q. Zhao et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2012), 2449–2456.

A quadruped with no actuated legs bounds, trots and turns by bending its spine.
2012
The function of the spine and its morphological effect in quadruped robot locomotion
Q. Zhao et al. IEEE International Conference on Robotics and Biomimetics (ROBIO 2012), 66–71.

The role of an actuated spine and its morphology in quadruped locomotion.
2013
Free-standing leaping experiments with a power-autonomous elastic-spined quadruped
J. L. Pusey et al. Proceedings of SPIE 8741, 87410W.

Canid, a power-autonomous quadruped with an actuated elastic spine, makes free-standing leaps.
2013
Benefits of an active spine supported bounding locomotion with a small compliant quadruped robot
M. Khoramshahi et al. IEEE International Conference on Robotics and Automation (ICRA 2013), 3329–3334.

An actuated spine helps a small compliant quadruped bound.
2013
Salamandra robotica II: an amphibious robot to study salamander-like swimming and walking gaits
A. Crespi et al. IEEE Transactions on Robotics 29(2), 308–320.

An amphibious salamander robot with a multi-joint trunk and one motor per leg.
2013
Spine dynamics as a computational resource in spine-driven quadruped locomotion
Q. Zhao et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2013), 1445–1451.

Uses the dynamics of a spine as a computational resource in spine-driven locomotion.
2013
The effect of spine actuation and stiffness on a pneumatically-driven quadruped robot for cheetah-like locomotion
Q. Zhao et al. IEEE International Conference on Robotics and Biomimetics (ROBIO 2013), 1807–1812.

How spine actuation and stiffness affect cheetah-like running of a pneumatic quadruped.
2013
Pneupard: a biomimetic musculoskeletal approach for a feline-inspired quadruped robot
A. Rosendo et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2013), 1452–1457.

A feline-inspired musculoskeletal quadruped robot.
2013
A bio-inspired quadruped robot with a global compliant spine
X. Zhang et al. IEEE International Conference on Robotics and Biomimetics (ROBIO 2013), 1312–1316.

A quadruped robot with a compliant spine along its whole body.
2014
Spine as an engine: effect of spine morphology on spine-driven quadruped locomotion
Q. Zhao et al. Advanced Robotics 28(6), 367–378.

How the shape of the spine affects locomotion when only the spine is actuated.
2014
Realization of three-dimensional walking of a cheetah-modeled bio-inspired quadruped robot
S. Nakatsu et al. IEEE International Conference on Robotics and Biomimetics (ROBIO 2014), 779–784.

Three-dimensional walking of a musculoskeletal quadruped modelled on the cheetah.
2015
Cheetah-cub-S: steering of a quadruped robot using trunk motion
K. Weinmeister et al. IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR 2015), 1–6.

A small quadruped steers by bending its trunk.
2015
Comparing the effect of different spine and leg designs for a small bounding quadruped robot
P. Eckert et al. IEEE International Conference on Robotics and Automation (ICRA 2015), 3128–3133.

Compares spine and leg designs on a small bounding quadruped.
2016
Model-based dynamic gait in a quadruped robot with waist actuation
C.-L. Chen et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2016), 2056–2061.

A quadruped with single-motor rotating legs and an actuated waist runs with dynamic gaits.
2016
Dynamic bending of bionic flexible body driven by pneumatic artificial muscles (PAMs) for spinning gait of quadruped robot
J. Lei, H. Yu, T. Wang. Chinese Journal of Mechanical Engineering 29(1), 11–20.

A flexible body bent by pneumatic muscles lets a quadruped turn on the spot.
2016
Development of a flexible coupled spine mechanism for a small quadruped robot
R. Kawasaki et al. IEEE International Conference on Robotics and Biomimetics (ROBIO 2016), 71–76.

A flexible coupled spine for a small cat-like quadruped.
2016
Hybrid quadruped bounding with a passive compliant spine and asymmetric segmented body
L. T. Phan et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2016), 3387–3392.

