The reviewed record of science sign in
Pith

arxiv: 2606.19699 · v1 · pith:K2IRPOR7 · submitted 2026-06-18 · cs.RO · cs.LG· cs.SY· eess.SY

Comparative Study on Agility, Efficiency, and Impact Absorption of Bipedal Robots with Active Toes

Joong-Gil Kim , Wontae Ye , Geunwoo Cho , Seong-Ho Yun , Se-Hyoung Cho , Yong-Jae Kim This is my paper

Reviewed by Pith2026-06-26 17:47 UTCgrok-4.3pith:K2IRPOR7open to challenge →

classification cs.RO cs.LGcs.SYeess.SY
keywords bipedal robotactive toesreinforcement learningcost of transportagilityimpact absorptionsimulation comparison
0
0 comments X

The pith

A biped robot with active toes cuts walking energy cost by 17.5 percent and path deviation by 25 percent versus a toe-less version in matched simulations.

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

The paper builds a 14-DOF biped model whose toes match the lightweight, high-torque, and robust traits of human toes, then trains identical reinforcement-learning policies on two versions: one with active toes and one with toes removed. Both versions use the same minimal reward function inside a high-fidelity simulator that includes real actuator dynamics, coupled transmissions, and measured power draw. The toe-equipped robot shows lower cost of transport, smaller heel-strike forces, and tighter path tracking on an agility task. These differences are presented as direct evidence that active toes improve efficiency, impact absorption, and agility.

Core claim

The simulation results indicate that, at 1.33 m/s walking, the toe-equipped robot reduced CoT by 17.5% and heel-strike GRF by 5.0% compared with the toe-ablation configuration. On the agility test, average and maximum path deviation decreased by 25.0% and 34.0%, respectively.

What carries the argument

The 14-DOF biped robot with active toes, paired with a high-fidelity simulation that models actuator dynamics and power consumption for fair RL policy comparison.

If this is right

  • Walking at 1.33 m/s requires 17.5 percent less energy when active toes are present.
  • Heel-strike ground reaction forces drop by 5 percent with active toes.
  • Path deviation on agility maneuvers falls by 25 percent on average and 34 percent at peak.
  • Identical minimal-reward training isolates the morphological contribution of the toes.
  • Toe ablation provides a controlled baseline that rules out confounding changes in control or mass.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the simulation-to-hardware gap is small, active toes could be added to existing biped platforms to raise efficiency without redesigning the entire leg.
  • The minimal-reward comparison method could be reused to test other morphological features such as ankle compliance or foot shape.
  • Lower heel-strike forces may extend hardware life or allow softer landing strategies on uneven surfaces.
  • The 1.33 m/s speed and straight-line plus turn tasks leave open whether the same toe benefit appears at higher speeds or on stairs.

Load-bearing premise

The high-fidelity simulation accurately captures real actuator dynamics, coupled transmissions, and power consumption such that RL policies trained in simulation will exhibit the reported performance differences when transferred to physical hardware.

What would settle it

Transfer the trained policies to the physical robot hardware and measure whether the toe-equipped version still shows at least a 15 percent lower cost of transport and 20 percent lower path deviation than the toe-ablated version at the same speed.

Figures

Figures reproduced from arXiv: 2606.19699 by Geunwoo Cho, Joong-Gil Kim, Se-Hyoung Cho, Seong-Ho Yun, Wontae Ye, Yong-Jae Kim.

