{"id":"b2f3934e-2339-416e-baf2-3005950ea336","arxiv_id":"2411.11216","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"An Explicit Reference Governor plus a conjugate momentum observer estimates ground reaction forces and prevents foot slip in a simulated thruster-assisted legged robot.","lead":"Researchers propose an optimization-free controller and a ground force estimator for a legged robot with thrusters, tested only in a simplified computer simulation. The work is a step toward letting legged-aerial robots walk without heavy onboard optimization solvers.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (10) does not enforce the lateral friction cone: its second row bounds sgn(F_x) F_y, not |F_y|; if implemented as written, the ERG cannot guarantee no slip in y.","rationale":"The reader's CONDITIONAL verdict is reasonable. The most load-bearing issue is not only the absence of hardware validation—acknowledged in the conclusion—but a specific, checkable problem in the central constraint. The ERG's advertised guarantee is friction-cone satisfaction in both horizontal directions; Eq. (10) as printed enforces it only in one direction and a sign-corrupted expression in the other. Fig. 8 provides no Fy check. This makes the no-slip claim unsupported as written, and it is independent of the model-simplification concerns. The momentum-observer result is standard and self-consistent in the reduced-order setting; the lateral-force inaccuracy noted in Section V is consistent with the lateral constraint gap. Because the error may be typographical and the central idea is plausible, the paper should be accepted only after correction of Eq. (10) and demonstration that the y-friction margin is nonnegative across the reported simulation; this keeps the verdict at CONDITIONAL, as the reader already set.","tokens_in":8419,"tokens_out":10840,"duration_ms":111170,"concrete_test":"Re-run the Section V simulation while logging, for every stance foot, the margin μ Fz - |Fy| (computed from the same spring-damper/Stribeck ground model) and, if possible, with a nonzero lateral velocity reference such as v_y,d = 0.1 m/s. If the margin goes negative or the stance foot's lateral velocity exceeds the slip threshold at any time, the implemented constraint does not match the friction cone required by the no-slip claim. Independently, replace the second-row sign term in Eq. (10) with -sgn(u_{gi,y}) and confirm that the constraint-satisfaction margin in Fig. 8 changes or the controller's admissible set changes; if it does, the printed equation is the source of the discrepancy.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III-A, Eq. (10) defines the ERG friction constraint as hr = [ -sgn(u_x) 0 μs; 0 -sgn(u_x) μs; 0 0 1 ] ug,i + [0;0;-umin] >= 0. Row 1 correctly enforces μs Fz >= |Fx|, and row 3 enforces Fz >= umin. Row 2, however, reads μs Fz >= sgn(Fx) Fy, which is not equivalent to μs Fz >= |Fy|. The correct friction-pyramid row would use -sgn(u_y) in the second entry. Thus, as written, the constraint set is not the friction cone and the controller can, in principle, admit reference states with |Fy| > μs Fz. The paper's supporting figure, Fig. 8, plots only Fx against μFz and never checks Fy, so the evidence does not close this gap. If the simulation code contains the correct sgn(u_y), then Eq. (10) is a misprint that must be fixed; if the code follows Eq. (10), the central 'no slippage at the foot end' claim is unsupported for lateral forces. Either way, the manuscript as written does not substantiate the y-direction constraint.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an optimization-free control and estimation framework for the Husky legged-aerial robot in a reduced-order simulation. A modified Explicit Reference Governor (ERG) filters velocity references to keep predicted ground reaction forces inside a friction pyramid, with the goal of preventing foot slip on slippery ground (mu=0.25), while also incorporating thruster forces from an attitude controller. A conjugate momentum observer is used to estimate the total ground reaction force wrench, and its output is compared against a constrained-model estimator. The claims are supported by a 10-second simulation of a two-point-contact gait, with qualitative plots of body states, foot states, constraint satisfaction, and force estimates.","tokens_in":8705,"tokens_out":7155,"duration_ms":67334,"significance":"If the results hold, the paper offers a useful step toward real-time legged-aerial control: it replaces online optimization for friction-cone enforcement with an explicit governor and applies a standard momentum observer for ground reaction force estimation. The momentum observer equations in Section IV-A are standard and correctly avoid joint-acceleration measurement and mass-inertia inversion. The simulation is not circular in the obvious sense: the estimator is not fed the target ground reaction forces, and the observer gain is not fitted to the ground model. The paper also candidly acknowledges the limitations of the reduced-order model and the need for hardware validation. However, the central no-slip guarantee rests on Eq. (10), which as written does not enforce a two-sided lateral friction cone, and the quantitative evidence in Section V is too thin to fully support the claimed tracking and anti-slip