Bounding with a passive compliant spine and an asymmetric segmented body.
2017
Core actuation promotes self-manipulability on a direct-drive quadrupedal robot
J. Duperret, B. Kramer, D. E. Koditschek. International Symposium on Experimental Robotics (ISER 2016), Springer Proceedings in Advanced Robotics, 147–159.

Actuation at the body core enlarges a quadruped's reachable workspace for leaping and self-manipulation.
2017
Empirical validation of a spined sagittal-plane quadrupedal model
J. Duperret, D. E. Koditschek. IEEE International Conference on Robotics and Automation (ICRA 2017), 1058–1064.

Tests a spined sagittal-plane model of a quadruped against a robot.
2017
Bio-inspired control strategy study for the quadruped robot with a segmented spine
C. Wang et al. Industrial Robot 44(1), 85–93.

Bio-inspired control of a quadruped with a segmented spine.
2017
Study on quadruped bounding with a passive compliant spine
L. T. Phan et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2017), 2409–2414.

Bounding of a quadruped with a passive compliant spine.
2018
Design, simulation, and testing of a flexible actuated spine for quadruped robots
A. P. Sabelhaus et al. arXiv:1804.06527 (preprint).

In Laika, a quadruped with unactuated legs, the tensegrity spine alone lifts each foot.
2018
Turning strategies for the bounding quadruped robot with an active spine
Z. Wei et al. Industrial Robot 45(5), 657–668.

A bounding quadruped turns by bending its active spine.
2018
Analysis of using an active artificial spine in a quadruped robot
D. Kuehn et al. International Conference on Control, Automation and Robotics (ICCAR 2018), 37–42.

Analyses the use of an active artificial spine in a quadruped.
2019
Development of the neurorobotic mouse
P. Lucas et al. IEEE International Conference on Cyborg and Bionic Systems (CBS 2019), 299–304.

NeRmo, a robotic mouse with a flexible spine.
2019
Affordances and control of a spine morphology for robotic quadrupedal locomotion
J. M. Duperret. PhD thesis, University of Pennsylvania.

A doctoral study of what a spine offers a quadruped and how to control it.
2019
Walking pattern generation algorithm with waist motion for improving energy efficiency of quadruped robot
C. H. Kim, J.-Y. Kim. Transactions of the Korean Society of Mechanical Engineers A 43(4), 241–252 (in Korean).

Walking patterns with waist motion to save energy, in simulation.
2019
Synchronization of non-linear oscillators for neurobiologically inspired control on a bionic parallel waist of legged robot
Y. Zhu et al. Frontiers in Neurorobotics 13, 59.

Coupled oscillators control a bio-inspired parallel waist of a legged robot.
2019
Toward a gecko-inspired, climbing soft robot
L. Schiller, A. Seibel, J. Schlattmann. Frontiers in Neurorobotics 13, 106.

A soft gecko-inspired robot climbs with bending actuators in its legs and torso.
2020
Towards rich motion skills with the lightweight quadruped robot Serval
P. Eckert et al. Adaptive Behavior 28(3), 129–150.

A lightweight quadruped with an actuated multi-axis spine.
2020
Decentralized control mechanism for body–limb coordination in quadruped running
A. Fukuhara et al. Adaptive Behavior 28(3), 151–164.

Decentralized control coordinates an active trunk with the legs in quadruped running.
2020
Realization of a bio-inspired cheetah robot with a flexible spine
C. Wang et al. IEEE International Conference on Mechatronics and Automation (ICMA 2020), 1185–1190.

A cheetah-inspired robot with a flexible spine.
2020
Study on effects of spinal joint for running quadruped robots
L. T. Phan et al. Intelligent Service Robotics 13(1), 29–46.

Effects of a spinal joint on running quadruped robots.
2022
Coordinating tiny limbs and long bodies: geometric mechanics of lizard terrestrial swimming
B. Chong et al. PNAS 119(27), e2118456119.