Figure 1
Figure 1. Figure 1: (a) 14-DOF biped robot design. (b) HyperLeg mechanism: 2-DOF ankle, 1-DOF toe. (c) Simulation model matching the actual robot. rain adaptability to some extent [18][19]. However, these approaches lack the dynamic force modulation seen in human toes. To address these limitations, we previously developed HyperLeg, a leg mechanism featuring two DOF in the an￾kle and one DOF in the toe, as shown in [PITH_FULL… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Dimensions of the 14-DOF biped robot. (b) Coordinate frames and link masses. (c) Range of motion. (d)-(f) Coupled belt-linkage actuation for the knee, ankle, and toe. tors are summarized in Table I. 2.2 Cooperative Actuation As shown in Figs. 2(d)-(f), the knee, ankle, and toe ac￾tuators are intentionally coupled: when the foot contacts the ground, they cooperate to extend the knee and per￾form ankle p… view at source ↗
Figure 4
Figure 4. Figure 4: Torque–speed envelopes of the CA mapping. (a)/(b) Left/right ankle motors. (c)/(d) Ankle pitch (L+R) and roll (L−R) joints, projected through the CA Jacobian. Red: motoring (τω ≥ 0); Blue: regenerative (τω < 0). 3. LEARNING-BASED CONTROL 3.1 Simulation Setup Minimizing Sim-To-Real Gap Although learning-based control has recently over￾come the limitations of traditional model-based control in locomotion res… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Hip actuator: U10 + cycloidal gear. (b)/(c) Knee and ankle/toe actuators: BLDC + planetary gear. (d) Implemented actuators. where ϕ, θ ∈ R7 are the motor and joint angle vectors, respectively. ϕ contains the hip yaw, roll, and pitch mo￾tors, followed by the knee, left and right ankle, and toe motors. θ contains the hip yaw, roll, and pitch joints, fol￾lowed by the knee, ankle pitch and roll, and toe jo… view at source ↗
Figure 5
Figure 5. Figure 5: Gait snapshots at 1.33 m/s. Top: toe-equipped; bottom: toe-ablation. 4.1 Efficient Walking and Impact Absorption To compare energy efficiency and impact absorption with and without an active toe, we performed ten straight￾line walking trials over a 20 m path at 1.33 m/s for each configuration. In [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: T-test agility comparison. slower, it exhibits greater agility in turning and stays closer to the prescribed path, finishing marginally faster overall [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: Gait-cycle-averaged right-leg power per joint (top) and total breakdown (bottom). 970.0 N) [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

Human legs exhibit high efficiency, agility, and impact absorption, with toes playing a crucial role in these capabilities. While many attempts have been made to implement human-like toes in robots, they have not fully replicated human characteristics nor rigorously validated their benefits. We propose a 14-DOF biped robot emulating human toes' lightweight, high-torque, robust nature. To quantitatively analyze the effectiveness of the active toes in terms of agility, efficiency, and impact absorption, we developed a high-fidelity simulation training environment that reflects actual actuators with coupled transmissions and accurate power consumption. To ensure a fair comparison between configurations with and without active toes, we designed a minimal RL reward function and applied an identical training procedure to both. The simulation results indicate that, at 1.33 m/s walking, the toe-equipped robot reduced CoT by 17.5% and heel-strike GRF by 5.0% compared with the toe-ablation configuration. On the agility test, average and maximum path deviation decreased by 25.0% and 34.0%, respectively.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims that a 14-DOF biped robot with active toes, trained via RL in a high-fidelity simulation that models actuators, coupled transmissions, and power consumption, outperforms a toe-ablated version in efficiency, impact absorption, and agility. Using identical minimal-reward training for both, it reports 17.5% lower cost of transport, 5.0% lower heel-strike GRF at 1.33 m/s walking, and 25.0%/34.0% lower average/max path deviation in agility tests.

Significance. This simulation-based comparative study offers controlled evidence for the advantages of active toes in bipedal locomotion under fair training conditions. The minimal reward design and identical procedures are strengths that reduce bias in the comparison. If the high-fidelity sim is accurate, the results could inform robot design, though the work is limited to simulation without physical validation.