performance.","major_comments":[{"comment":"The second row of the friction constraint is [0, -sgn(u_{gi,x}), mu_s], which enforces mu_s F_z >= sgn(F_x) F_y, not mu_s F_z >= |F_y|. As written, the admissible set is not the friction cone, so a reference state with |F_y| > mu_s F_z can satisfy the constraint whenever the sign of F_y opposes the sign of F_x. The correct row should use -sgn(u_{gi,y}) in the second entry. Fig. 8 plots only F_x against mu*F_z and never checks F_y, so the evidence in the paper does not close this gap. If the simulation code contains the correct sign, Eq. (10) is a misprint that must be corrected; if the code follows Eq. (10), the 'no slippage at the foot end' claim is unsupported for lateral forces. In addition, the vector d_r in Eq. (10) appears to contain four entries (0, 0, -u_min, g_{i,z}) while the matrix J_r is 3x3, so the dimensions are inconsistent; this must also be fixed.","section":"Section III-A, Eq. (10)"},{"comment":"The paper states that the ERG 'incorporates external thruster forces from an attitude controller,' but it never shows the ERG update law or the map from the filtered velocity reference and the applied thruster wrench u_t to the predicted ground reaction forces u_{g,i}. Eq. (9) only states the translational dynamics, and Eq. (10) only defines the constraint set; the construction of A and b, and the way u_t enters the constraint prediction, are omitted and referred to [18]. Since the thruster-aware modification is a stated contribution, this derivation should not be outsourced to a reference; the authors should include the explicit update rule or a self-contained derivation so that the claim can be checked.","section":"Section III-A"},{"comment":"The validation consists of one 10-second simulation run with qualitative plots. The claims that the foot 'doesn't slip' and that the momentum observer 'closely tracks' ground reaction forces are not accompanied by quantitative metrics: there is no foot slip distance or slip margin over the run, no RMSE or peak error for the F_x/F_y/F_z estimates, no convergence time for the observer, and no comparison against a baseline without the ERG or with different observer gains. The observer gain K_O = 1000*I_6 is stated but no sensitivity analysis is reported. The results section should include such metrics to substantiate the central claims.","section":"Section V"}],"minor_comments":[{"comment":"The manuscript contains several typos and grammatical errors, including 'V orndamme' in the references, 'the the' in the introduction, and 'the ERG is able to efficiently able to find' in Section V; a careful proofread is needed.","section":"Throughout"},{"comment":"The sentence 'The term ut ∈ R6 ut represents the actions exerted by the four thrusters' has a doubled 'ut'; it should read 'The term ut ∈ R6 represents ...'.","section":"Section II, after Eq. (5)"},{"comment":"The y-axis labels in Fig. 8 do not state units, and Fig. 10 has no in-plot legend distinguishing the actual, estimated, and constrained-model traces; adding units and legends would improve readability.","section":"Figures 8 and 10"},{"comment":"The statement 'The momentum observer is able to observe the sum total of the ground reaction forces shown in Fig. 10' should be rephrased to clarify that this is a simulation result for the reduced-order model, not a hardware observation.","section":"Section V"}],"recommendation":"major_revision","confidential_remarks":"The main technical issue, Eq. (10), may be a typographical error, but as submitted the manuscript does not establish the lateral no-slip constraint. I would also ask the editor to verify the novelty relative to the authors' own CDC 2021 paper [18]: the present paper's contribution is described as modifying the ERG to include thruster forces, but the modification is not derived in the text. The simulation study is preliminary; a revised version with a corrected constraint derivation, a self-contained ERG update rule, and quantitative metrics would be appropriate for a journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The new thing here is the specific combination: an ERG that accounts for thruster wrench from an attitude controller, paired with a conjugate momentum observer for ground reaction force estimation, on a legged-aerial platform. Neither piece is new — the ERG comes from the authors' own prior work and the momentum observer is textbook — but putting them together on a thruster-assisted quadruped is a reasonable extension, and the simulation results look internally consistent. The paper is clearly written and doesn't oversell itself; the conclusion openly lists the reduced-order model and stiff ground model as limitations.\n\nThe soft spot that actually bites is Eq. (10). The stress-test note is correct. Row 2 uses -sgn(u_{g i,x}) multiplying u_{g i,y}, which gives μs Fz ≥ sgn(Fx)Fy, not μs Fz ≥ |Fy|. That means the friction cone is only enforced laterally when the lateral force is opposite in sign to the longitudinal force; the other lateral direction is unconstrained. If the simulation code uses the correct row with -sgn(u_{g i,y}), then Eq. (10) is a misprint that needs fixing. If the code follows what is written, the advertised “no slippage” guarantee is simply not established for lateral forces. Figure 8 only plots Fx against μFz, so the evidence never closes that gap. This is the kind of thing a referee should catch, and it's fixable.