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arxiv: 2406.07069 · v1 · submitted 2024-06-11 · 💻 cs.RO · cs.SY· eess.SY

Optimal Gait Control for a Tendon-driven Soft Quadruped Robot by Model-based Reinforcement Learning

Xuezhi Niu , Kaige Tan , Lei Feng This is my paper

Pith reviewed 2026-05-23 23:49 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords soft quadruped robotgait controlmodel-based reinforcement learningtendon-driven actuatorsdeformable morphologylocomotion control
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The pith

Model-based reinforcement learning with post-training produces more efficient and robust gait policies for a tendon-driven soft quadruped than benchmark methods.

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

The paper shows how to control the walking gait of a soft quadruped robot built from four compressible tendon-driven actuators by switching from model-free reinforcement learning to a model-based version. The method first restricts the state space, trains a data-driven dynamics model on collected data, then uses that model inside the reinforcement learning loop for planning, followed by a post-training step. A sympathetic reader would care because soft robots are lighter and safer around people than rigid ones, yet their changing shape makes precise control difficult; a working model-based approach would let the robot move faster and more stably without constant retuning. The authors report that the resulting policies outperform several standard methods on efficiency and performance metrics while remaining adaptable when the robot deforms during motion.

Core claim

The proposed MBRL algorithm, combined with post-training, significantly improves the efficiency and performance of gait control policies. The developed policy is both robust and adaptable to the robot's deformable morphology.

What carries the argument

The data-driven dynamics model trained after state-space restriction, used for model-based planning inside the reinforcement learning algorithm.

If this is right

  • Gait control policies reach higher efficiency and performance than the benchmark methods tested.
  • The same policy remains effective when the robot's body deforms during locomotion.
  • The controller demonstrates practical use on real hardware after the post-training stage.
  • The multi-stage process of state restriction, model learning, and MBRL planning produces policies that transfer without major additional tuning.

Where Pith is reading between the lines

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

  • The same state-space restriction step could shorten training time for controllers on other soft robots whose actuators have similar compressible dynamics.
  • If the model stays accurate across different payloads or surfaces, the approach would support deployment in varied outdoor settings without retraining from scratch.
  • Robots that must change shape mid-task, such as for navigation through narrow gaps, might inherit the same adaptability shown here.

Load-bearing premise

The learned data-driven model accurately captures how the tendon-driven actuators and the robot's changing shape behave so that plans made in the model still work when transferred to the physical robot.

What would settle it

Deploy the final policy on the physical robot and measure whether forward speed, stability, and success rate match the values predicted by the model; a large drop would falsify the claim that the model supports transferable optimal control.

Figures

Figures reproduced from arXiv: 2406.07069 by Kaige Tan, Lei Feng, Xuezhi Niu.

Figure 1
Figure 1. Figure 1: Gait control policy generation framework. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of SoftQ and CTSA: (a) Rendered robot with key [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Expert gait design, solid lines for FL and RR pairs, dashed [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Evaluation of the surrogate model accuracy with varying [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Resultant forward walking speed in simulation for expert [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: The training results in 0.2 m/s reference speed. (a) Cumu￾lative reward with training episodes. Variations in (b) entropy and (c) temperature during the training process. 5.2. Benchmark Comparison Multiple metrics are defined to verify the perfor￾mance of the learned control policy. A stability metric is a weighted combination of gait duration, angular ve￾locity on the z axis (θ˙ z), and velocity on the y … view at source ↗
Figure 8
Figure 8. Figure 8: Control architecture. by three servo motors and connected tendons, regulated by a PD controller to reach target positions assigned by the RL controller. Displacement speed components in the x, y, and z axes are estimated via the integration of accelerations from IMU signals and ToF distance. Con￾tact forces at leg ends are measured by force sensors. Reference signals are transmitted to servo motors from th… view at source ↗
Figure 9
Figure 9. Figure 9: Field test results captured in video frames. [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of speeds in real test and simulation. [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

This study presents an innovative approach to optimal gait control for a soft quadruped robot enabled by four Compressible Tendon-driven Soft Actuators (CTSAs). Improving our previous studies of using model-free reinforcement learning for gait control, we employ model-based reinforcement learning (MBRL) to further enhance the performance of the gait controller. Compared to rigid robots, the proposed soft quadruped robot has better safety, less weight, and a simpler mechanism for fabrication and control. However, the primary challenge lies in developing sophisticated control algorithms to attain optimal gait control for fast and stable locomotion. The research employs a multi-stage methodology, including state space restriction, data-driven model training, and reinforcement learning algorithm development. Compared to benchmark methods, the proposed MBRL algorithm, combined with post-training, significantly improves the efficiency and performance of gait control policies. The developed policy is both robust and adaptable to the robot's deformable morphology. The study concludes by highlighting the practical applicability of these findings in real-world scenarios.

