Design of a 3-DOF Hopping Robot with an Optimized Gearbox: An Intermediate Platform Toward Bipedal Robots

Dongyun Kang; Gijeong Kim; Hae-Won Park; Hajun Kim; JongHun Choe; Min-su Kim

REVIEW 3 major objections 6 minor 26 references

Design of a 3-DOF Hopping Robot with an Optimized Gearbox: An Intermediate Platform Toward Bipedal Robots

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A flat-footed 3-DOF leg, with an optimized planetary gearbox and a learned controller, hops, flips, climbs, and recovers—the authors' case that the platform can grow into a bipedal robot.

desk verdict Real hardware platform with a new flat-foot hopping demo and verifiable gear design; the main gap is unquantified cable interaction, not the gear-ratio formula. read the letter →

arxiv 2505.12231 v2 pith:UF4BSQTB submitted 2025-05-18 cs.RO

JongHun Choe , Gijeong Kim , Hajun Kim , Dongyun Kang , Min-Su Kim , Hae-Won Park This is my paper · ORCID

classification cs.RO

keywords hoppingrobot3Kcompoundplanetarygearboxmixed-integernonlinearprogramminggearteethoptimizationreinforcementlearningcontrolflat-footleggedlocomotionbipedaldevelopmentsim-to-realtransfer

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper establishes that a single 3-DOF leg with a flat foot, arranged like a human lower limb with one knee and two ankle joints, can hop repeatedly, flip forward, climb steps, and recover from pushes when driven by actuators whose gearboxes are designed by mixed-integer nonlinear programming. Hopping matters as a test because it forces a leg to deliver high impact torque, stay agile, and manage intermittent ground contact—conditions a full bipedal robot will also face. Because the motor, the 3K compound planetary gearbox, the motor driver, and the communication interface were all custom-built to fit the joint geometry, the hardware experiments validate the actuation and structure as much as the controller. The authors conclude that the platform, weighing 12.45 kg, is an effective intermediate step toward a 13-DOF bipedal robot, with the gearbox optimization and the learned-control pipeline carrying over directly.

What carries the argument

The load-bearing mechanism is the 3K compound planetary gearbox of the knee actuator, a compact reducer in which two planet gears and two ring gears share one carrier to reach a high ratio within a small diameter. Its tooth counts are the outputs of a mixed-integer nonlinear program whose target is the ratio identity $G_{\text{target}} = \frac{2Z_{P1}(Z_F - Z_{P1} + Z_{P2})}{(Z_F - 2Z_{P1})(Z_{P1} - Z_{P2})}$, constrained by the structural equalities $Z_F = Z_S + 2Z_{P1}$ and $Z_O = Z_S + Z_{P1} + Z_{P2}$, by assembly conditions, and by carrier-interference and gear-size inequalities. This identity is what ties the chosen integers to the claimed 20:1 reduction, the hollow shaft, and the torque rating, and it lets the gearbox sit inside the motor rotor so the actuator stays compact. The complementary mechanism is the closed-loop parallel ankle linkage, with a universal joint at the foot and ball joints at the parallel actuator outputs, which the training simulation represents as a pin-constrained kinematic chain so the learned policy is aware of the coupling between the two ankle actuators.

What would settle it

Instrument the fabricated D151 gearbox: drive the sun gear at a known speed, measure the output ring speed, and compare the ratio to the 20:1 target; a large deviation would refute the gearbox claim. Independently, re-derive the ratio for the published tooth counts ($Z_S=44$, $Z_{P1}=44$, $Z_{P2}=32$, $Z_F=132$, $Z_O=120$) from standard compound-planetary kinematics and check it against Eq. (5); any mismatch would refute the optimization's central constraint rather than the prototype.