A robot with two body joints and four one-DoF limbs moves on granular media, coordinated by geometric mechanics.
2022
Development of a small-sized quadruped robotic rat capable of multimodal motions
Q. Shi et al. IEEE Transactions on Robotics 38(5), 3027–3043.

SQuRo, a small robotic rat with an actuated waist that turns tightly and recovers from falls.
2022
A cheetah-mimicking quadruped running robot with 2DOF articulated trunk
Q. Wang et al. Robot 44(3), 257–266 (in Chinese).

A cheetah-like running quadruped with a two-degree-of-freedom trunk that lengthens its stride.
2023
Lateral flexion of a compliant spine improves motor performance in a bioinspired mouse robot
Z. Bing et al. Science Robotics 8(85), eadg7165.

Sideways bending of a compliant spine improves a mouse robot's stability, stride, speed and turning.
2023
Dynamic locomotion of a quadruped robot with active spine via model predictive control
W. Li, Z. Zhou, H. Cheng. IEEE International Conference on Robotics and Automation (ICRA 2023), 1185–1191.

Dynamic locomotion of a quadruped with an active spine using model predictive control.
2023
High-speed running quadruped robot with a multi-joint spine adopting a 1DoF closed-loop linkage
O. Matsumoto et al. Frontiers in Robotics and AI 10, 1148816.

A fast running quadruped with a multi-joint spine driven by a single-degree-of-freedom linkage.
2023
Optimal kinematic design of a robotic lizard using four-bar and five-bar mechanisms
V. S. Rajashekhar, D. Ghose, A. S. Arockia Doss. arXiv:2308.08151 (preprint).

A robotic lizard whose body motion drives its legs through linkages.
2025
A bio-inspired adjustable posture quadruped robot with laterally undulating spine for terradynamically challenging environments
S. K. Dutta, Y. Ozkan-Aydin. Scientific Reports 15, 27143.

A quadruped whose two halves are joined by a yaw-and-pitch body joint, with one hip servo per leg, crosses difficult terrain with an undulating spine.
2025
Design and gait control of a quadruped robot with a waist joint
F. Li, W. Zhang, G. Hong. Mechanical Design and Simulation, Lecture Notes in Mechanical Engineering, 227–235.

A quadruped with four single-joint legs and a waist joint that helps it steer.
2025
Enhancing the flexibility of a quadruped robot with a 2-DOF active spine using nonlinear model predictive control
Z. Yang et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2025), 12526–12532.

A quadruped with a two-DoF active spine, controlled by nonlinear model predictive control.
2025
Latissimus-dorsi-inspired wire mechanism for improving energy efficiency of quadruped robot locomotion
O. Matsumoto et al. Advanced Robotics 39(1), 30–47.

A wire mechanism inspired by the latissimus dorsi improves a quadruped's energy efficiency.
2025
Latissimus-dorsi-inspired trunk torsion mechanism for quadruped robot spine design
O. Matsumoto et al. Advanced Robotics 39(13), 791–805.

A spine design in which the trunk twists, inspired by the latissimus dorsi.
2025
Quadrupedal spine control strategies: exploring correlations between system dynamic responses and human perspectives
N. Hafner et al. Advanced Robotics 39(6), 273–290.

Relates spine control strategies of a quadruped to how people perceive its motion.
2025
Design and evaluation of lizard-inspired single-actuated robot
S. Nansai, N. Kamamichi. ROBOMECH Journal 12, 16.

A lizard-inspired robot propels and turns itself with a single actuator.
2025
Mechanical design of a quadruped robot with a two degree of freedom compliant spine
C. Lu et al. IEEE International Conference on Cyborg and Bionic Systems (CBS 2025), 87–92.

Mechanical design of a quadruped with a two-degree-of-freedom compliant spine.
2026
Flexible-torso quadruped robots: biomimetic principles, structural designs, and torso-limb coordination – a review
R. Yu, B. Wu. Advanced Robotics, 1–33.