major comments (1)
  1. [Abstract and Results] The reported improvements (17.5% CoT reduction, 5.0% GRF reduction, 25%/34% path deviation reductions) are presented as point estimates in the abstract and results without error bars, standard deviations across seeds, or the number of independent training runs. RL training variance makes it necessary to establish that these differences exceed run-to-run variability to support the quantitative claims.
minor comments (2)
  1. The agility test protocol (path definition, speed, termination conditions) should be described in more detail to allow exact reproduction of the deviation metrics.
  2. A table summarizing the key metrics (CoT, GRF, path deviation) for both configurations, with any available statistics, would improve clarity and comparison.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive summary and for the constructive comment on statistical reporting. We agree that variability measures are important for RL-based comparisons and will revise the manuscript to address this.

read point-by-point responses

  1. Referee: [Abstract and Results] The reported improvements (17.5% CoT reduction, 5.0% GRF reduction, 25%/34% path deviation reductions) are presented as point estimates in the abstract and results without error bars, standard deviations across seeds, or the number of independent training runs. RL training variance makes it necessary to establish that these differences exceed run-to-run variability to support the quantitative claims.

    Authors: We acknowledge that the current manuscript reports point estimates from the training runs performed and does not include standard deviations or error bars. To strengthen the claims, we will rerun the training procedure for both configurations across multiple independent random seeds (at least five per configuration). In the revised version we will report means and standard deviations for CoT, heel-strike GRF, and path-deviation metrics, add error bars to the relevant figures, and update the abstract and results text to reflect these statistics. This will allow readers to verify that the reported differences exceed run-to-run variability. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper reports quantitative performance differences (CoT, GRF, path deviation) obtained by running identical RL training procedures on two distinct robot configurations inside the same high-fidelity simulator. No equations, parameter fits, or self-citations are presented that would make any reported metric equivalent to its own inputs by construction; the comparison is strictly empirical and internal to the simulation runs. The derivation chain therefore remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract alone, no explicit free parameters, axioms, or invented entities are stated; the simulation fidelity and RL reward design are treated as standard domain assumptions.

pith-pipeline@v0.9.1-grok · 5757 in / 1100 out tokens · 21486 ms · 2026-06-26T17:47:17.668081+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

28 extracted references · 6 canonical work pages · 2 internal anchors

  1. [1]

    Kinesiology of the Musculoskele- tal System: Foundations for Rehabilitation,

    D. A. Neumann, “Kinesiology of the Musculoskele- tal System: Foundations for Rehabilitation,” 3rd ed.,Elsevier, 2016, pp. 595, 717

    2016

  2. [2]

    Mann’s Surgery of the Foot and Ankle,

    M. J. Coughlin, C. L. Saltzman, and R. A. Mann, “Mann’s Surgery of the Foot and Ankle,” 9th ed., Elsevier, 2013, pp. 14

    2013

  3. [3]

    Man-System Integration Standards,

    NASA, “Man-System Integration Standards,” John- son Space Center, Houston, TX, 1995. [Online]. Available: https://msis.jsc.nasa.gov

    1995

  4. [4]

    The Role of the Great Toe in Balance Per- formance,

    S. Chou, H. Cheng, J. Chen, Y . Ju, Y . Lin, and M. Wong, “The Role of the Great Toe in Balance Per- formance,”Journal of Orthopaedic Research, vol. 27, no. 4, pp. 549–554, 2009

    2009

  5. [5]

    Berkeley Humanoid: A Re- search Platform for Learning-based Control,

    Q. Liao, B. Zhang, X. Huang, X. Huang, Z. Li, and K. Sreenath, “Berkeley Humanoid: A Re- search Platform for Learning-based Control,”arXiv preprint arXiv:2407.21781, 2024

    work page arXiv 2024

  6. [6]

    Learning-based legged locomo- tion: State of the art and future perspectives,

    S. Ha, J. Lee, M. van de Panne, Z. Xie, W. Yu, and M. Khadiv, “Learning-based legged locomo- tion: State of the art and future perspectives,”The International Journal of Robotics Research, 2025

    2025

  7. [7]

