{"id":"993062f9-f94e-491d-93e9-8c5346bfcdd2","arxiv_id":"2505.24116","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A bipedal control framework that includes external manipulation forces in both pattern generation and stabilization is derived and demonstrated on humanoid robots.","lead":"This paper derives the walking equations a humanoid robot uses when pushing or carrying objects, adding hand forces into the standard balance model. It then adds a stabilizer that corrects when real forces differ from planned ones, with tests on two real humanoid robots.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The stabilizer's exact force-error compensation rests on an unquantified constant-kappa assumption; vertical force errors change kappa and leave residual disturbance terms that are neither bounded in the paper nor tested experimentally.","rationale":"I agree with the reader's weakest assumption: the stabilizer's novel compensation is the part of the central claim that is least secure, and the constant-kappa linearization is its explicit soft spot. The pattern-generator contribution is well supported: the ext-ZMP reformulation is algebraically clean, test-case 2 verifies the kappa-scaled ZMP effect, and the preview-control extension is a direct substitution. The stabilizer derivation is internally consistent under its stated assumption, and the frequency-separation idea is plausible; however, the paper gives no quantitative range for Delta_kappa, no stability margin for the residual disturbance, and the real experiments are mostly horizontal-force tasks. This is a robustness gap rather than a demonstrated failure. A targeted simulation with vertical force errors would settle whether the gap matters. The use of the open-source mc_rtc framework, simulations, and real-robot demonstrations is genuine supporting evidence, but it does not quantify the assumption on which the stabilizer's exact cancellation rests. Because the reader already conditioned acceptance on this point, I keep the verdict unchanged rather than moving it.","tokens_in":13024,"tokens_out":13680,"duration_ms":138245,"concrete_test":"Re-run test-case 3 with the same horizontal sinusoidal disturbance and add a vertical hand-force error sweep, Delta_F_z = 0, +/-50, +/-100, +/-200 N per hand, while keeping the planner's nominal kappa in Eq. (22). Record peak |xi_bar_prime| and the minimum ZMP distance to the support-polygon edge. If the peak DCM error grows beyond the roughly 2 cm observed in Fig. 10 or the ZMP margin shrinks materially for Delta_kappa in the experimentally plausible range, the constant-kappa assumption is load-bearing; if the response is essentially unchanged, the stabilizer claim is robust. An analytical cross-check is to re-derive Eq. (14) without kappa^a = kappa^d and bound the extra term -omega Delta_kappa z^a over the measured ZMP range.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim's second half—that the stabilizer 'explicitly compensates for the error of manipulation forces'—is only as strong as the linearization in Section V-B1, where Eq. (13b) is subtracted from Eq. (13a) under the assumption 'kappa = kappa^a = kappa^d is constant.' The only justification is that the error of kappa is 'not so large,' but no bound, worst-case estimate, or stability analysis is supplied. If vertical hand-force errors are non-negligible, the cancellation in Eqs. (22) and (26) is imperfect: writing kappa^a = kappa + Delta_kappa leaves an extra term -omega Delta_kappa z^a in the error dynamics, and the feedforward term (1/kappa) gamma_bar^H cancels only the fraction kappa^a/kappa^d of the actual disturbance, leaving a residual proportional to Delta_kappa/kappa. A vertical force error of 10% of body weight gives Delta_kappa approximately 0.1, i.e., roughly 10% of the disturbance is uncompensated before feedback. Test-case 2's 200 N-per-hand vertical forces shift kappa from about 1.4 to 0.6, so kappa itself is not small; what matters is the unmeasured error Delta_kappa. The real experiments focus on horizontal forces (bobbin turning, cart pushing), so they do not exercise the regime in which kappa changes. The assumption is explicit, but the claimed 'accurate handling' of manipulation-force errors is not supported by a quantitative robustness analysis.