WaveForward: An Omnidirectional Passive Wheeled Quadruped Robot with Casters

Chuanlin Zhao; Qifeng Zheng; Shuhan Wang; Tiancheng Ma; Weixian Lin; Xin Luo

arxiv: 2606.25299 · v1 · pith:QNNMCJTPnew · submitted 2026-06-24 · 💻 cs.RO

WaveForward: An Omnidirectional Passive Wheeled Quadruped Robot with Casters

Chuanlin Zhao , Qifeng Zheng , Shuhan Wang , Tiancheng Ma , Weixian Lin , Xin Luo This is my paper

Pith reviewed 2026-06-25 21:29 UTC · model grok-4.3

classification 💻 cs.RO

keywords quadruped robotpassive casteromnidirectional mobilitycost of transportactor-critic controllegged locomotionwheeled-legged robot

0 comments

The pith

A quadruped robot with passive casters on its legs moves in any direction while cutting transport cost by up to 89.1 percent versus leg-only walking.

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

The paper presents a quadruped that mounts ordinary casters on each leg to gain omnidirectional mobility without powered wheels or extra actuators. An asymmetric actor-critic controller exploits knowledge of the casters' angles and speeds, while a posture adjustment strategy uses the leg joints to set the caster axis direction according to the commanded velocity. Multiple propulsion modes convert controlled caster twisting into forward force. Experiments including slalom runs and mode changes confirm that the approach delivers versatile movement and the stated energy savings relative to pure legged gaits.

Core claim

Equipping each leg of a quadruped with a standard passive caster, together with an asymmetric actor-critic controller that receives privileged caster angle and velocity data and a velocity-command-driven caster-base posture adjustment, enables omnidirectional locomotion and yields up to an 89.1 percent reduction in cost of transport compared with legged motion alone.

What carries the argument

Asymmetric actor-critic controller that ingests privileged caster angles and velocities, paired with a velocity-command-based caster base posture adjustment strategy that reorients the caster axis via actuated joints.

Load-bearing premise

The controller and posture strategy will continue to deliver the reported omnidirectional control and energy savings on real surfaces with varying friction, slopes, and sensor noise without added hardware or parameter changes.

What would settle it

A physical trial on uneven outdoor terrain with changing friction that measures whether the 89.1 percent COT reduction and full omnidirectional capability persist without controller retuning or extra sensors.

Figures

Figures reproduced from arXiv: 2606.25299 by Chuanlin Zhao, Qifeng Zheng, Shuhan Wang, Tiancheng Ma, Weixian Lin, Xin Luo.

**Figure 1.** Figure 1: The snapshot of the slalom test. motion capabilities. The incorporation of casters renders the system strongly underactuated. To address this challenge, we propose a posture adjustment strategy for the caster base, which adjusts its posture based on velocity reference commands. This approach enables the caster to generate a constraint-based propulsive force and alleviates the severe underactuation problem.… view at source ↗

**Figure 2.** Figure 2: Force analysis of the caster during propulsion. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: , with the normal support force set to 𝑁ό = 50𝑁 . Within the considered inclination range, the sign of 𝐹 is mainly determined by the sign of 𝛼: when 𝛼 > 0, 𝐹 > 0, whereas when 𝛼 < 0, 𝐹 < 0. When 𝛼 = 0, the swivel axis is perpendicular to the ground, and the ground static friction only provides grip to satisfy the no-slip constraint without producing a propulsive component. Thus, no propulsive force can be … view at source ↗

**Figure 4.** Figure 4: The omnidirectional passive wheeled quadruped framework is based on an asymmetric Actor-Critic. During training, the privileged observations, [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: The schematic diagram of caster base posture adjustment strategy. [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

**Figure 5.** Figure 5: 𝝓֏ and 𝝓̇֏ represent the caster swivel axis joint positions and velocities, while 𝒑̇֏ is the linear velocity observation of the torso in the world coordinate frame. D. Reward Function Design The reward functions are designed to encourage passive wheeled quadruped robots to learn the posture adjustment strategy of the caster base, as shown in Section B, and to use the periodic oscillations motion of differe… view at source ↗

