{"id":"8c34c20c-3622-446c-9ed0-683b6bdd7ba8","arxiv_id":"2411.17727","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A QP-based capture point controller that treats thruster force as a parameter stabilizes simulated trotting of the thruster-assisted Harpy biped.","lead":"Harpy, a small bipedal robot with ducted fans, was given a walking controller that blends the classic capture point balance rule with a quadratic programming optimizer. The authors show in simulation that the combined controller can keep the robot trotting in place, with thruster force acting like reduced gravity, or virtual buoyancy.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The capture-point derivation assumes thruster angle theta_T = 0 (Eq. 10 to Eq. 11), but no controller enforces this and the reported simulation shows nonzero body pitch (Fig.","rationale":"The reader's weakest_assumption correctly identifies the theta_T = 0 condition as unenforced and unmodeled, and my reading of the derivation confirms this is the central load-bearing assumption. The full plant model includes body pitch (Fig. 5), and the thruster geometry couples pitch into theta_T, so the unmodeled |u_t,c| sin theta_T term enters the sagittal dynamics. The magnitude estimate shows it is not negligible relative to the virtual-buoyancy stiffness, so the QP's internal model is not the true plant. The paper gives no torso controller, no robustness analysis, and no quantitative metrics that would show the controller's stability is attributable to the new capture point law rather than to generic feedback. This reinforces the CONDITIONAL verdict: the simulation may be plausible, but the central claim requires either enforcing theta_T = 0 with a posture controller or re-deriving the capture point law from the forced LIP Eq. (10). I do not see an internal inconsistency strong enough to reject the paper outright, since the reported simulation is qualitative and the gap is addressable. Therefore the reader's verdict should remain UNCHANGED (CONDITIONAL).","tokens_in":9568,"tokens_out":13720,"duration_ms":127589,"concrete_test":"In the existing Simscape model, add a constant angular offset of 0, 5, and 10 degrees between the thruster thrust axis and the body z-axis while leaving the controller's internal model at theta_T = 0, and rerun the 10 s trot for each offset. If the trot destabilizes or tracking error grows sharply with increasing offset, the theta_T = 0 assumption is load-bearing; if the trot remains stable across offsets, the controller is robust to the unmodeled term and the central claim is weaker than the paper suggests.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the reduction from Eq. (10) to Eq. (11), which requires theta_T = 0. Only under that assumption does the forced LIP become the homogeneous virtual-buoyancy model, and Eq. (11) is used to derive the orbital energy (13), eigenvectors (14), foot-placement law (15), and QP state-space model (19). The paper says this holds 'if through torso angle manipulation' theta_T = 0, but no torso-angle controller is presented; the QP decision variable is u (Figs. 5-6), and thruster force is an open-loop parameter (Fig. 9), not a feedback signal. Since Harpy's thrusters are mounted to the torso, theta_T equals the body pitch, and Fig. 5 shows pitch reaching about -6 degrees during the 10 s trot. For |u_t,c| = 10 N on m = 4.5 kg with theta_T = 6 deg, the neglected forcing term is |u_t,c| sin(theta_T)/m = 0.23 m/s^2, while the retained stiffness term is ((g - |u_t,c|/m)/z0) p_B,x = 12.7 p_B,x, which is of the same order for p_B,x = 0.1 m. Thus the controller's internal model does not match the plant, and the observed stability may be due to feedback robustness rather than the thruster-adjusted capture point law. Because the paper's central contribution is exactly that law, the assumption is load-bearing and must be addressed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a capture-point-based controller with thruster forces for Harpy, a bipedal robot with torso-mounted thrusters. The authors derive a variable-length inverted pendulum model with thrust as virtual buoyancy, define a capture point that is used in a QP-based tracking controller, and evaluate the controller in a 10-second MATLAB Simscape trotting simulation. The claimed contribution is a new thruster-dependent capture point law and evidence that increasing thrust changes the capture point and stability.","tokens_in":9945,"tokens_out":7023,"duration_ms":68338,"significance":"If the central derivation were correct, the work would be a useful step toward combining legged and aerial locomotion on a single platform, and the constrained QP formulation with explicit thruster-force parameters is relevant to the community. The full Lagrangian model in Section II is a strength, as is the explicit treatment of thruster magnitude as a tunable parameter. However, the central capture-point derivation omits the CoM position term, the key assumption theta_T=0 is unenforced, and the main thrust-effect evidence is self-contradictory. The simulation validation is also too thin to support the claimed stability. The idea is defensible after major corrections.","major_comments":[{"comment":"The quantity called the capture point omits the current CoM