{"id":"591e91b0-88f0-4bf3-b7fb-9e333caa0dfe","arxiv_id":"2502.01376","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A power-law damping admittance controller, inspired by shear-thickening fluids, lets robots comply with human traction while strongly damping sudden impacts.","lead":"This paper proposes a robot controller called shear-thickening fluid control, which mimics non-Newtonian fluid behavior: the robot moves softly under gentle human pulling but stiffens under sudden impacts. It could make collaborative robots safer in factories and homes by reducing dangerous jerks during physical human-robot interaction.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Discrete-time stability bound used to justify the 50 Hz mobile manipulator is derived under constant f_ext and is miscomputed: Eq. (21) gives 0.0145 s for the §7.1.2 parameters, not 0.023 s, so the implemented 0.02 s sample time lies outside the paper's own stability region.","rationale":"The strongest claim is plausible: a power-law damping term can give low apparent damping at low speeds and strong dissipation at high speeds, and the time-domain simulations and real-world demonstrations show smaller velocity jumps under SFC than under L-AC or N-AC. However, the paper's safety argument has a real soft spot: Theorem 3, the discrete stability guarantee used to justify low-control-frequency operation, is derived under constant or zero external force, while the controller's advertised regime is impulsive, time-varying impact. The arithmetic error in applying Eq. (21) to the mobile manipulator (0.023 s vs. 0.0145 s) makes the implemented 0.02 s sample time inconsistent with the paper's own constraint. The Appendix C continuous stability proof also contains a shifted-equation mistake, though that particular theorem is repairable by a monotonicity argument. The experimental evidence is qualitative and unrepeated, but it is real evidence and should not be dismissed. Overall, the central claim is not disproven, but it is not fully supported as written. The reader's CONDITIONAL verdict is appropriate and should be maintained: the authors need to correct the discrete-time analysis for time-varying forces, fix the sample-time calculation, and provide repeated trials with error bars before the safety and low-frequency claims can be accepted.","tokens_in":45416,"tokens_out":4587,"duration_ms":42936,"concrete_test":"Independently evaluate Eq. (21) with m=1, mu=20, n=3, f_ext,max=70 N: Delta T_bound = 2*20^{-1/3}*3^{-1}*70^{-2/3} ≈ 0.0145 s. If the value is not 0.023 s, the Section 7.1.2 claim is arithmetically false. Then simulate the discrete recursion (20) with a 70 N pulse of 0.1 s duration at Delta T = 0.02 s and Delta T = 0.01 s, recording whether acceleration or velocity oscillates or diverges. If Delta T = 0.02 s remains stable for time-varying f_ext, the practical impact is mitigated; if it oscillates or diverges, the paper's discrete stability guarantee fails exactly where it is used.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim includes reliable operation under impact disturbances, and for the mobile manipulator this rests directly on Theorem 3's discrete sample-time bound. Appendix E explicitly assumes 'the external force is assumed to be zero or constant' immediately before Eq. (74), i.e., f_ext(t)-f_ext(t+1)=0. The intended operating regime is impulsive, 40-70 N impacts, so the derivation's core assumption is violated exactly where the controller is supposed to work. The bound is also arithmetically wrong as applied: substituting the mobile-manipulator parameters (m=1, mu=20, n=3, f_ext,max=70) into Eq. (21) gives Delta T < 2*20^{-1/3}*3^{-1}*70^{-2/3} ≈ 0.0145 s, not the 0.023 s claimed in Section 7.1.2. The implemented 0.02 s sample time therefore violates even the paper's own bound. Since the mobile-manipulator experiments are single demonstrations without error bars or repeated trials, the low-frequency impact-resistance claim is not backed by the paper's stability analysis. I also note that Appendix C's shifted stability equation is incorrect: with s = x_dot - x_dot*, the damping term should be mu(|x_dot*+s|^{n-1}(x_dot*+s) - |x_dot*|^{n-1}x_dot*), not mu|s|^{n-1}s; the conclusion may be salvageable by monotonicity, but the proof as written is invalid.