{"id":"a1c288eb-9ce0-43d8-9b10-ce74ce5a0ae5","arxiv_id":"2506.00351","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"HapticRRT plans over the quasi-static equilibrium manifold and discovers contact-rich manipulation strategies for pendulum pushing, spring-clip opening, and crowded bookshelf insertion.","lead":"HapticRRT adapts the classic RRT path planner to plan on the equilibrium manifold of quasi-static, contact-rich manipulation, treating contacts as essential rather than obstacles. It discovers push, wedge, and insert strategies for three real robot tasks, offering a fast, interpretable alternative to learning-based manipulation planning.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Branch discovery claim is unsupported: HapticRRT stops at haptic obstacles (det ≤ λ, Eq. 3), so a single-seed tree cannot cross the singularities that separate distinct stable branches of Meq; Figs. 8/11 likely show one connected sheet, not multiple branches.","rationale":"The reader's weakest_assumption focuses on fidelity of the hand-crafted potential and missing parameters, but the reader's rationale also lists 'the unexplained mechanism for reaching multiple branches' as a strong concern. I agree that the missing-parameters issue is real but secondary: parameters can be specified and potential errors can be corrected by retuning. The branch-switching issue is more load-bearing because it threatens a stated central contribution (ii) and appears to be an internal inconsistency rather than an empirical gap. Under the algorithm's own termination rule, no edge can pass through a point where the Hessian loses rank, and distinct stable branches of the equilibrium manifold are separated precisely by such points. Hence, from a single seed, the tree is confined to one connected component of the stable manifold. The fact that the paper shows both grey and orange meshes therefore either means those meshes are on the same component (in which case 'branches' is a misnomer and the claimed multiplicity is not demonstrated) or the algorithm would need a mechanism that is not described. Both possibilities undercut the paper's headline claim. The proposed numerical-continuation test would settle which case holds. Since the reader already required conditional acceptance with major clarifications, my analysis does not change the verdict, but it makes the required clarification concrete: report the connected-component structure of the stable equilibrium set and explain how the tree can reach more than one component, or revise the claim. The other concerns (W^β with possibly negative W, unreported Σ and β, small real-world samples) remain valid but are subordinate; they affect robustness and reproducibility, not the logical coherence of the central argument.","tokens_in":14202,"tokens_out":10425,"duration_ms":105368,"concrete_test":"Re-run the clip and bookshelf experiments while logging det(∂^2_zz W) along every tree edge, and compute the connected components of the stable set {det(∂^2_zz W) > λ} for the potentials in Eqs. 14–15 using numerical continuation (e.g., pseudo-arclength). If the orange and grey meshes of Figs. 8 and 11 lie in different components, HapticRRT from a single start cannot reach both, falsifying contribution ii. If they lie in the same component, the paper must reword 'branches' and the claimed contribution reduces to exploring one connected sheet.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Contribution ii) claims HapticRRT discovers multiple manipulation strategies corresponding to branches of the equilibrium manifold (Sec. II-B, Figs. 8 and 11). But the algorithm cannot switch branches as specified. EXTEND (Alg. 2, Sec. III-B) terminates any edge as soon as det(∂^2_zz W) ≤ λ (Eq. 3, haptic obstacle), and distinct stable equilibrium branches of a smooth potential are separated by fold/saddle-node bifurcations where ∂^2_zz W loses rank. Starting from a single seed (Alg. 3), every tree node is reached by continuous ODE integration (Eq. 8) within the same connected component of the stable part of Meq. Therefore the orange and grey regions in Figs. 8 and 11 cannot both be discovered by the tree unless they lie on one connected sheet. If they are connected, 'multiple branches' is a misnomer and the claimed discovery of distinct branches is not established; if they are disconnected, the algorithm as written cannot reach the second branch from the initial node. The paper provides no mechanism (multiple seeds, random jumps, or dynamic transitions) that would permit branch crossing, and Sec. II-B only notes that multiplicity exists, not how the planner exploits it. This is an internal consistency problem, not a missing parameter.