{"id":"e4bfcb59-7098-4cd8-b113-3f8764488702","arxiv_id":"2411.14596","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A conjugate momentum observer estimates thruster forces on a simulated bipedal legged-aerial robot, using either direct ground-force knowledge or contact-constraint estimates.","lead":"This paper uses a momentum-based observer to estimate the force produced by the thrusters of a legged-aerial bipedal robot while it walks. The estimator runs in simulation on the Harpy robot, with and without knowledge of the ground contact forces.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Constraint-model GRF estimate is coupled to the residual it feeds, so the low NRMSE is only shown under exact-model, no-slip conditions; no error-propagation bound is given.","rationale":"I read the paper as a simulation-level demonstration that a standard momentum observer can be applied to thruster-assisted bipedal walking, with the novel part being the use of a contact-constraint GRF model instead of direct force sensing. The derivation is essentially the De Luca momentum observer, and the mechanics of the estimator are plausible. The reader's weakest assumption already flags exact model knowledge and zero foot acceleration. I agree that these are load-bearing, and I would sharpen the concern: the constraint-model pipeline creates a feedback path from the residual into the GRF estimate and back into the residual, so model mismatch and foot slip are not merely sources of bounded disturbance; they can be amplified through the loop. The paper's response is to raise K0 by two orders of magnitude, which is a tuning fix, not a robustness argument. This does not make the simulation claim false, but it means the reported NRMSE values are conditional on an idealized setting. The reader's CONDITIONAL verdict already captures this, so I do not recommend changing the verdict. The concrete test I propose would turn the conditional into a quantitative robustness statement or reveal that the result collapses under small perturbations.","tokens_in":7869,"tokens_out":7580,"duration_ms":79544,"concrete_test":"Repeat the Section IV walking simulation with M-hat = 0.9 M (10% mass error on body and legs) and with a small stance-foot slip (e.g., impose 0.02 m/s tangential foot velocity in the constraint model), keeping all observer gains and contact parameters unchanged. Recompute Table I; if any NRMSE exceeds about 0.5 or the residual drifts monotonically, the constraint-model accuracy is not robust to the paper's own stated assumptions. As a secondary check, rerun the constraint-model observer with K0 set to the ground-model values (diag(1,1,1,1,25,...)) to see whether the result depends on the high-gain tuning.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing weakness is the coupled estimation loop in the constraint-model case. Eq. (16) computes GRF as lambda = (Jc M^-1 Jc^T)^dagger [Jc M^-1(-r - Bj uj + h) - Jdot qdot], using the residual r that is itself produced by the observer. Eq. (14) then feeds this lambda back into the residual integral. Under exact model knowledge (M-hat = M, beta-hat = beta) and exact zero foot acceleration, the loop is consistent and the Table I NRMSE values follow. But the paper gives no error-propagation, passivity, or small-gain analysis for this loop; it only says 'we can increase the observer gain' (Section IV-B), and indeed K0 jumps from 25 in the ground-model case to 3000 in the constraint-model case. Therefore the reported 0.05-0.19 accuracy is a tuned, exact-simulation property, not a demonstrated property under the model error, joint friction, and foot slip that the Harpy platform will introduce. Since the paper's motivation is onboard estimation under real battery and terrain conditions, the central claim 'observer can accurately track thruster force with constraint-model terrain information' is conditional on untested assumptions.