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a shear-thickening-fluid-inspired nonlinear admittance controller, SFC (Eq. 11): m x_ddot + mu |x_dot|^{n-1} x_dot = f_ext with n > 1, intended to make a robot simultaneously compliant to low-amplitude human traction (near 5 N) and resistive to high-amplitude impulsive impacts (40-70 N) using a single fixed nonlinear law. The authors provide a stability/passivity/phase-trajectory analysis (Appendix C), an inverse describing-function frequency-domain analysis (Theorem 2), bandwidth/time-constant/gain-variation corollaries, a discrete-time sample-time constraint (Theorem 3), a coupled-stability condition (Theorem 4), and an auto-tuning algorithm (Algorithm 1). The results are supported by Simulink verification (Tables 3-5) and by real-world experiments on a fixed manipulator (UR16e, 500 Hz) and a mobile manipulator (50 Hz), plus a qualitative factory case study. The central empirical claim, that SFC limits velocity jumps under 40-70 N impacts to about one-third to one-half the jumps of L-AC and N-AC while preserving a similar traction response near 5 N, is plausible and, for the fixed manipulator, well illustrated.","tokens_in":45762,"tokens_out":27549,"duration_ms":215689,"significance":"The central idea is simple and appealing: a single, fixed nonlinear admittance law that behaves softly for small forces and stiffly for large forces, without mode switching or explicit force classification. If the results hold, the contribution is practically relevant for walk-through programming and collaborative handling, and the analytical package - the inverse describing function, the bandwidth and time-constant scaling rules, and an auto-tuning procedure with explicit design inputs - is a genuine step beyond ad hoc nonlinear admittance tuning. The paper deserves credit for checking analytical predictions against simulation rather than fitting them post hoc, for testing the fixed manipulator across traction-only, impact-only, and simultaneous traction/impact conditions, and for demonstrating operation on a low-bandwidth 50 Hz mobile platform. The auto-tuning algorithm gives falsifiable parameter recipes from user requirements. However, the theoretical load-bearing claims currently contain three specific errors (Appendices C, D, and E), and the paper's own stability computation does not support the mobile-manipulator sample-time choice.","major_comments":[{"comment":"The equilibrium shift is incorrect. With s = x_dot - x_dot*, where x_dot* = |f_ext/mu|^{1/n} sign(f_ext), substitution into Eq. (11) gives m s_dot + mu(|x_dot* + s|^{n-1}(x_dot* + s) - |x_dot*|^{n-1} x_dot*) = 0, not m s_dot + mu |s|^{n-1} s = 0. The cross terms in s are omitted, so the Lyapunov argument in Property 2 proves stability only of a different system and, as written, is invalid. The conclusion is salvageable: the damping function eta(s) = mu |x_dot* + s|^{n-1}(x_dot* + s) is strictly increasing in s, so with V = s^2 one obtains V_dot = -2 s (eta(s) - eta(0))/m < 0 for s != 0, giving global asymptotic stability. The corrected proof should be presented, since Property 2 is one of the three safety guarantees claimed in Theorem 1.","section":"Appendix C, Eq. (34)"},{"comment":"Theorem 3's sample-time bound is derived under the explicit assumption, stated immediately before Eq. (74), that the external force is zero or constant (f_ext(t) - f_ext(t+1) = 0). The controller's intended operating regime is impulsive 40-70 N impacts, for which the force difference across one sample is large; precisely there the derivation drops the term m^{-1}(f_ext(t) - f_ext(t+1)) and the bound does not follow. In addition, the application of the bound in Section 7.1.2 is arithmetically wrong: with m = 1, mu = 20, n = 3, and f_ext,max = 70 N, Eq. (21) gives Delta T < 2 * 1 * 20^{-1/3} * 3^{-1} * 70^{-2/3} = 0.0145 s, not 0.023 s. The implemented 0.02 s sample time therefore violates the paper's own stated stability region, contradicting the sentence that the sample time 'met this requirement and assured the stability of the system under discrete control'. The claim that SFC is validated for low control frequencies needs either a re-derivation of the bound for time-varying forces, a re-tuning that satisfies the corrected bound, or an explicit statement that the bound is only sufficient and the 50 Hz results are empirical.","section":"Appendix E, Eq. (74) and Section 7.1.2"},{"comment":"The describing-function coefficient Psi(n) = 2 sqrt(pi) Gamma(1 + n/2)/Gamma((3 + n)/2) in Eq. (13) is a factor pi too large. Computing the fundamental Fourier coefficient of D(x_dot) = mu |x_dot|^{n-1} x_dot under x_dot = B sin(omega t) gives b_1 = (2/sqrt(pi)) mu B^n Gamma(1 + n/2)/Gamma((3 + n)/2); the paper's Psi differs by exactly pi. A direct consistency check is the linear case: n = 1 must reproduce m x_ddot + mu x_dot = f_ext, whose response amplitude is 1/sqrt((m omega)^2 + mu^2), whereas Eq. (14) with Psi(1) = pi gives 1/sqrt((m omega)^2 + (mu pi)^2). The error propagates into the bandwidth formula (16), the time constant (17), the coupled-stability quantity Q in Theorem 4, and Step 4 of Algorithm 1, where mu is computed pi times too small, so the realized bandwidth is pi^{-1/n} lower than designed (about 32% lower for n = 3). Because Tables 3-4 report 0-10% agreement between the formulas and the 'numerical' simulations, and a direct simulation of Eq. (11) with the corrected coefficient would differ by pi^{1/n} = 1.46 for n = 3, the verification pipeline appears to reproduce the same factor error; the authors should recompute Psi, rerun the verification against Eq. (11), and re-derive the tuning formulas.","section":"Appendix D, Eqs. (13)-(17) and Tables 3-4"}],"minor_comments":[{"comment":"The bandwidth values (1.05, 4.90, 22.75) are computed from Eq. (16), which yields rad/s, and Fig. 13 uses rad/s, but Table 3 labels the column 'Hz'; the unit should be corrected.","section":"Table 3 / Section 6.3.1"},{"comment":"The self-excited oscillations of N-AC are attributed to a possible limit cycle, but no phase portrait, spectrum, or supporting analysis is provided, and the quantitative comparisons in Table 6 and Figs. 17-22 appear to come from single trials without repeated runs or error bars; the claims would be stronger with repeated measurements or with explicit single-trial reporting.","section":"Sections 7.2.4 and 7.3"},{"comment":"The theorems and corollaries state n > 0, but the shear-thickening behavior and the claimed traction/impact differentiation depend on n > 1; the domain n > 1 should be used consistently in all statements that feed the design algorithm.","section":"Theorem 2 and Corollaries 1-3"},{"comment":"In Step 1, Eq. (84) involves ratios of logarithms of quantities that are both less than 1 for the intended requirements, so the inequality direction and sign handling should be spelled out; line 3 of the algorithm should also state explicitly which form of the bandwidth constraint (including the force-ratio factor of Eq. (22)) is being checked.","section":"Appendix F / Algorithm 1"},{"comment":"The paper alternates between 'sample time', 'sampling time', and 'control frequency' for Delta T; the terminology should be unified, and the role of g (set to 1 in the analysis but non-unit in Table 2) should be clarified in the time-constant and gain-variation simulations.","section":"Sections 3-7"}],"recommendation":"major_revision","confidential_remarks":"The manuscript has real merit: the phenomenon is plausible, the fixed-manipulator experiments are informative, and the analytical program is ambitious. However, the three major comments above are all in the paper's own load-bearing theorems, and none of them should be treated as purely cosmetic. The Appendix D factor-pi error is especially concerning because the reported simulation 'verification' tracks the erroneous formula; I would ask the editor to require the authors to provide the simulation scripts or exact parameter values for Tables 3-4 so the verification can be independently checked. The paper is within the journal's scope, and I expect the errors to be fixable within a major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper proposes a fixed nonlinear admittance law—power-law damping, m x¨ + μ|ẋ|^{n-1} ẋ = f_ext with n>1—that behaves compliantly under gentle human traction and stiffly under hard impacts. The idea is simple and the simulations plus real-world demos suggest it works. But the stability support for the low-frequency mobile manipulator has a real hole: the discrete-time bound in Theorem 3 is derived assuming zero or constant external force, and the authors misapply it. Substituting their §7.1.2 parameters into Eq. (21) gives ΔT < 0.0145 s, not 0.023 s as claimed; the implemented 0.02 s sample time is outside the paper's own stated stability region.\n\nWhat is actually new: the STF framing is a fresh way to motivate an existing family of nonlinear dampers, and the inverse describing-function analysis gives usable, verified formulas for bandwidth and time constant (within 2–10% in simulation). The auto-tuning pipeline is practical and the experimental comparison with L-AC and N-AC is well designed, even if it is qualitative. The paper also clearly shows that N-AC's force-dependent damping saturates and can cause self-excited oscillations, which is a nice contrast.