A review of flexible-torso quadruped robots.
2026
Unlocking fast robotic locomotor propulsion through dynamic spine-leg synergy
R. Wang et al. Science Advances 12(39), eaed5603.

Dynamic coordination of spine and legs speeds up a small quadruped robot.

Legged robots with few motors

26 works

1998
SCOUT: a simple quadruped that walks, climbs, and runs
M. Buehler et al. IEEE International Conference on Robotics and Automation (ICRA 1998), 1707–1712.

One motor per leg, with a prototype that walks, turns and climbs a step, while running and stair climbing are shown in simulation.
1999
The design and control of Scout I, a simple quadruped robot
K. S. Yamazaki. MEng thesis, McGill University.

Design and control of Scout I, a simple quadruped with one actuated joint per leg.
1999
Stable open loop walking in quadruped robots with stick legs
M. Buehler et al. IEEE International Conference on Robotics and Automation (ICRA 1999), 2348–2353.

Stable open-loop walking of a quadruped with stick legs and one motor per leg.
2001
RHex: a simple and highly mobile hexapod robot
U. Saranli, M. Buehler, D. E. Koditschek. International Journal of Robotics Research 20(7), 616–631.

A hexapod with one motor per leg that moves fast over rough terrain.
2001
Quadruped robot running with a bounding gait
S. Talebi et al. Experimental Robotics VII, Lecture Notes in Control and Information Sciences, 281–289.

A quadruped with one actuator per leg runs with a bounding gait.
2004
Model-based dynamic self-righting maneuvers for a hexapedal robot
U. Saranli, A. A. Rizzi, D. E. Koditschek. International Journal of Robotics Research 23(9), 903–918.

RHex rights itself on the ground with dynamic, model-based leg maneuvers.
2004
"Cheap" rapid locomotion of a quadruped robot: self-stabilization of bounding gait
F. Iida, R. Pfeifer. Intelligent Autonomous Systems 8 (IAS-8), IOS Press, 642–649.

A quadruped driven only at the hips bounds with self-stabilization.
2004
Rotary gallop in the untethered quadrupedal robot Scout II
J. A. Smith, I. Poulakakis. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2004), 2556–2561.

A rotary gallop that traces a circle on a quadruped with one motor per leg.
2004
An approach to design a quadruped walking machine with a single actuator
H.-S. Yan, Y.-G. Chen. Transactions of the Canadian Society for Mechanical Engineering 27(4), 353–374.

Design of a quadruped walking machine driven by one actuator.
2005
Modeling and experiments of untethered quadrupedal running with a bounding gait: the Scout II robot
I. Poulakakis, J. A. Smith, M. Buehler. International Journal of Robotics Research 24(4), 239–256.

Scout II runs untethered with a bounding gait, with one hip actuator per leg.
2005
Exploiting body dynamics for controlling a running quadruped robot
F. Iida, G. Gómez, R. Pfeifer. International Conference on Advanced Robotics (ICAR 2005), 229–235.

One control parameter sets the speed of a running quadruped that exploits its body dynamics.
2006
PAW: a hybrid wheeled-leg robot
J. A. Smith, I. Sharf, M. Trentini. IEEE International Conference on Robotics and Automation (ICRA 2006), 4043–4048.

A wheeled-leg quadruped with one hip motor per leg.
2006
Bounding gait in a hybrid wheeled-leg robot
J. A. Smith, I. Sharf, M. Trentini. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2006), 5750–5755.

Bounding on a wheeled-leg quadruped with one hip motor per leg.
2010
Bounding with active wheels and liftoff angle velocity adjustment
J. A. Smith et al. International Journal of Robotics Research 29(4), 414–427.

Bounding with actuated wheels, with forward speed rising as the legs lift off at larger angles.
2011
Running and turning control of a quadruped robot with compliant legs in bounding gait
X. Wang et al. IEEE International Conference on Robotics and Automation (ICRA 2011), 511–518.

Running and turning of a quadruped with compliant legs and one actuator per leg.
2013
Toward a vocabulary of legged leaping
A. M. Johnson, D. E. Koditschek. IEEE International Conference on Robotics and Automation (ICRA 2013), 2568–2575.