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes HapticRRT, a sampling-based planner that adapts classical RRT to operate on the quasi-static equilibrium manifold M_eq defined by the zero-gradient condition of a manipulation potential W(z,u). The planner samples in control space, selects nearest neighbors with a potential-weighted Mahalanobis distance, and extends tree edges by integrating an adaptive ODE that tracks M_eq while measuring haptic distance. The authors claim three contributions: adapting RRT to contact-rich manipulation on M_eq, discovering multiple equilibrium branches corresponding to distinct manipulation strategies, and validating the method on three real-world tasks (pendulum pushing, spring-loaded clip opening, crowded bookshelf insertion). The experimental sections report success rates of 4/5 to 5/5 and compare planning time against the authors' earlier DMP-BBO method.","tokens_in":14601,"tokens_out":7034,"duration_ms":72809,"significance":"If the central claims hold, the paper offers a transparent, interpretable alternative to optimization-based contact-rich planning: a single differentiable potential per task, combined with a classical RRT-style exploration of the equilibrium manifold, yields executable policies with substantially lower planning time than the DMP-BBO baseline. The real-world validation across three qualitatively different tasks, including force-profile comparisons, is a genuine strength, as is the explicit visualization of haptic metrics and obstacles. However, the genuinely new algorithmic claim—autonomous discovery of multiple equilibrium branches—is not supported by the algorithm as written, and the termination conditions in the pseudocode are internally inconsistent. The framework itself is largely inherited from the authors' prior work [12]–[14], and the only nontrivial baseline is also the authors' own method, so the significance of the incremental contribution depends on whether the branch-discovery claim can be substantiated or appropriately revised.","major_comments":[{"comment":"The termination logic in Alg. 2 is internally inconsistent and contradicts the text. Section III-B states that one termination condition occurs when the haptic distance satisfies phi(t) <= epsilon, but line 3 of Alg. 2 stops when phi(t) > epsilon; since phi(0)=0, the text's condition would stop immediately, while the pseudocode extends past the intended distance. In addition, Eq. (3) defines a haptic obstacle as det(d^2_zz W) > lambda > 0, but the surrounding text and Fig. 5 identify haptic obstacles with singularities, i.e., with det near zero, and Alg. 2 line 5 stops and marks DEAD END when det > lambda, which would terminate expansion at every high-stiffness stable configuration. These contradictions make the algorithm as specified unexecutable; please correct the inequality directions and specify the stopping rule unambiguously.","section":"Sec. III-B, Alg. 2, Eq. (3)"},{"comment":"The claim that HapticRRT discovers multiple branches of M_eq is not supported by the algorithm as written. EXTEND terminates an edge as soon as the ODE encounters a haptic obstacle (Eq. 3), and distinct stable equilibrium branches are separated by fold or saddle-node bifurcations where det(d^2_zz W) vanishes. Starting from a single seed node (Alg. 3), every tree node is reached by continuous integration within one connected component of the stable part of M_eq, so the tree cannot cross the singularity that separates the grey and orange meshes in Figs. 8 and 11. The paper provides no mechanism for branch crossing, such as multiple initial seeds or random jumps, and does not state whether the two meshes come from the same run or from different initial conditions. Please either provide such a mechanism, report the initial conditions used for each mesh, or revise the branch-discovery claim and the associated abstract/conclusion language.","section":"Sec. V-B, Fig. 8, Sec. VI-B, Fig. 11"},{"comment":"Key algorithm parameters are not reported or studied: the potential weight beta, the Mahalanobis covariance Sigma, the haptic-obstacle threshold lambda, the ODE step size eta, the extension distance epsilon, and the stiffness constants kmin, kmax, d0, Kc, K1, K2, k_theta. These quantities directly determine the nearest-neighbor bias, the termination of edges, the accuracy with which the ODE tracks M_eq, and the shape of the manifold itself. Without reporting their values or providing a sensitivity study, the success rates and planning times cannot be reproduced, and it is unclear whether the results depend on fine-tuned constants rather than on the proposed method.","section":"Sec. III-A, III-B, IV, V, VI"},{"comment":"The adaptive ODE in Eq. (7) is cited from prior work, but the paper does not analyze its behavior for finite integration steps near singularities. The Newton-correction term eta (d^2_zz W)^{-1} d_z W becomes unbounded as det(d^2_zz W) approaches zero, and the planner's correctness depends on the ODE tracking M_eq closely enough during each EXTEND step. Please provide a local error bound, a practical criterion for choosing eta and lambda, or an ablation demonstrating that