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a generalized-momentum (conjugate momentum) observer to estimate thruster forces on the Harpy bipedal robot, a platform that combines legged locomotion with thruster actuation. The observer is derived in Section III and is evaluated in simulation during thruster-assisted walking. Two variants are presented: one that uses ground reaction forces from the compliant ground model directly, and one that estimates ground reaction forces from a contact constraint model. The reported results are normalized RMSE values between 0.05 and 0.19 for the generalized force/torque components in the constraint-model case (Table I). The paper claims that the observer accurately tracks thruster forces and that the method is suitable for onboard estimation where thrust-stand characterization is insufficient.","tokens_in":8128,"tokens_out":4845,"duration_ms":46856,"significance":"If the result holds, the paper offers a sensorless thruster-force estimation scheme for a multimodal legged-aerial robot, which is relevant for downstream MPC/QP control. A strength is that the paper builds on the well-established momentum-observer framework, avoiding acceleration estimation and matrix inversion. Another strength is that the simulation includes full-dynamics evaluation and reports quantitative errors, not just qualitative plots. However, the contribution is incremental relative to the existing momentum-observer literature, and the reported accuracy is obtained under strong ideal-model assumptions. The paper does not yet demonstrate robustness to model error, foot slip, or state-estimation delay, which are central to the stated motivation of onboard estimation under real operating conditions.","major_comments":[{"comment":"The observer equation is not self-contained: the equality rdot = K0(Bt ut - r) = K0(pdot - pdot_hat) introduces pdot_hat without a definition or an explicit relation to the state and known inputs. In the standard momentum-observer derivation, one obtains rdot = K0(pdot - beta - r - Bg lambda - Bj uj), and the equivalence to K0(pdot - pdot_hat) must be shown. Please define pdot_hat and state the exact residual dynamics used in the simulator.","section":"III, Eq. (13)"},{"comment":"The zero-foot-acceleration constraint is stated as Jc qddot = Jdot qdot, but differentiating Jc qdot = 0 gives Jc qddot = -Jdot qdot. Equation (16) contains the correct minus sign, so this is an inconsistency in the text rather than in the implemented formula; please correct the sentence to avoid confusion.","section":"III-A"},{"comment":"The constraint-model estimator is a feedback loop: lambda in Eq. (16) is computed from the residual r, and r is integrated in Eq. (14) using that lambda. No passivity, small-gain, or error-propagation analysis is given for this loop, and the only mitigation offered is raising K0 from 25 to 3000. Because Table I is generated under the ideal assumptions M-hat = M, beta-hat = beta, and no foot slip, the reported 0.05-0.19 NRMSE is not yet demonstrated as robust to the model error and terrain variation expected on hardware. Please add a sensitivity analysis (e.g., parameter perturbations, friction/slip, state-estimation delay) or a bounded-error argument.","section":"IV-B"},{"comment":"The stated contribution is a comparison of estimation with and without terrain knowledge, but Table I reports NRMSE only for the constraint-model case. The ground-model case (Fig. 6) is only qualitative. Please report the same NRMSE metric for both cases so the comparison is quantitative.","section":"IV, Table I"}],"minor_comments":[{"comment":"There are numerous grammatical errors and typos, such as 'such our state-of-the-art Harpy platform' and 'we can characterize thruster force using a thrust stand but it generally does not account for working conditions.' Please proofread the manuscript.","section":"Abstract and Section I"},{"comment":"Harpy's height is stated as 600 cm, which is presumably a typo for 60 cm. Please correct the unit.","section":"II"},{"comment":"The composition of u_t from u_t,c and u_t,L/u_t,R is unclear; specify the dimensions and the frames in which the components are expressed.","section":"II-C, Eq. (9)"},{"comment":"The observer gains are reported for the two cases, but no tuning procedure or criterion is given. State how the gains were selected and whether the results are sensitive to their values.","section":"IV-B"},{"comment":"The 'Normalized RMSE' metric is not defined. Specify the normalization denominator (e.g., range, mean, standard deviation) so that the values in Table I are interpretable.","section":"IV-B, Table I"},{"comment":"The term 'conjugate momentum' is used, but the derivation is the standard generalized momentum observer. Consider clarifying the terminology or providing a reference that uses this name.","section":"III"}],"recommendation":"major_revision","confidential_remarks":"The paper is a straightforward application of the standard momentum observer to a thruster-assisted biped. The main novelty is the coupling with a contact-constraint-based GRF estimator, but the lack of stability/error analysis for that loop and the absence of