position. The standard capture point is xi = x + xdot/omega, and the stable-manifold condition E=0 is x = -xdot/omega. Equation (15) instead states p_B,x = xdot_B,x * sqrt(z0/(g - |u_t,c|/m)), i.e., x = xdot/omega, which is the unstable eigenvector and has the wrong sign for a foot placement that stops the CoM. Consequently, Eq. (17) defines xi exclusively from velocity error, so the QP in Eq. (19) is not a capture-point controller. This must be corrected and the derivation repeated before the central claim can be assessed.","section":"Section III-A, Eqs. (15)-(17)"},{"comment":"The reduction from Eq. (10) to Eq. (11) requires theta_T = 0, but no controller enforces this condition. Because Harpy's thrusters are fixed to the torso, theta_T equals body pitch, and Fig. 5 shows pitch of about -6 degrees during the trot. With the reported |u_t,c| = 10 N and m = 4.5 kg, the neglected horizontal forcing is |u_t,c| sin(theta_T)/m, approximately 0.23 m/s^2, which is the same order as the retained stiffness term (g - |u_t,c|/m) x/z0 for x near 0.1 m. The internal model used by the QP therefore does not describe the plant, and the simulation outcome cannot be attributed to the thruster-adjusted capture point law.","section":"Section III-A, Eqs. (10)-(11)"},{"comment":"The two panels of Fig. 9 present contradictory results: the top panel is described as showing that higher thrust reduces the capture point and increases stability, while the bottom panel shows higher thrust increasing capture point length, attributed to the fixed thruster position and falling motion. Since this figure is the primary evidence for the effect of thrust on the capture point, the contradiction must be resolved with a single consistent metric and explanation, or the claim should be removed from the conclusions.","section":"Section IV, Fig. 9"},{"comment":"The state-space model in Eq. (19) is not reproducible as written: the state vector is two-dimensional while the matrix entries mix scalar and vector terms; the control input u is not defined before Eq. (24); and Eq. (18) is derived for constant xdot_ref even though xdot_ref appears as an input. With Kx = Ky = 1, xi is merely (xdot - xdot_ref)/omega, not a capture point. The QP formulation needs a complete, dimensionally consistent derivation.","section":"Section III-B, Eqs. (17)-(24)"},{"comment":"The simulation validation lacks quantitative support: no contact or friction model parameters, foot-slip measures, ground reaction force limits, or tracking error statistics are reported, and only a single 10-second trial is discussed. The claim of stable trotting needs well-defined metrics and at least a brief sensitivity analysis before it can be accepted.","section":"Section IV"}],"minor_comments":[{"comment":"The statement that Harpy's height measures 600 cm is clearly a typo; for a 4.5 kg platform the intended value is likely 60 cm or 0.6 m.","section":"Introduction"},{"comment":"The axis labels in Fig. 5 contain corrupted characters (e.g., '? A 3', '!x', '!y', '!z'); the Euler-angle convention and angular-velocity labels should be cleaned up.","section":"Fig. 5"},{"comment":"The symbol u is overloaded: u_t for thruster force, u_j for joint torques, and u for QP control input; please use distinct symbols such as f_t, tau, and u_QP.","section":"Notation throughout"},{"comment":"Reference [28] (Bickel et al., capture and modeling of soft tissue) does not appear relevant to capture-point control and should be replaced or removed.","section":"References"},{"comment":"The sign convention in Eq. (14) relative to Eq. (15) is not stated; the stable and unstable manifolds are distinguished only by the sign of xdot relative to x, so this ambiguity should be resolved in the text.","section":"Eq. (14)"},{"comment":"The legend labels '9u=0' etc. should read 'u=0' (and similarly for the other values).","section":"Fig. 9"},{"comment":"The word 'sinusodal' should be 'sinusoidal'.","section":"Section III-B"}],"recommendation":"major_revision","confidential_remarks":"This manuscript is closer to an extended abstract than a full journal paper. The missing position term in Eq. (15) is a fundamental error in the central derivation, and the unenforced theta_T=0 assumption plus the contradictory Fig. 9 make the current evidence insufficient. If the authors can correct the derivation, enforce or compensate for the thruster angle, and provide a consistent validation, a resubmission could be viable. I would also verify the novelty relative to [29] and the authors' own prior work [32], since the relationship is not clearly delineated in the text."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is a simulation study of a QP-based capture point controller using thruster forces as a parameter for the Harpy robot. What's actually new is the virtual buoyancy interpretation: the thrust reduces effective gravity g' = g - |u|/m, which changes the walking frequency and the foot placement law. That is a legitimate idea for legged-aerial platforms, but the derivation in Eqs. (8)-(16) is the standard linear inverted pendulum capture point under a coordinate rescaling, and the QP setup in Eqs. (19)-(25) is the standard MPC-for-capture-point recipe. So novelty is modest.