\n\nThe soft spots are proportionate: the power-law damper itself is not new (Lai 2014 and others), so the novelty is moderate. The Appendix C stability proof shifts the equilibrium incorrectly—the damping term in the error coordinates should be μ(|ẋ*+s|^{n-1}(ẋ*+s) − |ẋ*|^{n-1}ẋ*), not μ|s|^{n-1}s. The proof is invalid, though the result is salvageable by monotonicity. The discrete-time issue is more serious because it undermines the safety claim for the 50-Hz robot. And the experiments are single demonstrations without repeated trials or error bars, so the empirical evidence is suggestive, not strong.\n\nWho this is for: pHRI researchers and practitioners who want a simple nonlinear admittance controller with no mode switching and who can tolerate a purely dynamical (rather than detection-based) method for distinguishing traction from impact. This deserves a serious referee, but the authors need to correct the arithmetic and either re-derive the discrete bound for time-varying forces or soften the stability claim.","headline":"A practical power-law admittance law for pHRI with promising impact resistance, but the mobile-manipulator stability bound is miscomputed and the Appendix C proof is wrong as written.","tokens_in":46313,"tokens_out":4824,"would_cite":true,"duration_ms":42228,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["93C85","93C10","93D05"],"pacs":[],"model":"deepseek-v4-flash","headline":"A power-law damping law lets one fixed admittance controller comply with gentle pulls near 5 N while cutting velocity jumps from 40--70 N impacts to a third or half of linear alternatives.","keywords":["physical human-robot interaction","shear-thickening fluid","nonlinear admittance control","impact resistance","traction compliance","describing function","passivity","discrete-time stability"],"falsifier":"Re-run the arithmetic and the experiment: substituting $m=1$, $\\mu=20$, $n=3$, and $|f_{\\mathrm{ext,max}}|=70$ N into Eq. (21) gives $\\Delta T \\approx 0.014$ s, not the 0.023 s the text reports, so driving the Euler-discretized SFC with the mobile manipulator's $\\Delta T = 0.02$ s under repeated 70 N impulses and watching whether acceleration diverges would settle whether the claimed stability region holds; a comparison run at $\\Delta T = 0.014$ s would show the predicted boundary. A second check: because Theorem 3 assumes constant external force, feeding a 70 N half-sine pulse rather than a step and recording whether the oscillation boundary in Fig. 12 shifts would test the assumption where it is weakest.","tokens_in":45185,"feed_emoji":"🤖","tokens_out":11993,"duration_ms":92807,"temperature":0.7,"pith_summary":"The paper claims that a single fixed nonlinear admittance law can make a collaborative robot comply with gentle human pulling while resisting hard impact blows, with no mode switching and no classification of the incoming force. The law, borrowed from the constitutive equation of shear-thickening fluids, is $m\\ddot{x} + \\mu|\\dot{x}|^{n-1}\\dot{x} = f_{\\mathrm{ext}}$ with $n > 1$: because damping grows faster than velocity, a small traction force moves the robot about as easily as a linear admittance controller does, while a 40--70 N impact produces only a fraction of the velocity jump. If true, this resolves a central safety-versus-transparency trade-off in physical human-robot interaction, letting one fixed parameter set serve both collaborative guidance and unexpected collisions. The authors support the claim with stability, passivity, and describing-function analysis, a discrete-time stability constraint, a parameter auto-tuning procedure, and real-world experiments on fixed and mobile manipulators, including a water-carrying task that survives impacts.","feed_headline":"One fixed law cuts impact velocity jumps by half or more","feed_subtitle":"Shear-thickening-style damping keeps the robot just as easy to pull while absorbing hard blows.","key_machinery":"The central object is the shear-thickening admittance law of Eq. (11), $m\\ddot{x} + \\mu|\\dot{x}|^{n-1}\\dot{x} = f_{\\mathrm{ext}}$, whose damping term is copied from the power-law constitutive equation of shear-thickening fluids. Its defining property is that the damping-to-velocity ratio $\\mu|\\dot{x}|^{n-1}$ grows without bound as speed rises: at crawling speeds the robot feels nearly undamped and follows the human's pull, while at impact-driven speeds the damping overwhelms the force and caps the velocity jump. The argument is carried by three supporting constructions: the nonlinear spatial velocity ratio $R_{\\mathrm{sv}} = -(\\mu/m)|x_2|^{n-1}$ describing phase-plane convergence in free motion; the inverse