**Figure 6.** Figure 6: The simulation results of the posture adjustment strategy. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 10.** Figure 10: The variable motion mode switch results from masking the legs’ [PITH_FULL_IMAGE:figures/full_fig_p006_10.png] view at source ↗

**Figure 8.** Figure 8: The results of the actuated joint angles variation curves during the [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗

**Figure 12.** Figure 12: The power curves of the caster and the point foot in the same [PITH_FULL_IMAGE:figures/full_fig_p007_12.png] view at source ↗

**Figure 11.** Figure 11: The experiment trajectories of a quadruped on campus. The blue [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗

read the original abstract

Wheeled-legged robots possess both agile mobility for traversing complex terrains and high efficiency, making them suitable for long-distance transportation applications. Conventional actuated wheeled robots require specialized hardware and electrical design due to the incorporation of wheel components. We propose a novel and low-cost passive wheeled legged robot equipped with standard casters on each leg to obtain omnidirectional mobility. The control method employs an asymmetric actor-critic structure, enabling the utilization of the privileged information of the passive caster's angles and velocities. We develop a caster base posture adjustment strategy based on velocity commands, utilizing actuated joints to modify the caster base joint axis posture and thereby adjust the propulsion direction of the casters. Moreover, we implemented multiple propulsion modes to achieve varying degrees of caster twisting oscillation, converting these into propulsive force. We conducted a slalom test and mode switch experience, which shows the passive wheeled quadruped could achieve omnidirectional movement versatility, and reduce the cost of transport (COT) by up to 89.1% with respect to legged motion.

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.

Desk Editor's Note private letter to a colleague

Passive-caster quadruped with asymmetric RL control claims big COT gains but rests on privileged caster states that low-cost hardware probably cannot observe directly.

read the letter

The paper builds a quadruped with ordinary passive casters bolted to the feet and shows it can move omnidirectionally by combining legged steps with wheeled propulsion. They train an asymmetric actor-critic that sees caster angles and velocities during training, add a simple posture adjustment on the leg joints to steer the caster direction, and run several propulsion modes that turn caster twist into forward force. The reported outcome is a slalom test plus mode switches and an 89.1 % drop in cost of transport versus pure legged walking.

The hardware idea is straightforward and the efficiency number is large enough to notice if the measurement is clean. Adding cheap casters to existing legs avoids the extra motors and wiring that most wheeled-legged designs require, which is a practical step for low-cost platforms.

Two issues stand out. First, the abstract gives no measurement protocol, baseline robot, trial count, or variance for the COT figure, so it is impossible to judge how solid the 89 % claim actually is. Second, the controller explicitly uses privileged caster angle and velocity information. On a truly passive, sensor-free caster the robot cannot observe those states without either adding hardware (which undercuts the low-cost story) or running an estimator whose error would likely shrink the reported gains. The stress-test note correctly flags this observability gap; nothing in the supplied abstract shows it has been closed.

The work is aimed at groups already building hybrid wheeled-legged robots who need cheap omnidirectional options. It is worth sending to a serious referee because the design is simple to replicate and the efficiency claim is falsifiable, but the review will have to press on the sensing question and the missing experimental details before the numbers can be trusted.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes WaveForward, a low-cost passive wheeled quadruped robot equipped with standard casters on each leg to enable omnidirectional mobility. Control relies on an asymmetric actor-critic reinforcement learning structure that exploits privileged information on caster angles and velocities, combined with a velocity-command-based caster base posture adjustment strategy and multiple propulsion modes that convert caster twisting oscillation into propulsive force. Slalom and mode-switch tests are reported to demonstrate omnidirectional versatility and up to 89.1% reduction in cost of transport relative to pure legged motion.

