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REVIEW 4 major objections 5 minor 33 references

TriphiBot: A Triphibious Robot Combining FOC-based Propulsion with Eccentric Design

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read A quadcopter with two passive wheels and an eccentric center of gravity can fly, drive, and swim using a single set of rotors.

desk verdict A credible triphibious hardware demo with a genuinely simple eccentric-CoG design; the efficiency and 'seamless' claims are narrower than the evidence, but the prototype deserves a serious referee. read the letter →

arxiv 2602.01385 v2 pith:K5FT44FO submitted 2026-02-01 cs.RO

Xiangyu Li , Tiancheng Lai , Mingwei Lai , Junxiao Lin , Mengke Zhang , Junping Zhi , Chao Xu , Fei Gao
show 1 more author
Yanjun Cao
This is my paper · ORCID
classification cs.RO
keywords triphibiousroboteccentriccenterofgravityfield-orientedcontrolhybridnonlinearmodelpredictivecross-domaintransitionpassivewheelsunderwaterpropulsiontorquematching
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 argues that a single minimalist platform—a quadcopter frame with two freely rotating wheels and no extra actuators—can operate across air, land, and water. The key efficiency claim is that by deliberately shifting the center of gravity toward the front, the rotor thrust vector aligns with the direction of ground motion by default, so nearly all thrust contributes to propulsion instead of lifting the robot against gravity. To handle the vastly different torque demands of air and water, the authors propose a unified propulsion system based on field-oriented control (FOC) that gives precise, fast bidirectional rotor thrust. A hybrid nonlinear model predictive controller, combined with PID for underwater entry and exit, coordinates seamless transitions between modes. If correct, the design offers a lightweight, high-efficiency alternative to existing dual-mode and mechanically complex triphibious robots.

What carries the argument

The load-bearing elements are (1) the eccentric CoG: a shift δ of 1.5 cm from the geometric center to the mass center, which creates a gravity restoring torque and aligns thrust with ground motion, eliminating the need for active tilting mechanisms; (2) the FOC-based unified propulsion system, which uses encoder-measured rotor position to generate precise rotating magnetic fields, enabling high torque at low speed, very high speed in air, and fast bidirectional switching; and (3) the differential flatness of the terrestrial dynamics, which lets a single HNMPC controller, switching on altitude, command both aerial and ground modes using the same rotor inputs.

What would settle it

Run the robot on a surface with measurable slip or a gentle slope and compare trajectory-tracking RMSE to the flat-ground case; if RMSE degrades sharply or the HNMPC diverges when θT deviates from zero, the central claim that thrust is '100% aligned with motion by default' and that the flat-output mapping is valid would be falsified. Alternatively, measure the actual thrust direction with a load cell while the robot pitches during obstacle crossing: the 100% utilization claim depends on θT = 0.

Watch

Extended reading notes

Core claim

The paper's central discovery is that an eccentric CoG—a small forward shift of the center of gravity relative to the geometric center, following the roly-poly principle—makes the ground mode of a passive-wheeled quadcopter inherently efficient. When the wheels touch the ground, gravity rotates the body so the propeller plane is vertical; the restoring torque τr = mgδ sinθT passively stabilizes pitch, and the thrust vector is aligned with motion, allowing 100% of thrust to be used for propulsion. The authors show that the terrestrial dynamics are differentially flat with flat output [pW,x, pW,y, θT], permitting a unified HNMPC to plan and track trajectories across aerial and terrestrial mode

Load-bearing premise

The paper's efficiency and flatness claims assume a flat supporting surface, no wheel skidding, no lateral wheel motion, and pitch angle kept near zero during ground travel; the moment the robot pitches to cross an obstacle, the flat-output mapping used by the controller is no longer valid.

Editorial extensions

If this is right

  • Triphibious robots can be built from a standard quadcopter plus two passive wheels and a CoG shift, without added weight or actuators, preserving flight endurance.
  • The FOC propulsion unit can replace ESC-based drivers in aerial-aquatic robots to enable rapid, low-speed precise thrust control and better underwater energy efficiency.
  • The differential flatness result means trajectory generation and tracking on flat ground can reuse the same control pipeline as aerial flight, simplifying software and reducing tuning effort.
  • Smooth air-land-water transitions become possible with a single rotor set, reducing mechanical complexity and transition time compared to transformable designs.
  • The efficiency advantage of ground mode relative to flight becomes accessible without dedicated mechanical transformations, as the paper notes prior work achieving up to 95.37% energy savings.