the planner's performance is insensitive to these choices.","section":"Sec. III-B, Eq. (7)"}],"minor_comments":[{"comment":"The abstract contains a grammatical error: 'we presents Haptic Rapidly-Exploring Random Trees' should be 'we present Haptic Rapidly-Exploring Random Trees'.","section":"Abstract"},{"comment":"The text refers to 'Table IV' when presenting the pendulum results, but the actual table is labeled Table I; please correct the cross-reference.","section":"Sec. IV-E"},{"comment":"Eq. (5) defines a matrix G_m, but Eq. (6) uses G_m^2 in the line element. Please clarify whether the haptic metric is G_m or its square, and define the notation consistently.","section":"Sec. II-C, Eq. (6)"},{"comment":"The gravitational potential term 1/2 m g L0 sin z_theta has an unusual factor of 1/2 and no stated reference configuration; please clarify the zero of potential and the coordinate convention for z_theta.","section":"Sec. IV-B, Eq. (12)"},{"comment":"The statement that z_y = 0 corresponds to a fully inserted book is confusing because Fig. 11a plots z_y against u_y and u_theta; please specify the world-frame axes and the insertion direction.","section":"Sec. VI-B, Fig. 11"},{"comment":"The state vector z includes z_r, the positions of the dual-arm end effectors, while u contains the desired positions; please clarify why the actual end-effector positions are treated as internal states rather than as controlled outputs under impedance control.","section":"Sec. V-A, Eq. (14)"}],"recommendation":"major_revision","confidential_remarks":"The paper's core framework (haptic metric, equilibrium manifold, adaptive ODE, task potentials) is taken from the authors' own prior work [12]–[14], and the genuinely new component is the integration of RRT with that framework plus the branch-discovery claim. As it stands, the branch-discovery claim is not supported by the algorithm as written, and the termination conditions in Alg. 2 and Eq. (3) are mutually contradictory. These issues are fixable—by correcting the pseudocode, adding multiple seeds or an explicit branch-crossing mechanism, or rewriting the claim—but they are load-bearing rather than cosmetic. The evaluation would also be considerably stronger with an independent baseline; currently the only nontrivial baseline is the authors' own DMP-BBO method."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear Colleague,\n\nShort version: HapticRRT is a plausible RRT-style planner for quasi-static contact-rich manipulation, tested on three real robot tasks, but the paper's second contribution—discovering multiple branches of the equilibrium manifold—is not supported by the algorithm as written. That's an internal consistency problem, not a missing parameter.\n\nWhat's genuinely new here is the planning loop: sampling in control space, a nearest-neighbor metric that mixes Mahalanobis distance with a W^β potential penalty, and tree extension by integrating an adaptive ODE on the equilibrium manifold until a haptic-distance threshold or a haptic obstacle is hit. The underlying potential-based framework (haptic metric, manifold, adaptive ODE) comes from the authors' prior papers, but the RRT adaptation is theirs. The real-world experiments are real: 5/5 on the pendulum and clothespin cases, mostly 4/5 on the clipboard and bookshelf variants, and the force-trace comparisons look qualitatively consistent.\n\nNow the soft spots, in proportion. The branch claim does not hold up. EXTEND terminates any edge as soon as det(∂²_zz W) ≤ λ, which is exactly the rank-drop that separates distinct stable branches of a potential. Starting from one seed, the tree cannot cross such a singularity. So the grey and orange regions in Figs. 8 and 11 cannot be separate branches reachable by HapticRRT as specified. Either they're on one connected sheet and the \"multiple branches\" language is misleading, or they're disconnected and the algorithm can't reach both. The paper gives no mechanism—no multiple seeds, no random restarts—to get around this.\n\nSecond, reproducibility is weak. The planner depends on beta, Sigma, lambda, eta, epsilon, and the stiffness parameters in the potentials, and none of them are reported. No code is linked. The equations are there, so a determined reader could reconstruct things, but the parameters are load-bearing and absent.\n\nThird, baselines are thin: AtlasRRT is a purely kinematic constraint planner and DMP-BBO is the authors' own method. That's fine for a first look, but the efficiency claims (2.7 s vs 16 s, etc.) would be stronger against an independent baseline.\n\nWho should read this: people working on contact-rich manipulation who want a fast, interpretable alternative to policy search. The planner idea is worth taking seriously and the experiments give it some credibility. The branch claim needs to be either fixed with a mechanism or dropped/re-framed. Also, release the parameters.