\n\nThe algebra is internally consistent when θ_T = 0, and the paper is honest enough to state that assumption. But that assumption is load-bearing and no controller enforces it. Harpy's thrusters are fixed to the torso, so θ_T equals body pitch; Figure 5 shows pitch reaching about -6 degrees during the trot. With |u|=10 N on m=4.5 kg, the neglected horizontal term |u| sin θ_T / m is 0.23 m/s², which is the same order as the retained stiffness term for CoM positions around 0.1 m. So the internal model used by the QP does not describe the plant during the reported simulation, and the observed stability may just be feedback robustness.\n\nThere is also a conceptual mismatch: Eq. (15) defines the \"capture point\" as \\dot p / ω, omitting the current CoM position that appears in the classic capture point ξ = p + \\dot p / ω. This is a velocity-only control law, which may work, but calling it a capture point is misleading. The QP state-space model in Eq. (19) is a rearrangement of that definition, so Figure 9 does not independently validate the effect of thrust; the trend is built in.\n\nThe results section is the weakest. Figure 9's text says both that increasing thrust reduces the capture point and that it increases the capture point length. That needs to be fixed. The paper reports no quantitative tracking errors, no disturbance rejection tests, and no code or data. The \"without QP\" comparison shows drift rather than instability, so it is not a strong baseline.\n\nWhat the paper does well: it lays out the ROM and controller in a clear way, respects control and torque bounds in simulation, and identifies an interesting design idea for Harpy. For a reader working on legged-aerial robots, this is a reasonable starting point, but as a paper it is more of a workshop contribution than a finished result.\n\nI would send it to peer review with the expectation of heavy revision: enforce or justify the θ_T = 0 condition, fix the capture point definition, resolve the Figure 9 contradiction, and add quantitative evaluation. It deserves referee time because the platform motivation is real and the gap is addressable.","headline":"The core derivation is the standard LIP capture point with a modified gravity constant and the load-bearing θ_T = 0 assumption is unenforced, while the sim results are thin; still, the Harpy platform motivation is real and the paper deserves a serious referee with heavy revision.","tokens_in":10517,"tokens_out":2681,"would_cite":false,"duration_ms":25210,"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":"Thruster force modifies the capture point law through effective gravity, and a QP controller using this law stabilizes Harpy's trotting in simulation.","keywords":["capture point","thruster-assisted locomotion","virtual buoyancy","variable-length inverted pendulum","quadratic programming","bipedal walking","Harpy robot","trotting"],"falsifier":"Run the trotting simulation with the body pitch free and compare the center-of-mass acceleration to Eq. (11) whenever the torso tilt is nonzero; a deviation matching $|\\mathbf{u}_{t,c}|\\sin\\theta_T$ would show the capture-point law does not describe the real plant.","tokens_in":9406,"feed_emoji":"🤖","tokens_out":6422,"duration_ms":58733,"temperature":0.7,"pith_summary":"This paper tries to show that a bipedal robot with body-mounted thrusters can be stabilized by a capture point law in which the thrust force simply reduces effective gravity. The central formula replaces $g$ with $g - |\\mathbf{u}_{t,c}|/m$ in the linear inverted pendulum, so the capture point becomes $p_{B,x} = \\dot p_{B,x}\\sqrt{z_0/(g - |\\mathbf{u}_{t,c}|/m)}$, and a quadratic-programming controller that treats thruster force as a parameter is built around this law. If correct, thrusters give a bipedal walker a 'virtual buoyancy' knob: increasing thrust lowers walking frequency and shortens the step needed to stabilize a given velocity. The paper reports a 10-second MATLAB Simscape simulation in which Harpy trots in place and the controller holds the body near its reference position, whereas the same system without the QP loop drifts.","feed_headline":"Thrusters rewrite the capture-point rule for walking robots","feed_subtitle":"A QP controller using effective gravity keeps Harpy trotting stably in simulation.","key_machinery":"The central object is the capture point: the foot location at which the center of mass can come to rest over the support foot. The paper derives it from a variable-length inverted pendulum (VLIP) with a thruster force term, projected onto sagittal and frontal planes. With the thrust kept perpendicular to the ground, the system acts as a virtual-buoyancy model whose effective gravity is $g - |\\mathbf{u}_{t,c}|/m$; the capture point is the stable-eigenvector condition of this model, giving Eq. (15). A dense quadratic program over the discretized capture-point dynamics then tracks a reference velocity with the thruster force as a parameter.","core_discovery":"The paper's claim is that the classical capture point remains valid for thruster-assisted walking once gravity is replaced by an effective gravity $g - |\\mathbf{u}_{t,c}|/m$, where $|\\mathbf{u}_{t,c}|$ is the combined thruster force about the center of mass and $m$ is the robot mass. Under the assumption that the thrust vector stays