Reading between the lines

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

  • A natural extension is applying the eccentric-CoG principle to other rotorcraft (e.g., fixed-wing hybrids or tailsitters) to reduce ground rolling resistance without servo-tilt mechanisms.
  • The flat-ground, no-slip assumption is the main boundary: on uneven or slippery terrain the flat-output mapping breaks, so a slip-aware or terrain-estimating version of the controller would be a logical next step.
  • The FOC driver's torque matching may make it a drop-in upgrade for existing aerial-aquatic vehicles, but the reported specific-thrust improvements should be replicated independently before broad adoption.
  • The water-to-air transition logic relies on rotor-speed monitoring to detect leaving the surface; a more robust state estimator using pressure or IMU sensing would likely be needed in waves or currents.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. TriphiBot is a triphibious robot built from a 1.1 kg quadcopter frame plus two passive wheels, with no additional actuators. The paper claims aerial, terrestrial, and aquatic locomotion, smooth transitions between these modes, and an eccentric center-of-gravity design that aligns rotor thrust with ground motion so that, in the nominal terrestrial configuration, 100% of thrust contributes to propulsion. A second contribution is a Field-Oriented Control (FOC) propulsion system intended to provide fast, precise bidirectional thrust and automatic torque matching in air and water. The paper derives aerial and terrestrial dynamics, proves differential flatness for both modes, and proposes a hybrid NMPC-PID control architecture. Experiments include propulsion bench tests, aerial and terrestrial figure-eight tracking, a 9 cm obstacle crossing, underwater attitude tracking, and water-to-air takeoff. The hardware demonstrations support the existence claim that the robot can fly, roll, swim, and transition among these modes; however, the strength of the efficiency and modeling claims is limited by the assumptions in the terrestrial model and by the absence of repeated trials and uncertainty quantification.

Significance. If the design and modeling claims hold, this is a useful minimalist contribution to cross-domain robotics: the eccentric-CoG idea is elegant, the FOC-based unified propulsion unit is plausible and experimentally supported, and the hybrid control architecture is a practical step toward seamless air-land-water operation. The paper clearly demonstrates the central hardware capability in real experiments, which is the strongest part of the work. It also provides quantitative comparisons with prior propulsion systems (e.g., specific thrust 0.825 N/W vs. 0.059 N/W for ESC, and vs. 0.265 N/W for TJ-FlyingFish), which are valuable even if single-trial. The main caveat is that the terrestrial flatness proof and the associated efficiency claims are derived under a flat, no-skid, horizontal-surface assumption that the paper's own obstacle and seabed experiments violate, so the theoretical guarantees are narrower than the claimed operational capability. The paper would be acceptable after substantial revision that honestly delimits these assumptions or extends the model.

major comments (4)
  1. [§III.B, Eq. (9), (14), (17); §V.D, Fig. 14(c); §V.E, Fig. 14(a)] The terrestrial differential-flatness proof and the HNMPC that relies on it are built on assumptions that the paper's own experiments violate. Eq. (9) constrains the robot to motion in a horizontal plane with p_z=0 and no lateral wheel velocity; Eq. (14) sets ψ_T from the velocity direction under a no-skid assumption; Eq. (17) then derives the required thrust from longitudinal acceleration. The 9 cm obstacle test in §V.D deliberately uses θ_T≠0 and contact with the obstacle, and the seabed experiment in §V.E operates on loose sediment where no-skid rolling is implausible. No slip model, terrain model, or disturbance/uncertainty term is provided. As a result, the flat-output mapping used by the HNMPC in Eqs. (18)–(20) is not valid in these demonstrated scenarios, and the '100% of thrust used for propulsion' claim holds only on a flat, high-friction, horizontal surface. This is load-bearin
  2. [§II.A and §V.B] The 95.37% energy-saving figure is not measured for TriphiBot; it is taken from prior work by overlapping authors (Lai et al. [14]) on a different, transformable robot. The statement 'Existing research has confirmed that robots using this method for ground movement can achieve energy savings of up to 95.37%' may be technically true, but it is presented in the introduction of the current paper as if it supports the eccentric-CoG design. The paper provides no onboard energy-consumption comparison between ground and flight modes for the actual TriphiBot prototype. Since ground-mode efficiency is a central contribution, the authors should either report a direct efficiency measurement for this platform, or clearly state that the figure is a literature result for a related mechanism and should not be attributed to the present design without further evidence.
  3. [§IV.A, Eq. (18)–(20)] The hybrid dynamics f(x,u)=η f_t(x,u)+(1−η) f_a(x,u) is not well-defined as written. The state vector X in §III.A contains both aerial states (v_A, Θ_A, ω_A) and terrestrial states (v_l, θ_T, ψ_T, ω_T), but f_t and f_a are defined on different state spaces and propagate different subsets of X. To be a valid single transition function for the NMPC constraint x_{i+1}=f(x_i,u_i), the unused states must be explicitly carried or their evolution during the transition must be defined. In addition, Eq. (20) sets η from the reference height p_W,z,k, whereas §V.F says the switch is based on 'real-time altitude and pitch angle.' If the switching is reference-based, a tracking error can trigger the wrong mode; if it is state-based, Eq. (20) is incorrect. This is a modeling/control consistency issue that should be clarified and reconciled.
  4. [§V.B–§V.E] The quantitative claims of superiority are based on single trials with no error bars, repeated runs, or statistical analysis. For example, the specific-thrust comparison (0.825 vs. 0.059 N/W, a 14× margin), the underwater startup time (0.14 s), and the trajectory-tracking RMSE values (aerial 0.096 m, terrestrial 0.074 m, hybrid 0.084 m) are reported without any indication of variance across runs. The underwater attitude-tracking maximum error of 31° is likewise a single observation. Given that the paper makes strong comparative claims, at least a few repeated trials and a measure of spread (or a clear statement that the data are representative) should be provided.
minor comments (5)
  1. [Fig. 2 caption] Typo: 'devided' should be 'divided'.
  2. [§V.B] The text states that underwater thrust T relates to rotational speed ω by T = c_a ω²; the coefficient should be the underwater thrust coefficient c_t,w, and the sign/direction dependence should be specified. Also, Table I lists c_t,a and c_t,w, but the notation in the text is inconsistent.
  3. [Fig. 13(a)] The legend reads 'TrofyBot', which is not defined; it should refer to 'Lai et al. [14]' and the comparison should be mentioned in the caption for clarity.
  4. [§III.B, Eq. (17)] If θ_T=0 is assumed for maximum energy efficiency, writing cosθ_T in the denominator is misleading because the expression is then just T = m ˙v_l. If θ_T is allowed to be nonzero in the flat-output parameterization, the text should state that Eq. (9) is modified accordingly, since a nonzero θ_T generally changes the vertical geometry and ground-contact constraints.
  5. [§II.B] The phrase 'maximum speed of up to 200,000 eRPM' refers to the electrical RPM capability of the driver electronics, not necessarily the mechanical rotor speed. Please clarify to avoid a misleading hardware claim.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: flatness/FOC/eccentric-CoG results are self-contained; only a minor non-load-bearing self-citation for the 95.37% energy-saving figure.