robustness tests are the key technical gaps. The authors should also decide whether the journal venue expects hardware validation; as presented, the results are entirely simulation-based. The manuscript is likely salvageable with the requested revisions, but it needs a clearer observer derivation and a quantitative sensitivity study before it can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: this is a textbook momentum observer applied to Harpy, the thruster-assisted biped, in simulation. What is new is not the estimator but the platform and the specific comparison: feeding the observer with terrain information from a contact constraint model versus a known ground model, and showing the constraint-model version still tracks thruster forces with NRMSE 0.05-0.19. That is a modest but real step for the legged-aerial subfield.\n\nThe paper does a few things well. The derivation is standard but clean, and the authors are honest about the limitations: they explicitly say the constraint-model estimate is coupled to the residual it feeds, and they note that any error in the observer will propagate into the GRF estimate. They also flag the double-support rank deficiency. That level of candor is welcome.\n\nThe soft spots are proportional to the contribution. It is simulation-only, with no code or data release, so the numbers in Table I are not independently checkable. The observer gains are hand-tuned—K0 jumps from 25 to 3000 between the ground-model and constraint-model cases—and there is no sensitivity analysis for model error, friction, or foot slip. The paper assumes M-hat = M and beta-hat = beta, which is fine for an ideal simulation but not for hardware. The sign typo in the constraint equation (Jc qddot = Jcdot qdot instead of the negative) is minor and does not appear to carry into equation (16), which has the right sign. Also, the comparison to the iRonCub EKF is too brief; a direct baseline would have made the claim stronger.\n\nThe stress-test note about the coupled loop is correct, but the paper already concedes it. That does not make the weakness go away—it remains unquantified—but it is not a hidden flaw. The central claim, that the observer can track thruster forces under exact-model simulation, holds up. What is not demonstrated is robustness under the conditions Harpy will actually see.\n\nWho is this for? People working on legged-aerial robots, especially the Harpy project itself. A serious referee should be able to ask for code, a sensitivity analysis, and ideally a hardware trial. I would accept it for peer review with revisions, though I would not cite it myself unless I worked on that platform.\n\nRecommendation: send it out, with the understanding that the authors need to release code/data and address the robustness gap.","headline":"Standard momentum observer, honestly applied to a new platform; simulation-only and no sensitivity analysis, but a plausible niche contribution.","tokens_in":8692,"tokens_out":2161,"would_cite":false,"duration_ms":20290,"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":"A conjugate-momentum observer estimates thruster forces on a legged-aerial biped to within 5–19 percent error.","keywords":["conjugate momentum observer","thruster force estimation","legged-aerial locomotion","bipedal robot","ground reaction force estimation","contact constraint model","Harpy robot","external wrench estimation"],"falsifier":"Measure the actual thruster force with a thrust stand while Harpy walks with thrusters on hardware and compare it with the observer's output: if the normalized RMSE grows well beyond the 0.05–0.19 range under realistic model mismatch, joint friction, or foot slip, the central claim fails. Alternatively, instrument the foot with a force plate to check whether the stance-foot acceleration is truly zero while the constraint model is active.","tokens_in":7703,"feed_emoji":"🤖","tokens_out":7841,"duration_ms":66169,"temperature":0.7,"pith_summary":"This paper proposes a conjugate-momentum observer that estimates thruster forces online for Harpy, a bipedal robot with electric ducted fans that can walk and fly. The aim is to establish that the observer can track the true generalized thruster forces while the robot performs thruster-assisted walking in simulation, avoiding the need for thrust-stand calibration that misses working conditions such as battery voltage drop. Estimation requires ground-reaction-force information; the paper shows two routes: feeding the compliant ground model's forces directly, or estimating them from a