perpendicular to the ground ($\\theta_T = 0$), the variable-length inverted pendulum equations reduce to $\\ddot p_{B,x} = (g - |\\mathbf{u}_{t,c}|/m) p_{B,x}/z_0$, whose stable eigenvector gives the foot placement rule $p_{B,x} = \\dot p_{B,x}\\sqrt{z_0/(g - |\\mathbf{u}_{t,c}|/m)}$. The paper then embeds this modified capture point in a discrete-time state-space model and solves a dense QP at each step to track a desired reference velocity. The simulation evidence is that the QP controller stabilizes Harpy's body position toward the reference while keeping control efforts and joint torques within bounds.","pith_inferences":["Because the modified law is just a substitution of effective gravity, the same substitution should transfer to related centroidal templates, such as divergent-component-of-motion or preview-control formulations, potentially shortening development of thruster-assisted walking controllers.","The $\\theta_T = 0$ assumption is not enforced by any torso controller, so on hardware the body pitch will rotate the fixed thrusters and inject an unmodeled horizontal force; a version with pitch regulation or gimbaled thrusters would test the model under realistic conditions.","The reported scaling of capture point with thrust suggests a clean experimental check: hold velocity and height fixed, vary thrust, and see whether foot placement follows $\\sqrt{z_0/(g - |\\mathbf{u}_{t,c}|/m)}$; any systematic deviation would point to missing terms such as thrust misalignment or aero effects."],"forward_implications":["Commanding a larger thruster force lowers effective gravity, so the same center-of-mass velocity requires a smaller sagittal capture point; the paper reports exactly this trend in its thrust-sweep figure.","Without the QP loop the simulated robot drifts, while with it the body position settles near the reference, so the QP reference tracking is doing the stabilization, not the plant alone.","The state-space model in Eq. (19) is linear with respect to the capture point once $\\omega$ is fixed by thrust, so the same QP structure can be reused for different thrust levels by updating $\\omega$.","The paper's stated next step is to add ground reaction forces and thruster forces as QP decision variables; that extension is a natural corollary of treating them as parameters here."],"supporting_citations":[{"why":"Introduces the original capture point definition and foot-placement rule that Eq. (15) generalizes.","marker":"[31]"},{"why":"Supplies the extended capture point and optimization-based control structure that Eq. (17) follows.","marker":"[29]"},{"why":"The authors' prior capture point control for thruster-assisted bipedal locomotion, which this work extends with QP-based reference tracking.","marker":"[32]"},{"why":"Provides the qpSWIFT solver used to execute the QP in the Simulink loop.","marker":"[33]"}],"fun_headline_variants":["Thrusters change the capture point for legged robots","Effective gravity remaps capture point for thruster walking","QP control uses thrusters to keep robot upright","Thruster-based capture point for dynamic walking","Wing-assisted walking robot relies on modified capture point"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole derivation assumes the thruster force always points straight up, and the paper does not include a controller that keeps it that way; if the robot's torso tilts, the thrust adds a sideways push the model ignores.","fun_headline_variants_meta":{"raw":{"variants":["Thrusters change the capture point for legged robots","Effective gravity remaps capture point for thruster walking","QP control uses thrusters to keep robot upright","Thruster-based capture point for dynamic walking","Wing-assisted walking robot relies on modified capture point"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000213,"raw_usage":{"total_tokens":1429,"prompt_tokens":961,"completion_tokens":468,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":577,"completion_tokens_details":{"reasoning_tokens":393}},"tokens_in":577,"tokens_out":468,"duration_ms":4754,"temperature":1.0,"reasoning_tokens":393,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:07:58.506759+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the trotting simulation with the body pitch free and compare the center-of-mass acceleration to Eq. (11) whenever the torso tilt is nonzero; a deviation matching $|\\mathbf{u}_{t,c}|\\sin\\theta_T$ would show the capture-point law does not describe the real plant.","supporting_citations":[{"cited_title":"Capture Point: A Step toward Humanoid Push Recovery,","cited_arxiv_id":null,"evidence_quote":"Introduces the original capture point definition and foot-placement rule that Eq. (15) generalizes."},{"cited_title":"Extended Capture Point and Optimization- based Control for Quadrupedal Robot Walking on Dynamic Rigid Surfaces,","cited_arxiv_id":null,"evidence_quote":"Supplies the extended capture point and optimization-based control structure that Eq. (17) follows."},{"cited_title":"Capture Point Control in Thruster-Assisted Bipedal Locomotion","cited_arxiv_id":"2406.14799","evidence_quote":"The authors' prior capture point control for thruster-assisted bipedal locomotion, which this work extends with QP-based reference tracking."}],"review_version":1}