    Deep Reinforcement Learning for Robotic Bipedal Locomotion: A Brief Survey,

    L. Bao, J. Humphreys, T. Peng, and C. Zhou, “Deep Reinforcement Learning for Robotic Bipedal Locomotion: A Brief Survey,”arXiv preprint arXiv:2404.17070, 2024

    work page arXiv 2024

  8. [8]

    How to Train Your Robot with Deep Reinforcement Learning; Lessons We’ve Learned,

    J. Ibarz, J. Tan, C. Finn, M. Kalakrishnan, P. Pastor, and S. Levine, “How to Train Your Robot with Deep Reinforcement Learning; Lessons We’ve Learned,” arXiv preprint arXiv:2102.02915, 2021

    work page arXiv 2021

  9. [9]

    Torque-based Deep Reinforcement Learn- ing for Task-and-Robot Agnostic Learning on Bipedal Robots Using Sim-to-Real Transfer,

    D. Kim, G. Berseth, M. Schwartz, and J. Park, “Torque-based Deep Reinforcement Learn- ing for Task-and-Robot Agnostic Learning on Bipedal Robots Using Sim-to-Real Transfer,”IEEE Robotics and Automation Letters, vol. 8, no. 10, pp. 6051–6058, Oct. 2023

    2023

  10. [10]

    Learning locomotion skills for cassie: Iterative design and sim-to-real,

    Z. Xie, P. Clary, J. Dao, P. Morais, J. Hurst, and M. van de Panne, “Learning locomotion skills for cassie: Iterative design and sim-to-real,” inProc. of Conference on Robot Learning (CoRL), pp. 317– 329, 2020

    2020

  11. [11]

    Learning to walk without dynamics random- ization,

    J. Dao, H. Duan, K. R. Green, J. Hurst, and A. Fern, “Learning to walk without dynamics random- ization,” inConference on Robot Learning (CoRL), 2020

    2020

  12. [12]

    Robust feedback motion policy design using rein- forcement learning on a 3d digit bipedal robot,

    G. A. Castillo, B. Weng, W. Zhang, and A. Hereid, “Robust feedback motion policy design using rein- forcement learning on a 3d digit bipedal robot,” in Proc. of IEEE/RSJ International Conference on In- telligent Robots and Systems, pp. 5136–5143, 2021

    2021

  13. [13]

    Bioinspired Control of Walking With Toe-Off, Heel-Strike, and Disturbance Rejection for a Biped Robot,

    X. Chen, Z. Yu, W. Zhang, Y . Zheng, Q. Huang, and A. Ming, “Bioinspired Control of Walking With Toe-Off, Heel-Strike, and Disturbance Rejection for a Biped Robot,”IEEE Transactions on Industrial Electronics, vol. 64, no. 10, pp. 7962–7971, Oct. 2017

    2017

  14. [14]

    Hybrid toe and heel joints for biped/humanoid robots for natural gait,

    R. P. Kumar, N. Handharu, J. Yoon, and G. Kim, “Hybrid toe and heel joints for biped/humanoid robots for natural gait,” inProc. of International Conference on Control, Automation and Systems, Seoul, Korea, pp. 2687–2692, 2007

    2007

  15. [15]

    Effect of toe joint stiffness and toe shape on walking biome- chanics,

    E. C. Honert, G. Bastas, and K. E. Zelik, “Effect of toe joint stiffness and toe shape on walking biome- chanics,”Bioinspiration & Biomimetics, vol. 13, no. 6, 2018

    2018

  16. [16]

    Ef- fects of toe-off and heel-off motions on gait perfor- mance of biped robots,

    M. Ezati, M. Khadiv, and S. A. A. Moosavian, “Ef- fects of toe-off and heel-off motions on gait perfor- mance of biped robots,” inProc. of 3rd RSI Inter- national Conference on Robotics and Mechatronics (ICROM), Tehran, Iran, pp. 7–12, 2015

    2015

  17. [17]