\n\nMy recommendation: yes, send to peer review, but expect major revision. The core idea deserves referee time; the current claims do not all survive contact with the algorithm.","headline":"Solid RRT-on-manifold planner with real robot demos, but the headline branch-discovery claim is unsupported by the algorithm as written.","tokens_in":15048,"tokens_out":3067,"would_cite":false,"duration_ms":29030,"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":"This paper claims that an RRT variant planning on a force-balanced equilibrium manifold, with edge lengths set by a haptic metric, turns contact-rich manipulation into a tree-search problem solvable from one potential per task.","keywords":["HapticRRT","quasi-static manipulation","equilibrium manifold","haptic metric","haptic obstacle","sampling-based motion planning","contact-rich manipulation","manipulation potential"],"falsifier":"Run HapticRRT on a task whose governing physics include a contact mode intentionally omitted from the potential, such as dry friction or jamming between the inserted object and the shelf; if the planner yields a policy whose simulated force profile diverges from measured forces, or if the ODE drifts off $M_{\\mathrm{eq}}$ near a singularity, the claim that a single smooth potential suffices is falsified.","tokens_in":14006,"feed_emoji":"🤖","tokens_out":8094,"duration_ms":77672,"temperature":0.7,"pith_summary":"This paper claims that a classical sampling-based motion planner can be made to plan contact-rich manipulation if planning happens on the quasi-static equilibrium manifold rather than on collision-free configuration space. To that end it introduces HapticRRT, an RRT variant whose nodes live on the manifold $M_{\\mathrm{eq}} = \\{(z,u)\\mid \\partial_z W(z,u)=0\\}$ defined by a single differentiable manipulation potential $W$, and whose edge length is measured by the haptic metric, the squared Hessian of the reduced potential. The paper argues that this recasting turns force reasoning into geometry: haptic obstacles are places where the Hessian determinant crosses a stiffness threshold, tree branches are distinct manipulation strategies, and the planner discovers strategies no one programmed, such as pushing books aside before inserting, opening a clip before inserting, or sustaining directional force on a pendulum. It supports the claim with three real-robot tasks, each built from one potential, with success rates of 4/5 to 5/5 and planning times far below a prior optimization-based method. A sympathetic reader would take the central assertion to be that contact-rich skills do not require contact-phase engineering or reward design if force is encoded through a smooth potential and geometry is allowed to do the searching.","feed_headline":"A force-aware RRT plans contact-rich skills without hand-coded phases","feed_subtitle":"It searches a force-balanced manifold instead of free space, and solves shelves, clips, and pendulums in most real trials.","key_machinery":"The load-bearing object is the quasi-static equilibrium manifold $M_{\\mathrm{eq}} := \\{(z,u) \\in Z \\times U \\mid \\partial_z W(z,u)=0\\}$ generated by a smooth manipulation potential $W$; on this manifold the system is always in force balance, so every point is a stable or unstable contact configuration. Two associated objects carry the planner: the haptic metric $G_m = \\partial^2_{uu} W - \\partial^2_{uz} W (\\partial^2_{zz} W)^{-1} \\partial^2_{zu} W$, the Schur complement of the Hessian evaluated on $M_{\\mathrm{eq}}$, whose square root defines haptic distance and therefore the tree's edge length, and the haptic obstacle condition $\\det(\\partial^2_{zz} W) > \\lambda$, which marks where the manifold folds and expansion must stop. The adaptive ODE $\\dot z = -(\\partial^2_{zz}W)^{-1}\\partial^2_{uz}W\\,\\dot u - \\eta(\\partial^2_{zz}W)^{-1}\\partial_z W$ simultaneously tracks the infinitesimal projection of control changes onto $z$ and applies Newton corrections that hold the state on $M_{\\mathrm{eq}}$. Branches of $M_{\\mathrm{eq}}$ (multiple stable $z^*$ for the same $u$) are what the tree explores, and each branch corresponds to a distinct manipulation strategy.","core_discovery":"The paper's central claim is that adapting RRT to operate on the implicit equilibrium manifold of a quasi-static manipulation system turns strategic contact reasoning into a standard tree-search problem. For a system with internal state $z$ and control $u$ described by a manipulation potential $W(z,u)$, the planner samples candidate controls, selects the nearest surviving tree node using a Mahalanobis-plus-potential distance, and extends edges by integrating an adaptive ODE that keeps the system on $M_{\\mathrm{eq}}$ while accumulating haptic distance; expansion stops when a fixed haptic distance is reached or when $\\det(\\partial^2_{zz}W)$ crosses a stiffness threshold, marking a haptic obstacle. Because $M_{\\mathrm{eq}}$ can have multiple stable