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript extends the standard LIPM/DCM framework for bipedal walking to humanoid loco-manipulation. It derives forced LIPM and DCM equations that include external manipulation forces, introduces an 'ext-ZMP' variable that absorbs scaling and offset effects of those forces, and reuses preview control for pattern generation. The stabilizer extends DCM feedback control by separating the error between actual and desired manipulation forces into a low-frequency component handled by a CoM strategy and a high-frequency component handled by a ZMP strategy, with feedforward compensation terms. The approach is evaluated in three simulation test cases and in real-robot experiments (HRP-5P bobbin rolling and HRP-2Kai cart pushing).","tokens_in":13339,"tokens_out":19220,"duration_ms":175628,"significance":"If the claims hold, this is a practical and computationally cheap extension of widely used humanoid walking controllers to tasks with sustained hand forces. The derivation from Newton-Euler to the forced LIPM/DCM is clean and internally consistent, the ext-ZMP formulation is elegant, and the frequency-domain separation of force errors is a useful engineering idea. The real-robot demonstrations on HRP-5P and HRP-2Kai are valuable and support the pattern-generation part of the paper. The main weakness is that the stabilizer's force-error compensation is derived under an unquantified assumption on the ZMP scaling factor kappa and is not validated in the regime where that assumption matters, namely errors in vertical manipulation forces.","major_comments":[{"comment":"The linearized DCM error dynamics is derived under the assumption that kappa^a = kappa^d = kappa is constant. When vertical hand-force errors are present, this assumption fails: writing kappa^a = kappa + Delta_kappa introduces an additional term -omega Delta_kappa z^a in the DCM error dynamics, and the feedforward terms (1/kappa) gamma_bar^a_H and (1/(kappa rho)) dot_gamma_bar^a_H in Eqs. (22) and (26) then cancel only a fraction kappa^a/kappa^d of the actual disturbance, leaving a residual proportional to Delta_kappa/kappa. The only justification given, that the error of kappa is 'not so large', is not a quantitative statement. Because the explicit compensation of manipulation-force errors is a central contribution, this approximation is load-bearing. Please provide a quantitative bound on Delta_kappa in terms of the vertical force error, an analysis of the resulting residual disturbance and its effect on stability, or revise the claim to state that the force-error compensation applies to gamma while kappa errors are neglected.","section":"Section V-B1, Eqs. (13)-(14)"},{"comment":"The claimed robustness to vertical manipulation-force errors is not experimentally validated. Test-case 2 applies vertical forces of 200 N per hand but the actual forces track the reference, so it validates the pattern generator's ext-ZMP formulation, not the stabilizer's response to a mismatch in vertical forces. The real-robot experiments (bobbin turning, cart pushing) involve predominantly horizontal hand forces, for which kappa remains close to 1; they do not exercise the regime in which kappa changes. A dedicated experiment or simulation with a step or ramp error in the vertical force component is needed to support the second central contribution.","section":"Section VII and test-case 2"},{"comment":"The derivation of the CoM strategy assumes dot_gamma_bar^a_L is approximately zero (and consequently double-dot_gamma_bar^a_L is also zero) when the low-frequency force-error component is used to shift the desired CoM. The neglected terms double-dot_gamma_bar_L + rho dot_gamma_bar_L are not obviously small for components near the 1.0-s filter cutoff, and no bound or sensitivity study is provided. Please quantify this approximation or demonstrate that it has negligible effect on the closed-loop response.","section":"Section V-B4, Eqs. (17)-(20)"}],"minor_comments":[{"comment":"The barred variables, such as gamma_bar^a, are defined as the difference between actual and desired values, but this is only implicit; please state the definition explicitly for all barred symbols.","section":"Section V-B1"},{"comment":"The first-order lag is written directly for the error variable z_bar^a, which is valid only when the desired ZMP derivative dot_z^d is negligible; please state this assumption explicitly or include the dot_z^d term, since the desired ZMP changes during footstep transitions.","section":"Section V-B2, Eq. (15)"},{"comment":"The reported gain values (tilde_k_i = 0, tilde_k_p = 1.25, tilde_k_d = 0) are used with Eq. (22), but the value of kappa used to scale the conventional gains is not reported; please specify kappa for the simulation and experiments so the conventional gains can be recovered.","section":"Section VI"},{"comment":"The phrase 'papering' in the bobbin description should be corrected to 'paper' or 'paper products'.","section":"Section VII"},{"comment":"Reference [26] is cited as 'in press'; please update it with the final publication details if available.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"This is a strong RA-L candidate with a clean derivation and valuable real-robot experiments. The main issue is that the second central contribution, explicit compensation of manipulation-force errors, relies on an unquantified small-kappa-error assumption and is not validated in the vertical-force-error regime. The paper could become acceptable with a robustness analysis or a dedicated vertical-force-error experiment, or by narrowing the claim to gamma-error compensation with kappa treated as a known constant."