    Trajectory planning and control for biped robot with toe and heel joints,

    T. Sato, S. Sakaino, and K. Ohnishi, “Trajectory planning and control for biped robot with toe and heel joints,” inProc. of 11th IEEE International Workshop on Advanced Motion Control (AMC), Na- gaoka, Japan, pp. 129–136, 2010

    2010

  18. [18]

    Human-like walking with knee stretched, heel-contact and toe-off motion by a humanoid robot,

    Y . Ogura et al., “Human-like walking with knee stretched, heel-contact and toe-off motion by a humanoid robot,” inProc. of IEEE/RSJ Interna- tional Conference on Intelligent Robots and Systems (IROS), Beijing, China, pp. 3976–3981, 2006

    2006

  19. [19]

    A study of function of foot’s medial longitudinal arch using biped humanoid robot,

    K. Hashimoto et al., “A study of function of foot’s medial longitudinal arch using biped humanoid robot,” inProc. of IEEE/RSJ International Con- ference on Intelligent Robots and Systems (IROS), Taipei, Taiwan, pp. 2206–2211, 2010

    2010

  20. [20]

    HyperLeg: Biomechanics- Inspired High-DOF Leg and Toe Mechanism for Highly Dynamic Motions,

    D.-Y . Kim et al., “HyperLeg: Biomechanics- Inspired High-DOF Leg and Toe Mechanism for Highly Dynamic Motions,” inProc. of IEEE Inter- national Conference on Robotics and Automation (ICRA), Yokohama, Japan, pp. 2456–2462, 2024

    2024

  21. [21]

    Design of dynamic legged robots,

    S. Kim and P. Wensing, “Design of dynamic legged robots,”F oundations and Trends in Robotics, vol. 5, pp. 117–190, Jan. 2017

    2017

  22. [22]

    Locomotion: dealing with fric- tion,

    V . Radhakrishnan, “Locomotion: dealing with fric- tion,”Proc. of the National Academy of Sciences of the United States of America, vol. 95, no. 10, pp. 5448–5455, May 1998

    1998

  23. [23]

    Tello Leg: The Study of De- sign Principles and Metrics for Dynamic Humanoid Robots,

    Y . Sim and J. Ramos, “Tello Leg: The Study of De- sign Principles and Metrics for Dynamic Humanoid Robots,”IEEE Robotics and Automation Letters, vol. 7, no. 4, pp. 9318–9325, 2022

    2022

  24. [24]

    Experimental evalua- tion of simple estimators for humanoid robots,

    T. Flayols, A. Del Prete, P. Wensing, A. Mifsud, M. Benallegue, and O. Stasse, “Experimental evalua- tion of simple estimators for humanoid robots,” in Proc. of IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids), Birmingham, UK, pp. 889–895, 2017

    2017

  25. [25]

    Proximal Policy Optimization Algorithms

    J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Proximal Policy Optimization Al- gorithms,”arXiv preprint arXiv:1707.06347, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  26. [26]

    Isaac Lab: A GPU-Accelerated Simulation Framework for Multi-Modal Robot Learning

    M. Mittal et al., “Isaac Lab: A GPU-Accelerated Simulation Framework for Multi-Modal Robot Learning,”arXiv preprint arXiv:2511.04831, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  27. [27]

    Learn- ing Thermal-Aware Locomotion Policies for an Electrically-Actuated Quadruped Robot,

    L. Qian, Y . Wan, S. Wang, and X. Luo, “Learn- ing Thermal-Aware Locomotion Policies for an Electrically-Actuated Quadruped Robot,”arXiv preprint arXiv:2603.01631, 2026

    work page arXiv 2026

  28. [28]

    Reliability and validity of the T-test as a measure of agility, leg power, and leg speed in college-aged men and women,

    K. Pauole, K. Madole, J. Garhammer, M. Lacourse, and R. Rozenek, “Reliability and validity of the T-test as a measure of agility, leg power, and leg speed in college-aged men and women,”Journal of Strength and Conditioning Research, vol. 14, no. 4, pp. 443–450, Nov. 2000

    2000