Watch

Extended reading notes

Core claim

The paper's central claim is that dynamic, repetitive flat-foot hopping with a human-like leg layout is achievable on a 3-DOF prototype, and that this validates the hardware design as the foundation for a bipedal robot. In the authors' account, the knee actuator reaches a 320 N·m peak torque and a 20:1 reduction through a 3K compound planetary gearbox whose tooth counts ($Z_S = 44$, $Z_{P1} = 44$, $Z_{P2} = 32$, $Z_F = 132$, $Z_O = 120$) were selected by solving a mixed-integer nonlinear program that maximizes the hollow-shaft diameter for cable routing, minimizes mass, and enforces assembly, interference, and size constraints. The same custom-design approach extends to the motor drivers and the EtherCAT–CAN converter, which fit within the compact joint envelopes. On the control side, a reinforcement-learning policy trained in a simulation that models the closed-loop ankle linkage as a kinematic chain with a pin constraint transfers to the real robot without external support and produces the demonstrated behaviors: repetitive forward and backward hopping at 0.8 m/s, a complete front flip landing upright, an 85 mm step-up, and push recovery. The authors read these results as evidence that the actuators can deliver both the torque and the velocity that aggressive maneuvers demand, and that the platform can absorb the resulting impact loads.

Load-bearing premise

The entire actuator design rests on an unstated gear-ratio formula, Eq. (5): if that formula mis-models how the two planet gears and two ring gears interlock, the knee joint is not actually a 20:1 reducer and the hopping and flipping experiments do not validate the gearbox as designed.

Editorial extensions

If this is right

The mixed-integer nonlinear gearbox-design procedure—ratio, assembly, interference, and size constraints over integer tooth counts—applies directly to the joints of the planned 13-DOF biped, which the authors state is being built on the same electrical architecture and gearbox methodology.
The reinforcement-learned controller transfers from a simulation that explicitly models the closed-loop ankle, so the same training pipeline should extend to the more complex kinematics of a full leg without a new method.
The knee actuator reaching both its torque and velocity limits during the front flip means the D151 is sized at the envelope for aggressive maneuvers, giving a measured operating point for specifying the biped's actuators.
Flat-foot standing and push recovery are demonstrated on a single leg with a small support polygon; the biped's larger support polygon and second leg should make the same learned behaviors easier to maintain.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A standalone check of the uncited ratio formula, Eq. (5), is the fastest way to confirm the gearbox claim independently: re-deriving it from standard compound-planetary kinematics and comparing with the published tooth counts takes a short calculation.
Because the same controller handled an 85 mm step with no retraining, its terrain margin is probably larger than demonstrated; a sweep of increasing step height would quantify how much headroom the sim-to-real training left on the table.
The experiments run tethered, so the onboard battery and the custom converter have not been stressed by repeated impacts; running the same motions on battery power would test whether the power and communication chain, not just the actuators, survives dynamic loads.
A measured push-impulse limit for the single-leg policy would double as a lower-bound disturbance-rejection benchmark for the biped, since balancing on one flat foot is harder than on two.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Read arXiv:2505.12231. The headline: this is a real hardware platform paper with a genuinely new demonstration—a 3-DOF flat-foot hopper doing repetitive hopping, front flip, step-up, and push recovery—and the gear-design optimization is verifiable. The selected teeth satisfy Eq. (5), and re-deriving the 3K ratio from the Willis relation gives the same formula, so the reader's Eq. (5) worry does not land. The paper earns credit for shipping a working 12.45 kg robot with custom hollow-shaft actuators, custom drivers, and an RL controller trained in RaiSim with closed-loop ankle kinematics. That is nontrivial engineering.

The soft spots are real but not fatal. First, all demos are tethered; the umbilical cable is the only stated support, but its mechanical interaction is never measured or bounded. For a hopping/front-flip validation, cable tension can assist stabilization or change touchdown loads, so the hardware claim is not fully clean. Second, there are no repeated-trial statistics or quantitative success rates; the evidence is snapshots and a few torque/velocity traces. That is typical for this kind of paper but still limits strength. Third, internal inconsistencies: abstract says 840 mm, body says 890 mm; Eq. (1) uses Z_P3 but the variable list defines only Z_P1 and Z_P2. Minor but should be fixed. No code, CAD, or data is released, which makes the RL and optimization hard to reproduce.

The citation pattern is okay: the MINLP gear optimization and barrier-RL are cited to prior work, and the flip policy is from a submitted anonymous paper—that citation is appropriate. Self-citation is not a problem here because the cited methods are actually used.

Who is this for? Legged-robotics hardware people, especially those building humanoid-scale joints. It is a credible intermediate platform report, not a breakthrough in control or design theory. It deserves a serious referee: the experiments should be repeated with measured cable force, and the paper needs trial counts and a cable-force bound. I would send it to review with a request for major revision along those lines, not desk-reject.