Significance. If the quantitative efficiency gains hold on hardware that truly lacks dedicated caster sensors, the combination of passive casters with actuated legs and the described control strategy would represent a practical route to high-efficiency omnidirectional locomotion without specialized wheel actuators, with potential value for long-distance transport tasks.

major comments (2)

[Abstract] Abstract: the central claim of up to 89.1% COT reduction (and the associated slalom/mode-switch results) is presented without any description of measurement method, baseline legged controller, number of trials, error bars, or statistical significance; these omissions are load-bearing because the performance numbers are the primary evidence offered for the robot's advantage.
[Control method] Control method description: the asymmetric actor-critic is stated to utilize 'privileged information of the passive caster's angles and velocities,' yet the manuscript provides no account of how these states are obtained or estimated on the low-cost passive platform; because the reported COT gains and omnidirectional behavior rest on this controller, the observability gap directly affects whether the empirical results can be realized on the described hardware.

minor comments (1)

[Abstract] Abstract: 'mode switch experience' appears to be a typographical error for 'mode switch experiment.'

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight important aspects of clarity in our presentation of results and methods. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim of up to 89.1% COT reduction (and the associated slalom/mode-switch results) is presented without any description of measurement method, baseline legged controller, number of trials, error bars, or statistical significance; these omissions are load-bearing because the performance numbers are the primary evidence offered for the robot's advantage.

Authors: We agree that the abstract would benefit from additional methodological context to support the reported performance claims. In the revised manuscript, we will expand the abstract to briefly describe the COT measurement approach, the baseline legged controller for comparison, the number of trials, and reference the error bars and statistical details provided in the experimental section of the main text. revision: yes
Referee: [Control method] Control method description: the asymmetric actor-critic is stated to utilize 'privileged information of the passive caster's angles and velocities,' yet the manuscript provides no account of how these states are obtained or estimated on the low-cost passive platform; because the reported COT gains and omnidirectional behavior rest on this controller, the observability gap directly affects whether the empirical results can be realized on the described hardware.

Authors: The asymmetric actor-critic utilizes privileged caster state information exclusively during simulation-based training. The deployed policy on hardware relies solely on the robot's proprioceptive sensors and does not require direct caster measurements. We will revise the control method section to explicitly distinguish the training and deployment phases and clarify how the policy achieves the reported results on the passive hardware platform. revision: yes

Circularity Check

0 steps flagged

No circularity; claims rest on empirical hardware tests

full rationale

The paper introduces a passive caster-equipped quadruped and an asymmetric actor-critic controller plus posture-adjustment strategy. All performance assertions (omnidirectional mobility, up to 89.1% COT reduction versus legged gait) are presented as outcomes of physical slalom and mode-switch experiments rather than any first-principles derivation, fitted parameter renamed as prediction, or self-citation chain. No equations appear that define a quantity in terms of itself or that reduce a claimed result to its own inputs by construction. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is limited to standard implicit assumptions in robotics control papers.

axioms (1)

domain assumption Standard rigid-body dynamics and caster rolling-without-slipping assumptions hold during locomotion
Required for any wheeled robot simulation or control derivation but not explicitly validated in abstract.

pith-pipeline@v0.9.1-grok · 5723 in / 1059 out tokens · 23101 ms · 2026-06-25T21:29:12.320392+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Max: A Wheeled-Legged Quadruped Robot for Multimodal Agile Locomotion,

Q. Zhou, S. Yang, X. Jiang, et al., “Max: A Wheeled-Legged Quadruped Robot for Multimodal Agile Locomotion,” in IEEE Transactions on Automation Science and Engineering, vol. 21, no. 4, pp. 7562-7582, Oct. 2024

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Skating with a Force Controlled Quadrupedal Robot,

M. Bjelonic, C. Dario Bellicoso, M. Efe Tiryaki and M. Hutter, “Skating with a Force Controlled Quadrupedal Robot,” 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain, 2018, pp. 7555-7561

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Pith/arXiv arXiv 2017

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