full rationale

The paper's central derivations are not circular. The terrestrial flatness proof in Section III.B is a constructive algebraic mapping: Eq. (14) sets yaw from the flat-output velocity under an explicitly stated no-skid assumption, Eq. (16) recovers the scalar ground speed, Eq. (17) recovers total thrust from the desired acceleration, and the remaining states/inputs follow from Eqs. (12), (15), and allocation (13). This is a standard flatness construction, not a prediction that reduces to fitted data. The 100%-thrust claim in Section II.A is a geometric consequence of the eccentric CoG design and θ_T = 0, not a fitted or renamed result. The FOC propulsion advantage is supported by independent static and step-response experiments in Section V.B, including comparisons against ESCs and an external platform. The only noteworthy self-citation is the 95.37% ground-mode energy-saving figure, which is borrowed from Lai et al. [14] with overlapping authorship and is not re-measured on this robot; however, it is a motivational benchmark rather than an input to the dynamics or control derivation, so it is not load-bearing circularity. The no-slip/flat-ground assumptions in Eqs. (9), (14), and (17) are violated by the obstacle-crossing and seabed experiments, but that is a modeling/robustness limitation, not circularity.

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

The central design relies on one hand-chosen geometric parameter (δ), several experiment-fitted coefficients, and unquantified hydrodynamic terms. The axioms are mostly standard dynamics and flat-ground assumptions, with one ad hoc modeling choice: switching between two different state-space models inside a single NMPC. No new physical entities are invented.

free parameters (6)
  • CoG offset δ = 1.5 cm
    Design choice claimed to align thrust with ground motion and provide passive pitch stability; no optimization or derivation of the value is given.
  • Thrust coefficients c_t,f, c_t,r, c_w,f, c_w,r, c_m = c_t,f=1.6e-8, c_t,r=7.79e-9 N·s^2; c_w,f=1.83e-5, c_w,r=8.68e-6 N·s^2; c_m=2.56e-10 N·m·s^2
    Fitted from static thrust tests; water coefficients are two-to-three orders of magnitude larger than air coefficients, and direction-dependent values are introduced for forward and reverse thrust.
  • Drag coefficients C_f and C_t = not reported
    Eq. (1) states they are set by manual adjustment or system identification; without values, the ground and water dynamics in Eqs. (6)–(12) are underdetermined.
  • Added mass m_a and added inertia M_a = not reported
    Introduced in Eqs. (6) and (7) for water mode but never quantified; all underwater dynamic claims depend on them.
  • MPC horizon, weights, and switching threshold = N=40, dt=0.05, Qp=diag(5000,5000,3000), etc.; h_judge not reported
    Hand-tuned; tracking RMSE depends on these values and on the fitted dynamics model.
  • PID gains for underwater and water-air transition control = not reported
    The attitude and water-exit controllers (Eq. 25) are central to the transition claims, but their gains are omitted.
assumptions (6)
  • standard math Standard multirotor dynamics and quadrotor differential flatness from prior work
    Used without proof in Section III.B for aerial mode, citing Mellinger-Kumar and related flatness results.
  • domain assumption Flat, horizontal, no-skid ground; no lateral wheel movement
    Section III.A Eq. (9) and Section III.B Eq. (14); violated on uneven terrain, slopes, or slippery seabeds.
  • domain assumption Ground-mode efficiency condition sets θ_T = 0 and ignores vertical motion of the body
    Section III.B; required to derive total thrust from horizontal acceleration (Eq. 17).
  • ad hoc to paper Hybrid dynamics f(x,u) = η f_t + (1−η) f_a with different state vectors can be fused in one NMPC
    Eqs. (18)–(19); no proof of stability or compatibility of the two state representations at the switching boundary.
  • domain assumption FOC motor parameters automatically identified by VESC software are accurate and unchanged after waterproofing
    Section II.B; parameter errors would degrade the claimed torque matching and low-speed control.
  • domain assumption Buoyancy center is vertically aligned with the CoG and slightly higher; robot has negative buoyancy
    Section II.A; not measured or verified, and underwater attitude dynamics depend on this balance.