Reading group maybe; I'd bring it if the group cares about hardware platforms.

Referee Report

3 major / 6 minor

Summary. The paper presents the design, fabrication, and experimental evaluation of a 12.45 kg, 3-DOF hopping robot with a flat foot and a human-like lower-limb layout (one knee DOF, two ankle DOFs), positioned as an intermediate platform toward a 13-DOF biped. The hardware contribution centers on a custom knee actuator (D151) containing a 20:1 3K compound planetary gearbox whose tooth counts (ZS=44, ZP1=44, ZP2=32, ZF=132, ZO=120) are selected by a mixed-integer nonlinear program with a hollow shaft for cable routing, plus custom motor drivers and an EtherCAT-CAN converter. The controller is a PPO-trained reinforcement-learning policy with barrier-based style rewards, trained in RaiSim with a closed-loop ankle model and deployed to hardware. Experiments demonstrate forward and backward hopping, an 85 mm step-up, a front flip, and push recovery, all with the robot tethered by an umbilical cable. The paper claims stable, repetitive hopping and concludes the platform is an effective intermediate testbed for bipedal robots.

Significance. If the claims are established, this is a useful contribution: the MINLP gear-tooth selection is concrete and the selected tooth counts verifiably satisfy the stated structural, assembly, and ratio equations, which is a strength; the hardware is real, and the periodic torque/velocity traces and video snapshots give external evidence that the system hops. I also confirmed that Eq. (5), though underived, is correct when derived from the Willis relation and constraints (2)-(3), so the gear-ratio concern raised by the companion stress-test does not land. However, the experimental evidence is anecdotal: there are no repeated-trial statistics, no quantitative performance metrics, and the umbilical cable's mechanical interaction is never measured or bounded. Because the paper's central claim is that the platform validates hardware for an untethered biped, these gaps are load-bearing. The strengths are real, but the validation standard needs to be raised.

major comments (3)

[Section IV, first paragraph; Section V] Section IV states that all experiments were performed 'without any external support except for the umbilical cable,' but the cable's mechanical interaction is never quantified or bounded. During flight and touchdown, tension in a power/communication tether can exert vertical and lateral forces on the 12.45 kg body, potentially assisting balance, jump height, and flip landing. Since the stated purpose is to validate hardware for an untethered biped (Abstract and Section V), this is a load-bearing gap. Please add a cable-force measurement (e.g., a load cell at the anchor), a slack/tension analysis, or an explicit demonstration that cable forces are negligible relative to body weight (about 122 N) and the measured joint torques. If such data are not available, the conclusions must be correspondingly tempered.
[Section IV, Figs. 7 and 8] The claims of 'repetitive hopping' and 'successfully completed a full rotation and landed upright' are supported by one snapshot sequence and one torque/velocity trace per behavior. There are no repeated-trial counts, success rates, or variability metrics such as hop height, hop period, aerial time, foot placement error, or landing success. A single successful demonstration does not establish repeatability or robustness. Please provide N repeated trials with quantitative summaries and, if failures occurred, report the failure rate.
[Section II-D, Eq. (5)] Equation (5), the gear-ratio formula for the 3K compound planetary gearbox, is stated without derivation or citation. I re-derived it from the Willis relation together with the structural constraints (2) and (3) and found it to be correct, so this is not a correctness objection; however, the derivation should be included or a source cited, because the selected tooth counts and the claimed 20:1 ratio and knee torque all rest on this formula, and the formula is not obvious.

minor comments (6)

[Abstract and Section II-A] The Abstract reports 840 mm as the fully extended length, while Section II-A reports 890 mm; these values should be made consistent.
[Eq. (1)] The cost function in Eq. (1) contains Z_{P3}^2, but the optimization variables define only Z_{P1} and Z_{P2}; this should be Z_{P2} to be consistent with the rest of the paper.
[Table II] Table II reports D151 rotor inertia as 'measured in the three-dimensional design software'; this is a CAD estimate, not a measurement, and should be labeled as such.
[Section III] The controller description refers to [16] for the observation vector details; since [16] is a preprint, include a full list of observations and training hyperparameters for reproducibility.
[Fig. 8] The claim that the knee actuator 'reached both its torque and velocity limits' is not verifiable from Fig. 8 because no limit lines or definitions of the limits are shown; please add them.
[References] Reference [26] is an anonymous submission under review; the final version should resolve the attribution and status of this citation according to journal policy.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (5) is a derivable kinematic gear-ratio relation, the MINLP tooth selection is a design synthesis with the target ratio as an input, and the RL controller is validated against measured hardware outcomes rather than its own reward terms.