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you should know: this paper does something genuinely useful. It re-derives the LIPM and DCM equations with external manipulation forces, introduces the ext-ZMP (kappa scale and gamma offset), and builds a pattern generator and stabilizer on that. Prior work treated hand forces only as a ZMP/CoM offset; here the vertical-force scale effect is included without approximation, and the stabilizer explicitly compensates for measured force errors. The math is clean and internally consistent: the derivation from Newton-Euler to (4) and (8) is straightforward, and the assumptions are the usual LIPM ones. The ext-ZMP trick lets the standard preview controller run unchanged. The force-error compensator's frequency split (CoM strategy vs ZMP strategy) is a sensible design, and the real-robot demos (bobbin rolling with HRP-5P, cart pushing with HRP-2Kai) back up the claims.\n\nThe soft spots are real but not fatal. In Section V-B1 the stabilizer linearizes the error dynamics under kappa = kappa^a = kappa^d constant. The paper dismisses the error as 'not so large' without a bound. The stress-test is right: if vertical force errors are substantial, Delta_kappa changes the error dynamics and the 1/kappa feedforward in (22) and (26) leaves a residual proportional to Delta_kappa/kappa. In the experiments, the force errors are predominantly horizontal, so kappa barely moves; the vertical-force test case (test-case 2) uses zero force error. So the claim 'explicitly compensating for the error of manipulation forces' is solid for horizontal errors but only plausibly true for vertical errors. A short robustness section or a bound on Delta_kappa (or a simulation with 10-20% vertical force error) would settle it. Minor points: the ZMP lag parameter rho is used but never given a value, which hurts reproducibility, and the hardware evidence is single-trial and qualitative. Also, the paper is a letter, so those are acceptable omissions, but a referee should ask.\n\nI was a bit skeptical about the stress-test, but on reading, the concern lands. It doesn't pick at a straw man; it targets a real unquantified assumption. That said, the contribution is good enough that I would not desk reject this. It deserves a serious referee. The math, data, and citations look solid, and the paper is honest about its scope.\n\nRecommended decision: send to peer review. If a revision is asked, the main item is the kappa-robustness analysis and a reported rho value. For a reading group, it's a good example of extending classical template dynamics to interaction tasks.","headline":"A clean, useful extension of LIPM/DCM to external manipulation forces; the stabilizer's force-error compensation is solid for horizontal errors but rests on an unquantified constant-kappa assumption for vertical errors.","tokens_in":13940,"tokens_out":3596,"would_cite":true,"duration_ms":34483,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"By folding external manipulation forces into a single ext-ZMP variable, this paper extends the standard preview-control pattern generator and DCM-based stabilizer so a humanoid can plan and stabilize walking while sustained or alternating…","keywords":["humanoid loco-manipulation","divergent component of motion","linear inverted pendulum mode","ext-ZMP","pattern generation","stabilization control","preview control","external manipulation forces"],"falsifier":"Apply a humanoid to a pushing task while a sinusoidal vertical hand-force error of growing amplitude is commanded, and monitor the closed-loop DCM error or the ZMP fluctuation. If the $1/\\kappa$ compensation terms in the stabilizer fail to keep the errors bounded beyond some force-error amplitude, the constant-$\\kappa$ linearization is inadequate. A related calculation is to compare the closed-loop eigenvalues predicted by equation (23), which assume constant $\\kappa$, with the response of the full nonlinear dynamics when $\\kappa$ varies in time.","tokens_in":12811,"feed_emoji":"🤖","tokens_out":3820,"duration_ms":36769,"temperature":0.7,"pith_summary":"This paper proposes a control strategy for humanoid robots that walk while manipulating objects, so that sustained hand forces act on the body. It re-derives the two standard models of bipedal walking, the linear inverted pendulum mode and the divergent component of motion, to include external manipulation forces instead of treating them as a small offset. From these formulas the authors build a pattern generator that plans center-of-mass motion from a reference ZMP and reference hand forces, and a stabilizer that explicitly corrects for differences between planned and actual hand forces. The claim is that this removes two approximations in prior loco-manipulation controllers: the vertical force effect