\n\nThe other limitations are less severe but real: one 10-second simulation, no quantitative force-tracking error or slip margin, no code or parameter release, and the ERG update rule delegated to a prior paper. The reduced-order model with massless legs and thrusters that only produce upward force in the body frame means the hardware story is genuinely future work. The comparison against the constrained model is useful and the discussion of why that model fails (rank-deficient Delassus matrix, impulsive normal forces) is sensible.\n\nI largely agree with the reader's conditional verdict. The central idea holds up as a simulation proof-of-concept, and the stress-test gap is concrete but probably a typo rather than a fatal flaw. That said, the manuscript as written does not substantiate the lateral no-slip claim.\n\nWho should read it: people working on legged-aerial control, reference governors, or momentum-based force estimation will get something from it, if only as a building block. It deserves a serious referee, but the authors should be asked to correct Eq. (10) and ideally to add quantitative results or a second simulation. I would not cite it in its current form, but I'd take a look at a revised version.","headline":"A plausible simulation study combining an established ERG with a momentum observer for legged-aerial robots, but the friction constraint as written does not enforce |Fy| ≤ μFz and the evidence is a single 10 s run.","tokens_in":9242,"tokens_out":2103,"would_cite":false,"duration_ms":21413,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"An optimization-free reference filter prevents foot slip on slippery ground, and a momentum observer recovers ground reaction forces in simulation.","keywords":["legged-aerial robot","explicit reference governor","momentum observer","ground reaction force estimation","friction cone constraints","reduced-order model","thruster-assisted walking","Husky robot"],"falsifier":"Run the ERG controller on the physical Husky on a floor with friction coefficient 0.25 while recording stance-foot velocity; if any stance foot's horizontal velocity relative to the ground exceeds the slip threshold defined by the Stribeck model while the computed constraint $h_r \\geq 0$ is satisfied, the reduced-order friction-cone guarantee is falsified.","tokens_in":8245,"feed_emoji":"🤖","tokens_out":9233,"duration_ms":77094,"temperature":0.7,"pith_summary":"This paper proposes a lightweight walking controller for a legged-aerial robot that replaces online optimization with an Explicit Reference Governor (ERG): a filter that adjusts the commanded body velocity until predicted ground reaction forces stay inside a friction pyramid, so the feet do not slip even on a low-friction surface (coefficient 0.25 in simulation). The same framework feeds thruster forces from an attitude controller into the governor, letting thrust assist walking without a heavy onboard solver. The paper also tests a conjugate momentum observer that estimates the total ground reaction wrench from proprioceptive states and known thruster inputs, and shows it tracks the simulated ground forces better than a constrained-model estimator, which loses rank during two-point contact. The motivation is that legged-aerial robots have conflicting payload and computing requirements, so an optimization-free controller that still respects friction constraints could make low-power onboard computers viable.","feed_headline":"Reference filter stops foot slip on slippery ground, no solver needed","feed_subtitle":"A lightweight ERG controller filters velocity commands; a momentum observer estimates ground forces in simulation.","key_machinery":"The two load-bearing mechanisms are the Explicit Reference Governor and the conjugate momentum observer. The ERG is a filter on the commanded reference that enforces constraints by projecting the reference onto the constraint-admissible set; here the constraint $h_r$ is a friction pyramid built from predicted ground reaction forces in the triangular inverted pendulum model, so satisfying $h_r \\geq 0$ means the foot force lies inside the friction cone and should not slip. The momentum observer defines a residual $r = K_O \\bigl(p(t) - \\int_0^t (r - \\hat\\beta + B_t u_t)\\,dt\\bigr)$ whose steady state approaches the external ground wrench as the observer gain grows, avoiding joint-acceleration measurements and mass-matrix inversion. The constrained-model estimator, by contrast, pseudo-inverts $J M^{-1} J^\\top$, and that matrix loses rank during two-point contact, which the paper identifies as the reason it fails to track the impulsive ground forces.","core_discovery":"On the authors' own terms, the central claim is that foot slip can be prevented without solving any optimization problem at run time. The ERG treats the robot as a triangular inverted pendulum in two-point contact, computes a friction-pyramid constraint $h_r \\geq 0$ from the predicted ground reaction forces, and filters the reference velocity so the applied gait never leaves the admissible set. Simulated on the Husky reduced-order model with a Coulomb/Stribeck friction coefficient of 0.25, the controller keeps the feet from slipping and also places feet laterally to manage roll caused by thruster