full rationale

Walking the paper's derivation chain, the load-bearing technical steps are the gearbox design and the learned controller, and neither reduces to its own inputs. The gear-ratio condition, Eq. (5), is stated as a constraint for the 3K compound planetary gearbox; although no derivation is shown in the paper, it is a kinematic relation of the same form used for compound planetary trains, and the selected tooth counts (ZS=44, ZP1=44, ZP2=32, ZF=132, ZO=120) are produced by an MINLP solver from the stated constraints. The target ratio of 20 is an input to the optimization, not a fitted output relabeled as a prediction, so the design process is not circular. The reinforcement-learning controller is trained in simulation using barrier rewards that encode the desired hopping style, but the paper's validation is the physical robot: measured torque and angular-velocity traces, repetitive forward/backward hopping, a front flip, step-up, and push recovery are all hardware outcomes that stand outside the training objective. The self-citations to [16] and [26] provide the control framework and flip-policy method, but the experimental success is not justified by those citations; it is justified by the reported hardware tests. The tethered-cable concern raised by the skeptical review is a threat to the validity of the hardware evidence because cable forces are never quantified, but that is an experimental confound, not a circular derivation. No equation or fitted parameter is shown to be equivalent by construction to a claimed prediction, so the circularity score is 0.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The hardware claim rests on gear kinematics (Eqs. 2 to 5) and assembly conditions (Eq. 4), plus a gear-ratio formula that is quoted without derivation. The controller claim rests on RaiSim closed-loop modeling and unstated sim-to-real transfer fidelity. Design values such as target ratio, module, rotor bore, and clearance are hand-chosen, and key controller hyperparameters including reward weights, PD gains, and desired hop frequency are unreported. No invented physical entities are introduced.

free parameters (9)

Target knee gear ratio G_target = 20
Chosen to meet knee torque and velocity requirements; enters Eq. (5) and drives the MINLP gear tooth selection.
Gear module M = 0.6
Design parameter used in cost function (1) and size constraint (8); assumed uniform for all gears.
Rotor inner diameter D = 79.4 mm
Used in cost function (1) and constraint (8) to ensure the gearbox fits inside the rotor; set by motor geometry.
Minimum carrier clearance alpha_min = not reported
Hyperparameter in inequality (6) controlling angular clearance for the carrier; numeric value not given.
Minimum tooth counts Z_S,min, Z_P1,min, Z_P2,min = not reported
Lower bounds in constraint (7) for shaft and bearing size; values are not stated.
Desired hopping frequency and foot clearance = not reported
Predefined motion style enforced via the barrier reward (Table III); the actual values are not reported.
Barrier reward weights gamma_i = all equal, value not reported
All barrier terms weighted identically to produce the hopping style; the exact weight controls behavior and is unspecified.
Command velocity for hopping experiments = 0.8 m/s
User-set joystick command in forward and backward hopping; an experimental condition rather than a fitted parameter.
Low-level PD gains = not reported
Action outputs target actuator positions for a PD controller (Section III); gains are required for replication and are not listed.

assumptions (6)

domain assumption The 3K gearbox ratio formula (Eq. 5) correctly models the fabricated gear kinematics.
Stated without derivation or citation in Section II-D3; the entire 20:1 ratio and torque rating depend on it.
domain assumption Assembly feasibility conditions (Eq. 4) from [15] apply to this gearbox with n_P planets.
The chosen tooth counts satisfy the conditions for n_P=4, but the paper does not state n_P explicitly.
domain assumption Meshing geometry equations Z_F = Z_S + 2 Z_P1 and Z_O = Z_S + Z_P1 + Z_P2 (Eqs. 2 and 3) hold.
Standard compound planetary geometry, stated without proof; necessary for the tooth selection.
domain assumption RaiSim's pin-constraint modeling of the closed-loop ankle mechanism is faithful, and the simulated controller transfers to hardware.
Section III; no domain randomization is described, so transfer depends on model fidelity and the sub-step alignment procedure.
domain assumption The four-bar knee transmission is exactly 1:1 with negligible backlash and compliance.
Section II-A states 1:1 ratio; any unmodeled elasticity would corrupt the torque and velocity mapping used in control.
domain assumption The flat-foot support polygon is sufficient for stable one-legged standing and hopping within the joint ranges.
Standing mode and lateral COM penalty (Tables III and IV) assume adequate foot-ground support; no friction or contact geometry analysis is provided.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Design of a 3-DOF Hopping Robot with an Optimized Gearbox: An Intermediate Platform Toward Bipedal Robots." pith.science (2026). https://pith.science/paper/UF4BSQTB