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Cite this review

Pith. "Pith review of TriphiBot: A Triphibious Robot Combining FOC-based Propulsion with Eccentric Design." pith.science (2026). https://pith.science/paper/K5FT44FO

@misc{pith2026260201385,
  author       = {Pith},
  title        = {Pith review of: TriphiBot: A Triphibious Robot Combining FOC-based Propulsion with Eccentric Design},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K5FT44FO}},
  note         = {Machine review of arXiv:2602.01385}
}
read the original abstract

Triphibious robots capable of multi-domain motion and cross-domain transitions are promising to handle complex tasks across diverse environments. However, existing designs primarily focus on dual-mode platforms, and some designs suffer from high mechanical complexity or low propulsion efficiency, which limits their application. In this paper, we propose a novel triphibious robot capable of aerial, terrestrial, and aquatic motion, by a minimalist design combining a quadcopter structure with two passive wheels, without extra actuators. To address inefficiency of ground-support motion (moving on land/seabed) for quadcopter based designs, we introduce an eccentric Center of Gravity (CoG) design that inherently aligns thrust with motion, enhancing efficiency without specialized mechanical transformation designs. Furthermore, to address the drastic differences in motion control caused by different fluids (air and water), we develop a unified propulsion system based on Field-Oriented Control (FOC). This method resolves torque matching issues and enables precise, rapid bidirectional thrust across different mediums. Grounded in the perspective of living condition and ground support, we analyse the robot's dynamics and propose a Hybrid Nonlinear Model Predictive Control (HNMPC)-PID control system to ensure stable multi-domain motion and seamless transitions. Experimental results validate the robot's multi-domain motion and cross-mode transition capability, along with the efficiency and adaptability of the proposed propulsion system.

Figures

Figures reproduced from arXiv: 2602.01385 by the authors.

Figure 1
Figure 1. A depiction of the mission profile of TriphiBot, a triphibious robot [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Illustration of the TriphiBot’s hardware layout. It can be devided into [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. (a) The coordinate frames of the dynamics model of TriphiBot. (b) [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: The electronic equipment of the TriphiBot. The propulsion system [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]
Figure 5
Figure 5. Figure 5: Conceptual diagram of cross-domain transitions. (a) After changing the [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: The hybrid control structure of TriphiBot. The controller automatically [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: The FOC algorithm, in which Iq ref determines the motor torque. This algorithm adjusts the current Iq ref based on the rotational speed error to achieve torque matching. The current Id ref is usually set to 0 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 9
Figure 9. Figure 9: The static performance testing of the propulsion system: (a) Test Plat [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 10
Figure 10. Figure 10: (a) The response of the rotor to high-speed forward and backward [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: (a) The underwater power-rotation speed curves of different drivers. [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]
Figure 12
Figure 12. Figure 12: (a) Reference and real pW,xyz when tracking an 8-shaped aerial trajectory. (b) Reference and real pW,xy when tracking an 8-shaped terrestrial trajectory, the green dashed rectangular box indicates the extracted section of the trajectory. (c) Reference and real pW,xyz …
Figure 13
Figure 13. Figure 13: (a) Our real θT , TrofyBot’s real θT and reference θT of Zhang’s reference trajectory from the terrestrial extracted section. (b) The test results of tracking sinusoidal attitude signal and the absolute value of the error. that by controlling θT to improve ground clea…
Figure 14
Figure 14. Figure 14: (a) The robot is moving forward underwater. (b) Taking off from [PITH_FULL_IMAGE:figures/full_fig_p010_14.png]

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.