forces. The second claim is that a conjugate momentum observer with sufficiently high gains recovers the sum total of ground reaction forces from the generalized momentum residual, and does so more faithfully than a constrained ground model, whose Delassus matrix $J M^{-1} J^\\top$ is rank-deficient during two-point contact.","pith_inferences":["The paper's simulation assumes massless legs and thrusters that act only upward in the body frame; if those assumptions fail on hardware, the actual contact force could leave the friction cone even though the computed constraint $h_r \\geq 0$ is satisfied, so slip could reappear.","The same residual signal used for ground force estimation could serve as a contact detector or terrain classifier, since its impulsive peaks coincide with foot-strike events in the simulation.","Adding leg inertia or joint compliance to the reduced-order simulation is a direct test of how much of the no-slip guarantee depends on the massless-leg assumption."],"forward_implications":["Walking control can run on low-power real-time hardware because it requires only reference filtering and constraint evaluation, not repeated convex optimization.","The same ERG formulation extends naturally to thrust-assisted gaits: the attitude controller's thruster wrench enters the force balance the governor uses to predict ground reactions.","Ground reaction forces can be estimated without joint accelerometers by integrating residual momentum, which is useful for contact and terrain monitoring on multimodal robots.","In two-point contact, constrained-model force estimation is structurally unreliable because the Delassus matrix is rank-deficient, so momentum-based estimation is the better fit for this gait.","With friction coefficient 0.25, the filtered reference selects foot placements, including lateral placement, that keep contact forces inside the friction pyramid."],"supporting_citations":[{"why":"Supplies the ERG formulation and the constraint-admissible reference update used to enforce the friction pyramid.","marker":"[18]"},{"why":"Provides the momentum observer residual theory and the high-gain argument that makes the residual approximate the external wrench.","marker":"[2]"},{"why":"Introduces the sensorless momentum/residual collision detection framework the observer builds on.","marker":"[1]"},{"why":"Provides the explicit reference governor framework for constrained nonlinear systems that the implementation relies on.","marker":"[17]"},{"why":"Shows residual-based contact estimation via a momentum observer for floating-base robots, the approach being extended here.","marker":"[9]"},{"why":"Describes the Husky robot platform whose reduced-order model is used in the simulations.","marker":"[13]"},{"why":"Demonstrates momentum-observer collision detection on legged robots, motivating its use in the legged-aerial setting.","marker":"[3]"}],"fun_headline_variants":["No solver, no slip: ERG filter for legged-aerial robot","Momentum observer estimates ground forces, no optimizer needed","Velocity filter stops foot slip without run-time optimization","Optimization-free ERG prevents slip in legged-aerial robot","Ground force from momentum observer, slip from ERG filter"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The no-slip guarantee rests on a reduced-order model in which the body is a point mass with massless legs, the gait is a perfect two-point contact, the lateral ground forces are assumed evenly distributed, and the thrusters act only upward in the body frame; if any of these fail on the real robot, foot slip can occur despite the governor's constraint being satisfied.","fun_headline_variants_meta":{"raw":{"variants":["No solver, no slip: ERG filter for legged-aerial robot","Momentum observer estimates ground forces, no optimizer needed","Velocity filter stops foot slip without run-time optimization","Optimization-free ERG prevents slip in legged-aerial robot","Ground force from momentum observer, slip from ERG filter"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000919,"raw_usage":{"total_tokens":3886,"prompt_tokens":828,"completion_tokens":3058,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":444,"completion_tokens_details":{"reasoning_tokens":2973}},"tokens_in":444,"tokens_out":3058,"duration_ms":22812,"temperature":1.0,"reasoning_tokens":2973,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T18:46:28.752984+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the ERG controller on the physical Husky on a floor with friction coefficient 0.25 while recording stance-foot velocity; if any stance foot's horizontal velocity relative to the ground exceeds the slip threshold defined by the Stribeck model while the computed constraint $h_r \\geq 0$ is satisfied, the reduced-order friction-cone guarantee is falsified.","supporting_citations":[{"cited_title":"Explicit Reference Governor for Constrained Nonlinear Systems,","cited_arxiv_id":null,"evidence_quote":"Provides the explicit reference governor framework for constrained nonlinear systems that the implementation relies on."},{"cited_title":"Residual-based contacts estimation for humanoid robots,","cited_arxiv_id":null,"evidence_quote":"Shows residual-based contact estimation via a momentum observer for floating-base robots, the approach being extended here."}],"review_version":1}