on the ZMP scale is included exactly, and force errors are compensated in the stabilizer. If true, the payoff is a humanoid that can plan and maintain balance while pushing or rolling heavy objects.","feed_headline":"New controller lets humanoids push heavy objects while walking","feed_subtitle":"The ext-ZMP trick lets pattern generation and balancing handle vertical loads without approximation.","key_machinery":"The central object is the ext-ZMP $\\hat{z} = \\kappa z - \\gamma$, a single variable that absorbs horizontal and vertical hand forces into a modified ZMP. Here $\\kappa = 1 - \\sum_i f^{(i)}_{\\mathrm{ex},z} / (m(\\ddot{c}_z + g))$ is the scale factor produced by vertical external forces, and $\\gamma$ collects the force and moment offsets. Substituting ext-ZMP into the preview-control pattern generator makes external-force reference tracking a drop-in extension, and the same definitions give the first- and second-order DCM error dynamics used to derive the stabilizer feedback law. The device carries the argument because all external-force effects are concentrated in one variable, so existing bipedal walking machinery survives intact.","core_discovery":"By reorganizing the Newton-Euler equations under the usual horizontal angular momentum assumptions, the paper shows that external manipulation forces enter the linear inverted pendulum mode only through a scale factor $\\kappa$ and an offset $\\gamma$, leaving the natural frequency $\\omega$ unchanged. This yields the ext-ZMP $\\hat{z} = \\kappa z - \\gamma$, so the conventional preview control can be reused directly. The divergent component of motion keeps its usual form, $\\dot{\\xi} = \\omega(\\xi - \\kappa z + \\gamma)$, so a DCM-based stabilizer can be extended without changing the unstable mode. The stabilizer separates the force-error offset into high-frequency and low-frequency components: fast errors are rejected by shifting the ZMP, slow errors by shifting the desired CoM, and the feedback gains are scaled by $1/\\kappa$ to match the conventional closed-loop response. Experiments show the robot walking while rolling a bobbin and pushing a cart with changing friction.","pith_inferences":["The frequency-domain separation in the stabilizer suggests a practical tuning recipe: the cutoff frequency can be chosen so that the fast ZMP strategy stays within the sole region while the slower CoM strategy handles drift, a design trade-off not explicitly quantified in the paper.","The same ext-ZMP derivation should apply to other sustained contacts besides the hands, such as walking with a walker, carrying a heavy load on the torso, or pushing with the shoulder, wherever a known vertical force acts on the body.","If a quantitative bound on $\\kappa$ error were established, the stabilizer could be made adaptive by estimating $\\kappa$ online from measured vertical forces rather than assuming it equals the desired value.","Because the paper assumes the reference manipulation forces are given, coupling the controller with online force-prediction methods would extend it to tasks where the required object force is not known in advance."],"forward_implications":["Walking pattern generation can incorporate vertical hand forces exactly, without approximation, while keeping the same preview-control structure and constant gains.","The stabilizer can reject manipulation-force errors directly by adjusting ZMP for fast components and CoM for slow components, rather than relying only on conservative whole-body motion.","The proposed formulas run within 2 ms control cycles on the robot's embedded computer, so the added capability does not raise computational cost.","The same ext-ZMP substitution extends naturally to other pattern-generation methods such as linear MPC and DCM-based walking control.","Previous pushing controllers that only added an offset to the ZMP or CoM can be upgraded to include the full vertical-force scale effect."],"supporting_citations":[{"why":"Supplies the preview-control method that the pattern generator extends by substituting ext-ZMP for the conventional ZMP.","marker":"[1]"},{"why":"Defines the 3D linear inverted pendulum mode that this paper re-derives with external forces.","marker":"[5]"},{"why":"Introduces the divergent component of motion, whose dynamics the paper re-derives in the presence of external manipulation forces.","marker":"[6]"},{"why":"Provides the DCM-based bipedal walking control framework that the stabilizer extends.","marker":"[3]"},{"why":"Gives the open-source stabilizer implementation whose DCM feedback control is extended to account for external force errors.","marker":"[4]"},{"why":"Establishes the capture-point error compensation and ZMP feedback law that underlies the proposed stabilizer.","marker":"[2]"},{"why":"Provides the foot damping control used to realize the command ZMP, which the stabilizer relies on.","marker":"[28]"},{"why":"Represents the