contact-constraint model. With the constraint model, normalized root-mean-square errors for generalized forces and torques lie between 0.049 and 0.195. The authors argue this is accurate enough to feed controllers such as MPC and QP, and that the constraint-model route removes the need for foot force sensors.","feed_headline":"Observer estimates thruster force within 5–19% error during robot walk","feed_subtitle":"A momentum-based observer lets the legged-aerial biped Harpy estimate thrust online, no test stand or foot sensors needed.","key_machinery":"The central object is the conjugate momentum observer, a standard momentum observer built on the generalized momentum $p = M\\dot q$. The estimated thruster force $r$ evolves as $\\dot r = K_0(B_t u_t - r)$, making $r$ a low-pass filter of the true thruster force with gain $K_0$; no joint accelerations or inertia-matrix inversions are needed. Because the observer equation needs ground reaction forces, the paper pairs it with a contact-constraint model that enforces zero stance-foot acceleration, $J_c \\ddot q = \\dot J_c \\dot q$, to compute the ground reaction force via a Moore-Penrose pseudo-inverse. The controller used for the simulated walking is built on a variable-length inverted pendulum (VLIP) reduced-order model, with thrusters stabilizing roll and yaw, while the full simulation uses an Euler-Lagrangian model with compliant ground contact.","core_discovery":"Using the generalized momentum $p = M\\dot q$, the observer defines an estimated generalized thruster force $r$ driven by $\\dot r = K_0(B_t u_t - r)$, so that $r$ is a low-pass filtered version of the actual thruster force. Under ideal conditions, $M$ and $\\beta$ are assumed exactly known. The body-frame thruster force is recovered with the Jacobian pseudo-inverse $\\hat u_t = [J_t^\\top J_t]^\\dagger J_t^\\top r$. When ground reaction forces are taken from the compliant ground model, the estimated generalized forces and torques match the actual values closely. When they are instead estimated through the contact constraint $J_c \\ddot q = \\dot J_c \\dot q$, the estimates still track but with larger error, and the paper reports NRMSE values of 0.1156 for $F_x$, 0.0492 for $F_y$, 0.1946 for $F_z$, 0.1102 for $\\tau_x$, 0.1342 for $\\tau_y$, and 0.1239 for $\\tau_z$. The vertical force $F_z$ has the largest error, which the authors attribute to the constraint model.","pith_inferences":["On hardware, the ideal-model assumption will be violated by joint friction and model error; the paper gives no sensitivity analysis, so the first test is whether the observer gain can absorb these errors without amplifying noise.","The rank deficiency in double support suggests a practical deployment would gate the estimator by contact state or blend the constraint-model ground reaction force with any available foot force sensing.","The same observer structure could be transferred to other thruster-augmented legged robots, since it only requires the generalized momentum, contact Jacobians, and a source of ground reaction force; the equations do not depend on Harpy's specific kinematics.","A direct experimental check would be to compare the observer's thrust estimate against a thrust stand while battery voltage drops during flight, quantifying how much of the 5–19% error persists outside simulation."],"forward_implications":["Controllers such as MPC and QP can use the estimated thruster forces directly, replacing thrust-stand calibration that misses battery voltage and other working conditions.","A contact-constraint-based ground reaction force estimate removes the need for foot force sensors, at the cost of higher estimation error, with $F_z$ the least accurate.","Because the estimator is a low-pass filter, its accuracy is governed by the quality of the ground reaction force information; better terrain knowledge yields better thrust estimates.","The double-support phase makes $J_c M^{-1} J_c^\\top$ rank-deficient, so ground force estimates are inherently less reliable during that phase.","A second-order filter is the paper's stated next step to reduce the filter lag visible in the y-direction torque estimate."],"supporting_citations":[{"why":"Supplies the momentum-observer framework and the low-pass-filter convergence statement that equation (13) builds on.","marker":"[1]"},{"why":"Introduces the generalized momentum observer for sensorless collision detection; the paper's observer dynamics and residual filter follow this formulation.","marker":"[2]"},{"why":"Shows external wrench estimation