A repertoire of leaps for a hexapod with one motor per leg.
2017
The merits of passive compliant joints in legged locomotion: fast learning, superior energy efficiency and versatile sensing in a quadruped robot
M. Hoffmann, J. Simanek. Journal of Bionic Engineering 14(1), 1–14.

Passive compliant knees help a quadruped with actuated hips learn gaits quickly and walk efficiently.
2019
Omni-directional gait of a passive-spine hexapod
Y. Tang et al. Robotics and Autonomous Systems 119, 231–246.

An omni-directional gait for a hexapod with a passive spine.
2020
Learning to walk in the real world with minimal human effort
S. Ha et al. Conference on Robot Learning (CoRL 2020), PMLR 155, 1110–1120.

A quadruped with planar legs learns to walk and to turn in place in the real world.
2020
Influence of compliant joints in four-legged robots
F. T. Spadaro, G. G. Muscolo. Frontiers in Mechanical Engineering 6, 16.

Simulates four-legged robots with hip servos and compliant knees and spine.
2021
A legged soft robot platform for dynamic locomotion
B. Xia et al. IEEE International Conference on Robotics and Automation (ICRA 2021), 11812–11819.

An untethered soft quadruped for dynamic locomotion driven by four motors.
2022
Simulation and analysis of a single actuated quadruped robot
C. Yan et al. Mechanical Sciences 13(1), 137–146.

Simulation and analysis of a quadruped driven by a single actuator.
2023
CurveQuad: a centimeter-scale origami quadruped that leverages curved creases to self-fold and crawl with one motor
D. Feshbach et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2023), 2485–2492.

A centimetre-scale origami quadruped that folds itself and crawls with a single motor.
2025
Synergy-based robotic quadruped leveraging passivity for natural intelligence and behavioural diversity
F. Stella et al. Nature Machine Intelligence 7(3), 386–399.

A quadruped whose twelve joints are driven by four actuators through synergies, with diverse behaviours.
2026
Dynamic modeling and MPC for locomotion of tendon-driven soft quadruped
S. Karan et al. arXiv:2602.16371 (preprint).

Modeling and model predictive control of a tendon-driven soft quadruped with four actuators.
2026
Vibration of soft, twisted beams for underactuated quadrupedal locomotion
Y. Jiang et al. IEEE/ASME Transactions on Mechatronics, 1–11.

Vibrating twisted beams drive an underactuated quadruped with two motors.

Modular and reconfigurable legged robots

8 works

2010
Design, construction and a compliant gait of “ModPod”: a modular hexpod robot
S. Rasakatla, K. M. Krishna, B. Indurkhya. IEEE International Conference on Robotics and Biomimetics (ROBIO 2010), 1341–1345.

A modular hexapod whose body segments are joined by an actuated two-DoF universal spine.
2012
Laboratory on legs: an architecture for adjustable morphology with legged robots
G. C. Haynes et al. Proceedings of SPIE 8387, 83870W.

Leg and body modules that combine into different legged robots, including the spined quadruped Canid.
2018
Rising STAR: a highly reconfigurable sprawl tuned robot
D. Zarrouk, L. Yehezkel. IEEE Robotics and Automation Letters 3(3), 1888–1895.

A highly reconfigurable legged robot that adjusts its sprawl.
2020
An open torque-controlled modular robot architecture for legged locomotion research
F. Grimminger et al. IEEE Robotics and Automation Letters 5(2), 3650–3657.

An open, modular architecture of actuators and legs for building small legged robots.
2021
Self-reconfigurable multilegged robot swarms collectively accomplish challenging terradynamic tasks
Y. Ozkan-Aydin, D. I. Goldman. Science Robotics 6(56), eabf1628.

Legged robots that link into larger multilegged robots to cross difficult terrain together.
2022
Origaker: a novel multi-mimicry quadruped robot based on a metamorphic mechanism
Z. Tang et al. Journal of Mechanisms and Robotics 14(6), 060907.