@misc{pith2026250512231,
  author       = {Pith},
  title        = {Pith review of: Design of a 3-DOF Hopping Robot with an Optimized Gearbox: An Intermediate Platform Toward Bipedal Robots},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UF4BSQTB}},
  note         = {Machine review of arXiv:2505.12231}
}

read the original abstract

This paper presents a 3-DOF hopping robot with a human-like lower-limb joint configuration and a flat foot, capable of performing dynamic and repetitive jumping motions. To achieve both high torque output and a large hollow shaft diameter for efficient cable routing, a compact 3K compound planetary gearbox was designed using mixed-integer nonlinear programming for gear tooth optimization. To meet performance requirements within the constrained joint geometry, all major components-including the actuator, motor driver, and communication interface-were custom-designed. The robot weighs 12.45 kg, including a dummy mass, and measures 840 mm in length when the knee joint is fully extended. A reinforcement learning-based controller was employed, and robot's performance was validated through hardware experiments, demonstrating stable and repetitive hopping motions in response to user inputs. These experimental results indicate that the platform serves as a solid foundation for future bipedal robot development.

Figures

Figures reproduced from arXiv: 2505.12231 by the authors.

**Figure 2.** Overview of the proposed hopping robot: (a) design and schematic [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Electrical architecture of the proposed hopping robot [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Exploded view of the D151 actuator for the knee joint. [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]

**Figure 5.** Figure 5: Photographs of the custom-designed components of the proposed [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

**Figure 6.** Figure 6: Geometric relationship between the compound planet gears and [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]

**Figure 7.** Figure 7: Snapshots from the experiments performed on the proposed 3-DOF hopping robot: (a) repetitive forward hopping, (b) repetitive backward hopping, [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 8.** Figure 8: Measured joint torques and angular velocities during the ex [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

26 extracted references · 15 canonical work pages

[1]

Single-legged hopping robotics research—a review,

A. Sayyad, B. Seth, and P. Seshu, “Single-legged hopping robotics research—a review,” Robotica, vol. 25, no. 5, pp. 587–613, 2007

work page 2007
[2]

M. H. Raibert, Legged robots that balance . MIT press, 1986

1986
[3]

A new approach to the control of the planar one-legged hopper,

C. Franc ¸ois and C. Samson, “A new approach to the control of the planar one-legged hopper,” The International Journal of Robotics Research, vol. 17, no. 11, pp. 1150–1166, 1998

work page 1998
[4]

Single actuator control analysis of a planar 3dof hopping robot

N. Cherouvim and E. Papadopoulos, “Single actuator control analysis of a planar 3dof hopping robot.” in Robotics: Science and Systems , 2005, pp. 145–152

work page 2005
[5]

Controlled passive dynamic running experiments with the arl-monopod ii,

M. Ahmadi and M. Buehler, “Controlled passive dynamic running experiments with the arl-monopod ii,” IEEE Transactions on Robotics , vol. 22, no. 5, pp. 974–986, 2006

work page 2006
[6]

The actuator with mechanically adjustable series compliance,

J. W. Hurst, J. E. Chestnutt, and A. A. Rizzi, “The actuator with mechanically adjustable series compliance,” IEEE Transactions on Robotics, vol. 26, no. 4, pp. 597–606, 2010

work page 2010
[7]

Design and experimental validation of a monopod robot with 3-dof morphable inertial tail for somersault,

J. An, X. Ma, C. H. D. Lo, W. Ng, X. Chu, and K. W. S. Au, “Design and experimental validation of a monopod robot with 3-dof morphable inertial tail for somersault,” IEEE/ASME Transactions on Mechatronics, vol. 27, no. 6, pp. 5072–5083, 2022

work page 2022
[8]