describing function $N(B,\\omega)$ that converts an assumed sinusoidal output velocity into the required input amplitude and yields closed-form bandwidth, time-constant, and gain-variation formulas; and the discrete recursion constraint on $\\Delta T$ that bounds the Euler-integration step against acceleration oscillation.","core_discovery":"On the paper's own terms, the discovery is that shear-thickening rheology, abstracted as power-law damping $D(\\dot{x}) = \\mu|\\dot{x}|^{n-1}\\dot{x}$ with $n > 1$, is a viable virtual dynamics for admittance-controlled robots: globally asymptotically stable under constant loads, passive under arbitrary external forces, and provably convergent in free motion, so it qualifies as a safe interaction law. The frequency-domain analysis via an inverse describing function yields three design handles---bandwidth that narrows as input amplitude falls, a time constant that shrinks as force grows, and a gain attenuation of $20w(1-n)/n$ dB per $10^w$-fold amplitude increase---which together explain and tune the traction/impact dichotomy. The paper further claims that the Euler-discretized controller remains stable when the sample time obeys $\\Delta T < 2m\\mu^{-1/n} n^{-1} |f_{\\mathrm{ext,max}}|^{(1-n)/n}$, and that with parameters set by its auto-tuning algorithm, SFC reproduces linear admittance control's responsiveness at traction levels near 5 N while holding end-effector velocity jumps during 40--70 N impacts to roughly one-third to one-half of those of linear or saturating-nonlinear alternatives.","pith_inferences":["Because the describing-function analysis treats the controller as a bijection between output velocity and input force, the amplitude-stratification argument should extend to multi-axis motion; a strong impact along one axis would raise the effective damping seen by the other axes, an effect the current experiments only glimpse in the orthogonal-direction test.","A direct substitution suggests the mobile-manipulator sample time may lie outside the stated stability region, which would mean the 50 Hz viability claim currently rests on the experiments rather than on Theorem 3.","A testable corollary of state-dependent damping is that SFC's post-impact settling time stays short even when the impact force vanishes abruptly, whereas a force-dependent N-AC lags; this could be measured as a settling-time metric in a repeat-impulse protocol."],"forward_implications":["A single fixed SFC parameter set replaces any impact-detection, thresholding, or mode-switching layer: the controller separates traction from impact purely through its amplitude-dependent gain.","On robots with low control rates, such as the 50 Hz mobile manipulator, SFC with parameters chosen under the discrete bound still suppresses impact energy above about 1 Hz, where linear and saturating-nonlinear admittance controllers let it through.","Because SFC's damping depends only on the velocity state, the controller retains high damping after an impact ends and returns to steady state faster than force-dependent nonlinear admittance controllers, which lose damping the moment the force drops.","The auto-tuning algorithm converts task-level requirements (traction force, impact force, desired traction speed, bandwidth, sample time) directly into the controller parameters $\\mu$, $n$, $g$, with an explicit condition for when the feasible bandwidth must be reduced.","The paper expects the same law to carry over to exoskeletons, teleoperated robots, and other non-Newtonian rheologies, where traction-compliant yet impact-resistant behavior would protect wearers and operators."],"supporting_citations":[{"why":"Supplies the virtual-dynamics admittance-control viewpoint that SFC extends, plus the human-operator impedance model used in the coupling analysis.","marker":"Keemink et al. (2018)"},{"why":"Establishes impedance and admittance control as the interaction paradigm and as a framework that can include nonlinear formulations.","marker":"Hogan (1984)"},{"why":"Provides the describing-function method used for SFC's frequency-domain analysis and for the phase argument in coupled stability.","marker":"Slotine and Li (1991)"},{"why":"Documents the excess-energy problem of Euler-integrated admittance control, motivating the discrete stability constraint, and supplies the low-level velocity controller assumption.","marker":"Ferraguti et al. (2019)"},{"why":"Supports the claim that forward-Euler integration can inject energy and cause vibration in discrete admittance implementations.","marker":"De Stefano et al. (2017)"},{"why":"Supplies