for flying robots via momentum observers, motivating use of the same idea to estimate thruster wrench.","marker":"[10]"},{"why":"Presents an alternative momentum-based EKF for thrust estimation on flying multibody robots that this paper contrasts with, arguing it does not transfer to contact-rich thruster-assisted walking.","marker":"[21]"},{"why":"Demonstrates sensorless ground reaction force observation in legged robots, supporting the claim that ground reaction force information is needed for the thruster estimator.","marker":"[7]"},{"why":"Provides a contact-model-based approach for terrain and contact estimation in legged locomotion that the paper's contact-constraint ground reaction force estimation resembles.","marker":"[8]"}],"fun_headline_variants":["Momentum-based observer estimates thruster force within 5–19% error","Online momentum observer tracks thruster force without test stand","Harpy robot estimates thrust in real time using momentum math","Momentum-based force observer gives live thrust estimates for legged-aerial bot","Conjugate momentum observer tracks thruster force in hybrid robot walk"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The estimator assumes the robot's mass and bias terms are known exactly, and that the stance foot never accelerates or slips while the contact constraint is enforced; onboard hardware will violate both assumptions to some degree.","fun_headline_variants_meta":{"raw":{"variants":["Momentum-based observer estimates thruster force within 5–19% error","Online momentum observer tracks thruster force without test stand","Harpy robot estimates thrust in real time using momentum math","Momentum-based force observer gives live thrust estimates for legged-aerial bot","Conjugate momentum observer tracks thruster force in hybrid robot walk"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00053,"raw_usage":{"total_tokens":2549,"prompt_tokens":938,"completion_tokens":1611,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":554,"completion_tokens_details":{"reasoning_tokens":1519}},"tokens_in":554,"tokens_out":1611,"duration_ms":12422,"temperature":1.0,"reasoning_tokens":1519,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:06:33.402466+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the actual thruster force with a thrust stand while Harpy walks with thrusters on hardware and compare it with the observer's output: if the normalized RMSE grows well beyond the 0.05–0.19 range under realistic model mismatch, joint friction, or foot slip, the central claim fails. Alternatively, instrument the foot with a force plate to check whether the stance-foot acceleration is truly zero while the constraint model is active.","supporting_citations":[{"cited_title":"Robot Collisions: A Survey on Detection, Isolation, and Identification,","cited_arxiv_id":null,"evidence_quote":"Supplies the momentum-observer framework and the low-pass-filter convergence statement that equation (13) builds on."},{"cited_title":"Sensorless Robot Collision Detection and Hybrid Force/Motion Control,","cited_arxiv_id":null,"evidence_quote":"Introduces the generalized momentum observer for sensorless collision detection; the paper's observer dynamics and residual filter follow this formulation."},{"cited_title":"External Wrench Estimation, Collision Detection, and Reflex Reaction for Flying Robots,","cited_arxiv_id":null,"evidence_quote":"Shows external wrench estimation for flying robots via momentum observers, motivating use of the same idea to estimate thruster wrench."},{"cited_title":"Momentum- Based Extended Kalman Filter for Thrust Estimation on Flying Multibody Robots,","cited_arxiv_id":null,"evidence_quote":"Presents an alternative momentum-based EKF for thrust estimation on flying multibody robots that this paper contrasts with, arguing it does not transfer to contact-rich thruster-assisted walking."},{"cited_title":"Sensorless Ground Reaction Force Observation With Disturbance Compensation in Heavy-Legged Robots,","cited_arxiv_id":null,"evidence_quote":"Demonstrates sensorless ground reaction force observation in legged robots, supporting the claim that ground reaction force information is needed for the thruster estimator."},{"cited_title":"Contact Model Fusion for Event-Based Locomotion in Unstructured Terrains,","cited_arxiv_id":null,"evidence_quote":"Provides a contact-model-based approach for terrain and contact estimation in legged locomotion that the paper's contact-constraint ground reaction force estimation resembles."}],"review_version":1}