Development of a biologically inspired hopping robot-

S.-H. Hyon and T. Mita, “Development of a biologically inspired hopping robot-” kenken”,” in Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No. 02CH37292) , vol. 4. IEEE, 2002, pp. 3984–3991

work page 2002

Show all 26 references

[9]

Stable one-legged hopping without feedback and with a point foot,

K. D. Mombaur, R. W. Longman, H. G. Bock, and J. P. Schloder, “Stable one-legged hopping without feedback and with a point foot,” in Proceedings 2002 IEEE International Conference on Robotics and Automation, vol. 4. IEEE, 2002, pp. 3978–3983

2002
[10]

Design principles for energy-efficient legged locomotion and implementation on the mit cheetah robot,

S. Seok, A. Wang, M. Y . Chuah, D. J. Hyun, J. Lee, D. M. Otten, J. H. Lang, and S. Kim, “Design principles for energy-efficient legged locomotion and implementation on the mit cheetah robot,” Ieee/asme transactions on mechatronics , vol. 20, no. 3, pp. 1117–1129, 2014

2014
[11]

Mit cheetah 3: Design and control of a robust, dynamic quadruped robot,

G. Bledt, M. J. Powell, B. Katz, J. Di Carlo, P. M. Wensing, and S. Kim, “Mit cheetah 3: Design and control of a robust, dynamic quadruped robot,” in 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) . IEEE, 2018, pp. 2245–2252

2018
[12]

High-speed bounding with the mit cheetah 2: Control design and experiments,

H.-W. Park, P. M. Wensing, and S. Kim, “High-speed bounding with the mit cheetah 2: Control design and experiments,” The International Journal of Robotics Research , vol. 36, no. 2, pp. 167–192, 2017

2017
[13]

Design of kaist hound, a quadruped robot platform for fast and efficient locomotion with mixed- integer nonlinear optimization of a gear train,

Y .-H. Shin, S. Hong, S. Woo, J. Choe, H. Son, G. Kim, J.-H. Kim, K. Lee, J. Hwangbo, and H.-W. Park, “Design of kaist hound, a quadruped robot platform for fast and efficient locomotion with mixed- integer nonlinear optimization of a gear train,” in 2022 International Confere...

2022
[14]

Design and control of the rapid legged platform gazelle,

H. Jeong, K. Lee, W. Kim, I. Lee, and J.-H. Oh, “Design and control of the rapid legged platform gazelle,” Mechatronics, vol. 66, p. 102319, 2020. [Online]. Available: https://www.sciencedirect.com/ science/article/pii/S0957415819301503

2020
[15]

Single planetary mechanism teeth matching conditions,

N. Zou, Y . Wei, S. Chang, and D. Zhou, “Single planetary mechanism teeth matching conditions,” in 2015 International Conference on Advanced Manufacturing and Industrial Application . Atlantis Press, 2015, pp. 42–45

2015
[16]

A learning framework for diverse legged robot locomotion using barrier-based style rewards,

G. Kim, Y .-H. Lee, and H.-W. Park, “A learning framework for diverse legged robot locomotion using barrier-based style rewards,” arXiv preprint arXiv:2409.15780, 2024

2024 arXiv
[17]

Baron: A general purpose global optimization software package,

N. V . Sahinidis, “Baron: A general purpose global optimization software package,” Journal of global optimization , vol. 8, pp. 201– 205, 1996

1996
[18]

Learning quadrupedal locomotion over challenging terrain,

J. Lee, J. Hwangbo, L. Wellhausen, V . Koltun, and M. Hutter, “Learning quadrupedal locomotion over challenging terrain,” Science robotics, vol. 5, no. 47, p. eabc5986, 2020

2020
[19]

Not only rewards but also constraints: Applications on legged robot locomotion,

Y . Kim, H. Oh, J. Lee, J. Choi, G. Ji, M. Jung, D. Youm, and J. Hwangbo, “Not only rewards but also constraints: Applications on legged robot locomotion,” IEEE Transactions on Robotics , 2024

2024
[20]

Robotkeyframing: Learning locomotion with high-level objec- tives via mixture of dense and sparse rewards,