the nonlinear admittance controller baseline (N-AC) whose force-dependent damping saturates, the main experimental comparator.","marker":"Lai (2014)"},{"why":"Provides the passivity-based criterion (apparent admittance phase within plus or minus 90 degrees) used to prove coupled stability of the human-robot loop.","marker":"Colgate and Hogan (1988)"}],"fun_headline_variants":["Power-law damping yields compliant yet impact-resistant pHRI","Shear-thickening control reduces robot impact jumps by half","Stable, passive, and impact-resistant pHRI via SFC","One controller: compliant for pulls, resistant to impacts","Shear-thickening-style damping: easy to pull, hard to hit"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The discrete-time stability guarantee is derived under a zero-or-constant external force assumption, even though the controller is meant to handle impulsive impacts, and the paper's stated 0.023 s bound for the mobile manipulator appears to be a miscalculation of its own Eq. (21), which at the stated parameters ($m=1$, $\\mu=20$, $n=3$, $|f_{\\mathrm{ext,max}}|=70$ N) gives roughly 0.014 s rather than 0.023 s.","fun_headline_variants_meta":{"raw":{"variants":["Power-law damping yields compliant yet impact-resistant pHRI","Shear-thickening control reduces robot impact jumps by half","Stable, passive, and impact-resistant pHRI via SFC","One controller: compliant for pulls, resistant to impacts","Shear-thickening-style damping: easy to pull, hard to hit"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001009,"raw_usage":{"total_tokens":4357,"prompt_tokens":1130,"completion_tokens":3227,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":746,"completion_tokens_details":{"reasoning_tokens":3141}},"tokens_in":746,"tokens_out":3227,"duration_ms":23893,"temperature":1.0,"reasoning_tokens":3141,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T15:32:36.585339+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the arithmetic and the experiment: substituting $m=1$, $\\mu=20$, $n=3$, and $|f_{\\mathrm{ext,max}}|=70$ N into Eq. (21) gives $\\Delta T \\approx 0.014$ s, not the 0.023 s the text reports, so driving the Euler-discretized SFC with the mobile manipulator's $\\Delta T = 0.02$ s under repeated 70 N impulses and watching whether acceleration diverges would settle whether the claimed stability region holds; a comparison run at $\\Delta T = 0.014$ s would show the predicted boundary. A second check: because Theorem 3 assumes constant external force, feeding a 70 N half-sine pulse rather than a step and recording whether the oscillation boundary in Fig. 12 shifts would test the assumption where it is weakest.","supporting_citations":[{"cited_title":"The International Journal of Robotics Research 37(11): 1421--1444","cited_arxiv_id":null,"evidence_quote":"Supplies the virtual-dynamics admittance-control viewpoint that SFC extends, plus the human-operator impedance model used in the coupling analysis."},{"cited_title":"In: Proceedings of the American Control Conference (ACC)","cited_arxiv_id":null,"evidence_quote":"Establishes impedance and admittance control as the interaction paradigm and as a framework that can include nonlinear formulations."},{"cited_title":"Prentice hall Englewood Cliffs, NJ","cited_arxiv_id":null,"evidence_quote":"Provides the describing-function method used for SFC's frequency-domain analysis and for the phase argument in coupled stability."},{"cited_title":"The International Journal of Robotics Research 38(6): 747--765","cited_arxiv_id":null,"evidence_quote":"Documents the excess-energy problem of Euler-integrated admittance control, motivating the discrete stability constraint, and supplies the low-level velocity controller assumption."},{"cited_title":"In: Proceedings of the International Conference on Intelligent Robots and Systems (IROS)","cited_arxiv_id":null,"evidence_quote":"Supports the claim that forward-Euler integration can inject energy and cause vibration in discrete admittance implementations."},{"cited_title":"In: Proceedings of the International Conference on Advanced Intelligent Mechatronics","cited_arxiv_id":null,"evidence_quote":"Supplies the nonlinear admittance controller baseline (N-AC) whose force-dependent damping saturates, the main experimental comparator."},{"cited_title":"International Journal of Control 48(1): 65--88","cited_arxiv_id":null,"evidence_quote":"Provides the passivity-based criterion (apparent admittance phase within plus or minus 90 degrees) used to prove coupled stability of the human-robot loop."}],"review_version":1}