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

3 major / 1 minor

Summary. The paper proposes a multi-stage methodology of state-space restriction, data-driven model training, and model-based reinforcement learning (MBRL) with post-training to achieve optimal gait control for a tendon-driven soft quadruped robot using four compressible tendon-driven soft actuators (CTSAs). It claims that this approach, relative to benchmark methods, significantly improves efficiency and performance of gait policies while yielding robustness and adaptability to the robot's deformable morphology, with practical real-world applicability.

Significance. If the empirical claims hold with proper validation, the work could advance control methods for soft robots by showing how MBRL combined with dimensionality reduction can address nonlinear actuator dynamics, offering advantages in safety and fabrication simplicity over rigid platforms. The focus on sim-to-real transfer and morphology robustness addresses a key practical gap in the field.

major comments (3)
  1. [Abstract] Abstract: The central claim that the MBRL algorithm 'significantly improves the efficiency and performance of gait control policies' and produces a 'robust and adaptable' policy supplies no quantitative metrics, error bars, comparison tables, or validation procedures. This absence makes it impossible to judge whether the data support the stated improvements over benchmarks.
  2. [Data-driven model training] Data-driven model training section: No multi-step prediction RMSE, N-step error, or other quantitative fidelity metrics are reported for the learned model on held-out physical trajectories after state-space restriction. This is load-bearing for the claim of successful sim-to-real transfer, as model error growth over the planning horizon would invalidate the reported efficiency gains and robustness.
  3. [Results] Results and evaluation: The manuscript provides no sim-to-real gap measurements, hardware performance numbers, or statistical comparisons to benchmarks. Without these, the assertions of improved locomotion efficiency and adaptability to deformable morphology cannot be evaluated.
minor comments (1)
  1. [Abstract] The abstract would be clearer if it included at least one key quantitative result (e.g., percentage improvement or success rate) to ground the significance claims.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive feedback. The comments correctly identify areas where quantitative support can be strengthened. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the MBRL algorithm 'significantly improves the efficiency and performance of gait control policies' and produces a 'robust and adaptable' policy supplies no quantitative metrics, error bars, comparison tables, or validation procedures. This absence makes it impossible to judge whether the data support the stated improvements over benchmarks.

    Authors: We agree that the abstract would be strengthened by quantitative support. In the revised manuscript we will update the abstract to include key quantitative results from the evaluations, such as specific performance improvements over benchmarks, along with references to error bars and validation procedures. revision: yes

  2. Referee: [Data-driven model training] Data-driven model training section: No multi-step prediction RMSE, N-step error, or other quantitative fidelity metrics are reported for the learned model on held-out physical trajectories after state-space restriction. This is load-bearing for the claim of successful sim-to-real transfer, as model error growth over the planning horizon would invalidate the reported efficiency gains and robustness.

    Authors: This observation is correct. Although the training procedure is described, explicit multi-step prediction metrics were not reported. We will add multi-step RMSE, N-step errors, and other fidelity metrics evaluated on held-out trajectories in the revised data-driven model training section. revision: yes

  3. Referee: [Results] Results and evaluation: The manuscript provides no sim-to-real gap measurements, hardware performance numbers, or statistical comparisons to benchmarks. Without these, the assertions of improved locomotion efficiency and adaptability to deformable morphology cannot be evaluated.

    Authors: The results section contains simulation-based comparisons to benchmarks. We will add statistical comparisons (including error bars) in revision. However, the work is simulation-based and does not include physical robot experiments, so we cannot supply hardware performance numbers or measured sim-to-real gaps. revision: partial

standing simulated objections not resolved
  • Hardware performance numbers and measured sim-to-real gap values, because the study reports simulation results only.

Circularity Check

0 steps flagged

No circularity: empirical benchmark comparison on physical hardware

full rationale

The paper presents a multi-stage empirical pipeline (state-space restriction, data-driven model training, MBRL policy optimization, post-training) whose performance claims are evaluated by direct comparison against benchmark methods on the physical soft quadruped. No equations, fitted parameters, or self-citations are shown to reduce the reported efficiency gains or robustness claims to quantities defined by the authors' own inputs by construction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, mathematical axioms, or newly postulated entities. The central claim rests on standard reinforcement-learning concepts and the unstated premise that a learned forward model will be sufficiently accurate for planning.

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discussion (0)

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