F. Zargarbashi, J. Cheng, D. Kang, R. Sumner, and S. Coros, “Robotkeyframing: Learning locomotion with high-level objec- tives via mixture of dense and sparse rewards,” arXiv preprint arXiv:2407.11562, 2024

2024 arXiv
[21]

Proximal policy optimization algorithms,

J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Proximal policy optimization algorithms,” arXiv preprint arXiv:1707.06347, 2017

2017 arXiv
[22]

Per-contact iteration method for solving contact dynamics,

J. Hwangbo, J. Lee, and M. Hutter, “Per-contact iteration method for solving contact dynamics,” IEEE Robotics and Automation Letters , vol. 3, no. 2, pp. 895–902, 2018

2018
[23]

Concurrent training of a control policy and a state estimator for dynamic and robust legged locomotion,

G. Ji, J. Mun, H. Kim, and J. Hwangbo, “Concurrent training of a control policy and a state estimator for dynamic and robust legged locomotion,” IEEE Robotics and Automation Letters , vol. 7, no. 2, pp. 4630–4637, 2022

2022
[24]

Dreamwaq: Learning robust quadrupedal locomotion with implicit terrain imagination via deep reinforcement learning,

I. M. A. Nahrendra, B. Yu, and H. Myung, “Dreamwaq: Learning robust quadrupedal locomotion with implicit terrain imagination via deep reinforcement learning,” in 2023 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2023, pp. 5078–5084

2023
[25]

Asymmetric actor critic for image-based robot learning,

L. Pinto, M. Andrychowicz, P. Welinder, W. Zaremba, and P. Abbeel, “Asymmetric actor critic for image-based robot learning,” arXiv preprint arXiv:1710.06542, 2017

2017 arXiv
[26]

Learning impact-rich rotational maneuvers via cen- troidal velocity rewards and sim-to-real techniques: A one-leg hop- per flip case study,

Anonymous, “Learning impact-rich rotational maneuvers via cen- troidal velocity rewards and sim-to-real techniques: A one-leg hop- per flip case study,” 2025, submitted to CoRL 2025 (Double-blind Review), under review

2025

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Single-legged hopping robotics research—a review,

A. Sayyad, B. Seth, and P. Seshu, “Single-legged hopping robotics research—a review,” Robotica, vol. 25, no. 5, pp. 587–613, 2007

work page 2007

[2] [2]

M. H. Raibert, Legged robots that balance . MIT press, 1986

1986

[3] [3]

A new approach to the control of the planar one-legged hopper,

C. Franc ¸ois and C. Samson, “A new approach to the control of the planar one-legged hopper,” The International Journal of Robotics Research, vol. 17, no. 11, pp. 1150–1166, 1998

work page 1998

[4] [4]

Single actuator control analysis of a planar 3dof hopping robot

N. Cherouvim and E. Papadopoulos, “Single actuator control analysis of a planar 3dof hopping robot.” in Robotics: Science and Systems , 2005, pp. 145–152

work page 2005

[5] [5]

Controlled passive dynamic running experiments with the arl-monopod ii,

M. Ahmadi and M. Buehler, “Controlled passive dynamic running experiments with the arl-monopod ii,” IEEE Transactions on Robotics , vol. 22, no. 5, pp. 974–986, 2006

work page 2006

[6] [6]

The actuator with mechanically adjustable series compliance,

J. W. Hurst, J. E. Chestnutt, and A. A. Rizzi, “The actuator with mechanically adjustable series compliance,” IEEE Transactions on Robotics, vol. 26, no. 4, pp. 597–606, 2010

work page 2010

[7] [7]

Design and experimental validation of a monopod robot with 3-dof morphable inertial tail for somersault,

J. An, X. Ma, C. H. D. Lo, W. Ng, X. Chu, and K. W. S. Au, “Design and experimental validation of a monopod robot with 3-dof morphable inertial tail for somersault,” IEEE/ASME Transactions on Mechatronics, vol. 27, no. 6, pp. 5072–5083, 2022

work page 2022

[8] [8]

Development of a biologically inspired hopping robot-

S.-H. Hyon and T. Mita, “Development of a biologically inspired hopping robot-” kenken”,” in Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No. 02CH37292) , vol. 4. IEEE, 2002, pp. 3984–3991

work page 2002