A quadruped built on a metamorphic mechanism that can take on several animal-like forms.
2026
Agile legged locomotion in reconfigurable modular robots
C. Yu et al. PNAS 123(10), e2519129123.

One-DoF leg modules combine into different robots that learn agile locomotion.
2026
Maneuverable multilegged locomotion through anisotropically arranged soft backbones in a single-actuator modular miniature robot
Y. Yaman et al. Advanced Intelligent Systems 8(4), e202501252.

A modular miniature robot driven by one actuator that steers through the arrangement of its soft backbones.

Learning to control spines and simple bodies

9 works

2004
Automated gait adaptation for legged robots
J. D. Weingarten et al. IEEE International Conference on Robotics and Automation (ICRA 2004), 2153–2158.

Automated tuning of the gait of the hexapod RHex.
2019
Learning active spine behaviors for dynamic and efficient locomotion in quadruped robots
S. Bhattacharya et al. IEEE International Conference on Robot and Human Interactive Communication (RO-MAN 2019), 1–6.

Deep reinforcement learning of active spine motion for fast, efficient quadruped gaits, in simulation.
2021
Biomimetic quadruped robot with a spinal joint and optimal spinal motion via reinforcement learning
Y. K. Kim, W. Seol, J. Park. Journal of Bionic Engineering 18(6), 1280–1290.

A quadruped with one spinal joint learns its spine motion with reinforcement learning.
2024
Spined torso renders advanced mobility for quadrupedal locomotion
J. Wang et al. IEEE International Conference on Robotics and Automation (ICRA 2024), 1457–1463.

A spined torso improves a quadruped's mobility, with learned trotting and bounding.
2024
A robust quadruped robot with twisting waist for flexible motions
Q. Qian et al. arXiv:2410.05884 (preprint).

A quadruped with a twisting waist and fewer leg joints, controlled through imitation learning.
2025
KLEIYN: a quadruped robot with an active waist for both locomotion and wall climbing
K. Yoneda et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2025), 8783–8789.

A quadruped with an active waist that learns both walking and wall climbing.
2026
Pushing physical limits and uncovering motion templates of spine-based quadruped locomotion via reinforcement learning
Z. Bing et al. IEEE Transactions on Robotics 42, 2305–2324.

Reinforcement learning uncovers spine motion templates for fast running and turning on a mouse robot.
2026
Gait optimization control of spinal quadruped robot based on deep reinforcement learning
G. Song et al. Sensors 26(8), 2407.

Deep reinforcement learning with a central pattern generator optimizes the gait of a spined quadruped.
2026
Evaluation of an actuated spine in agile quadruped locomotion
N. Bohlinger et al. arXiv:2605.07988 (preprint).

Evaluates an actuated spine for learned agile quadruped skills.

Robots that dance to music

21 works

2005
From lamprey to humanoid: the design and control of a flexible spine belly dancing humanoid robot with inspiration from biology
J. Or, A. Takanishi. International Journal of Humanoid Robotics 2(1), 81–104.

A humanoid whose flexible spine performs belly dance.
2007
A dancing robot for rhythmic social interaction
M. P. Michalowski, S. Šabanović, H. Kozima. ACM/IEEE International Conference on Human-Robot Interaction (HRI 2007), 89–96.

Keepon, a small, simple robot, dances in time with the rhythm it perceives.
2009
Keepon: a playful robot for research, therapy, and entertainment
H. Kozima, M. P. Michalowski, C. Nakagawa. International Journal of Social Robotics 1(1), 3–18.

A small creature-like robot used in research and entertainment, including dancing to music.
2009
Rhythmic attention in child-robot dance play
M. P. Michalowski, R. Simmons, H. Kozima. IEEE International Symposium on Robot and Human Interactive Communication (RO-MAN 2009), 816–821.

Children and a small robot dance together to music.
2010
Design and study of a highly articulated mini lion-dance robot
X. Dong et al. IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2010), 830–835.