conventional pushing-manipulation approach that handles external forces only by offsetting the ZMP, the baseline this paper improves.","marker":"[7]"},{"why":"Models pushing with hand reflect forces during dynamic walking, another prior method that ignores the vertical-force scale effect.","marker":"[8]"}],"fun_headline_variants":["Ext-ZMP trick lets humanoids push carts while walking","Walking while pushing: ext-ZMP handles vertical loads without approximation","Humanoid push-walk controller reuses preview control via ext-ZMP","Ext-ZMP stabilizer handles changing friction during push-walk","Humanoid push-walk: pattern gen and stabilization via ext-ZMP"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The stabilizer linearizes the DCM error dynamics by assuming that the scale factor $\\kappa$ computed from planned and measured vertical hand forces is equal and constant, so that vertical force errors do not change how the ZMP is scaled into the DCM dynamics; the paper states this error is 'not so large' but gives no quantitative bound.","fun_headline_variants_meta":{"raw":{"variants":["Ext-ZMP trick lets humanoids push carts while walking","Walking while pushing: ext-ZMP handles vertical loads without approximation","Humanoid push-walk controller reuses preview control via ext-ZMP","Ext-ZMP stabilizer handles changing friction during push-walk","Humanoid push-walk: pattern gen and stabilization via ext-ZMP"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000957,"raw_usage":{"total_tokens":4045,"prompt_tokens":876,"completion_tokens":3169,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":492,"completion_tokens_details":{"reasoning_tokens":3080}},"tokens_in":492,"tokens_out":3169,"duration_ms":22941,"temperature":1.0,"reasoning_tokens":3080,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:34:51.286180+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Apply a humanoid to a pushing task while a sinusoidal vertical hand-force error of growing amplitude is commanded, and monitor the closed-loop DCM error or the ZMP fluctuation. If the $1/\\kappa$ compensation terms in the stabilizer fail to keep the errors bounded beyond some force-error amplitude, the constant-$\\kappa$ linearization is inadequate. A related calculation is to compare the closed-loop eigenvalues predicted by equation (23), which assume constant $\\kappa$, with the response of the full nonlinear dynamics when $\\kappa$ varies in time.","supporting_citations":[{"cited_title":"Three-dimensional bipedal walking control based on divergent component of motion,","cited_arxiv_id":null,"evidence_quote":"Provides the DCM-based bipedal walking control framework that the stabilizer extends."},{"cited_title":"Biped walking pattern generation by using preview control of zero-moment point,","cited_arxiv_id":null,"evidence_quote":"Supplies the preview-control method that the pattern generator extends by substituting ext-ZMP for the conventional ZMP."},{"cited_title":"The 3d linear inverted pendulum mode: a simple modeling for a biped walking pattern generation,","cited_arxiv_id":null,"evidence_quote":"Defines the 3D linear inverted pendulum mode that this paper re-derives with external forces."},{"cited_title":"Real time motion generation and control for biped robot -1st report: Walking gait pat- tern generation-,","cited_arxiv_id":null,"evidence_quote":"Introduces the divergent component of motion, whose dynamics the paper re-derives in the presence of external manipulation forces."},{"cited_title":"Stair climbing stabilization of the hrp-4 humanoid robot using whole-body admittance control,","cited_arxiv_id":null,"evidence_quote":"Gives the open-source stabilizer implementation whose DCM feedback control is extended to account for external force errors."},{"cited_title":"Balance control based on capture point error compensation for biped walking on uneven terrain,","cited_arxiv_id":null,"evidence_quote":"Establishes the capture-point error compensation and ZMP feedback law that underlies the proposed stabilizer."},{"cited_title":"Biped walking stabilization based on linear MUROOKAet al.: HUMANOID LOCO-MANIPULATIONS PATTERN GENERATION AND STABILIZATION CONTROL 9 inverted pendulum tracking,","cited_arxiv_id":null,"evidence_quote":"Provides the foot damping control used to realize the command ZMP, which the stabilizer relies on."},{"cited_title":"Pushing manipula- tion by humanoid considering two-kinds of zmps,","cited_arxiv_id":null,"evidence_quote":"Represents the conventional pushing-manipulation approach that handles external forces only by offsetting the ZMP, the baseline this paper improves."},{"cited_title":"Pushing an object considering the hand reflect forces by humanoid robot in dynamic walking,","cited_arxiv_id":null,"evidence_quote":"Models pushing with hand reflect forces during dynamic walking, another prior method that ignores the vertical-force scale effect."}],"review_version":1}