A highly articulated four-legged robot that performs the lion dance.
2011
Aibo JukeBox – a robot dance interactive experience
C. Angulo, J. Comas, D. Pardo. International Work-Conference on Artificial Neural Networks (IWANN 2011), Lecture Notes in Computer Science, 605–612.

The robot dog Aibo dances to songs chosen by users.
2011
The trials of hula hooping by a musculo-skeletal humanoid KOJIRO nearing dancing motions using the soft spine
Y. Kekehashi et al. IEEE-RAS International Conference on Humanoid Robots (Humanoids 2011), 423–428.

A musculoskeletal humanoid hula-hoops with its soft spine, close to dance motions.
2013
Effects of robotic companionship on music enjoyment and agent perception
G. Hoffman, K. Vanunu. ACM/IEEE International Conference on Human-Robot Interaction (HRI 2013), 317–324.

A robot that moves to music changes how people enjoy the music.
2015
Emotionally expressive dynamic physical behaviors in robots
M. Bretan, G. Hoffman, G. Weinberg. International Journal of Human-Computer Studies 78, 1–16.

Emotionally expressive movement in a robot that responds to music.
2017
Keep on dancing: effects of expressive motion mimicry
R. Simmons, H. Knight. IEEE International Symposium on Robot and Human Interactive Communication (RO-MAN 2017), 720–727.

Effects of a robot mimicking a person's dance motion.
2018
Real-time dance generation to music for a legged robot
T. Bi et al. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2018), 1038–1044.

A quadruped generates dance moves to music in real time.
2022
Music and movement based dancing for a non-anthropomorphic robot
A. Rogel. ACM/IEEE International Conference on Human-Robot Interaction (HRI 2022), 1173–1175.

Dancing for a non-humanlike robot based on music and movement.
2023
Robot choreographer
M. Klingensmith et al. US Patent 11,691,292 B2 (Boston Dynamics; filed 2019, granted 2023).

A method for turning a script of dance moves into joint commands for a legged robot.
2023
DOC: differentiable optimal control for retargeting motions onto legged robots
R. Grandia et al. ACM Transactions on Graphics 42(4), 1–14.

Differentiable optimal control retargets expressive motions onto legged robots.
2023
Central pattern generators evolved for real-time adaptation to rhythmic stimuli
A. Szorkovszky, F. Veenstra, K. Glette. Bioinspiration & Biomimetics 18(4), 046020.

Evolved central pattern generators let a simulated quadruped adapt its gait to a rhythm.
2023
Toward cultures of rhythm in legged robots
A. Szorkovszky, F. Veenstra, K. Glette. Artificial Life Conference (ALIFE 2023).

Legged robots that pick up and pass on rhythms.
2024
May the dance be with you: dance generation framework for non-humanoids
H. Ahn. arXiv:2405.19743 (preprint).

A framework for generating dances for robots that are not humanoid.
2024
Mapping music onto robot joints for autonomous choreographies: PCA-based approach
G. Saviano, A. Villani, D. Prattichizzo. IEEE Forum on Research and Technologies for Society and Industry (RTSI 2024), 232–237.

Maps music onto robot joints for autonomous choreography.
2025
Music-driven legged robots: synchronized walking to rhythmic beats
T. Hou et al. IEEE International Conference on Robotics and Automation (ICRA 2025), 5357–5363 (arXiv:2503.04063).

A quadruped learns to walk with its steps synchronized to the musical beat.
2025
DFM: Deep Fourier Mimic for expressive dance motion learning
R. Watanabe, C. Li, M. Hutter. IEEE International Conference on Robotics and Automation (ICRA 2025), 9644–9650 (arXiv:2502.10980).

Expressive dance motions learned on a robot dog.
2026
QuadFM: foundational text-driven quadruped motion dataset for generation and control
L. Gao et al. arXiv:2603.24021 (preprint).

A dataset of quadruped motions, including dance, for generation and control.