branches over a single control, the tree can discover qualitatively different policies, and the paper shows this concretely: a grey branch where the book or object gets stuck and an orange branch where the robot first creates space or opens the clip, with the successful branch carrying lower potential. The claim is validated by real-world trials on a hinged pendulum with changing mass, spring-loaded clip insertion with varying object size, and crowded-shelf book insertion, where HapticRRT succeeds in most or all trials and matches simulated external forces with measured ones, while using substantially less computation than a prior DMP-BBO policy optimizer.","pith_inferences":["The same pipeline should transfer to any task whose mechanics can be written as a smooth potential, including compliant assembly, door and drawer opening, and multi-object rearrangement; the paper's three demonstrations sample that space but do not exhaust it.","Because tree edges are measured in haptic distance, the planner's notion of closeness is force cost, which suggests a natural route to cost-aware sampling: biasing $u_{\\mathrm{rand}}$ or pruning by accumulated haptic distance could trade path optimality for computation.","A direct testable extension is online adaptation: the adaptive ODE gives a local model of how $z$ responds to changes in $u$, so force feedback from joint torques could be used to correct the tree's predictions at execution time, addressing failures the paper attributes to jagged or excessive-force trajectories.","The branch structure itself could be used as a symbolic abstraction: detecting when a planned path crosses a haptic obstacle or jumps branches may be a way to segment a contact-rich skill into phases automatically."],"forward_implications":["One differentiable potential per task is sufficient to generate contact-rich policies; no manual contact-phase sequencing or per-phase controllers are required.","The planner naturally discovers multiple strategies because distinct branches of $M_{\\mathrm{eq}}$ are explored as separate RRT branches, and the successful branch is identifiable by lower potential.","Contact-rich planning inherits the computational properties of sampling-based planners: HapticRRT solved the clip task in 2.74 s and the book task in 48.71 s, versus 16.14 s and 791.22 s for the compared DMP-BBO optimizer.","Force predictions from $-\\partial_u W$ match measured external forces well enough that the planner can be validated sim-to-real across all three tasks.","HapticRRT generalizes to tasks where a purely kinematic constraint planner fails, because the potential encodes mass and contact, so the planner can infer a need for sustained pushing rather than only geometric feasibility."],"supporting_citations":[{"why":"Supplies the potential-based quasi-static model and the Hessian Schur complement that defines the haptic metric used for edge lengths.","marker":"[13]"},{"why":"Establishes the equilibrium-manifold view of quasi-static manipulation and the staircase branch for the pendulum task.","marker":"[14]"},{"why":"Earlier work that introduced the adaptive ODE and the book-insertion and DMP-BBO baselines that HapticRRT extends and compares against.","marker":"[12]"},{"why":"The classical RRT sample-nearest-extend loop whose structure HapticRRT adapts to the equilibrium manifold.","marker":"[2]"},{"why":"Provides the AtlasRRT constrained-planning baseline used as the comparison for kinematic-only planners.","marker":"[6]"},{"why":"The implicit function theorem whose application guarantees that $M_{\\mathrm{eq}}$ is a smooth embedded submanifold.","marker":"[25]"}],"fun_headline_variants":["HapticRRT: force-aware tree search for contact-rich skills","Tree search on equilibrium manifold replaces hand-coded contact phases","Force-aware RRT discovers contact strategies without phase scripts","Planning contact skills as tree search on a force-balance manifold","RRT on equilibrium manifold yields multiple contact strategies"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that one hand-written smooth energy function for the task, together with the quasi-static assumption, faithfully captures all physics that matter, so every useful contact behavior appears as a branch of the equilibrium manifold and the adaptive ODE can follow that branch reliably; if the potential omits friction, jamming, or an unmodeled collision, the planned policy can fail.","fun_headline_variants_meta":{"raw":{"variants":["HapticRRT: force-aware tree search for contact-rich skills","Tree search on equilibrium manifold replaces hand-coded contact phases","Force-aware RRT discovers contact strategies without phase scripts","Planning contact skills as tree search on a force-balance manifold","RRT on equilibrium manifold yields multiple contact strategies"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000655,"raw_usage":{"total_tokens":3043,"prompt_tokens":1032,"completion_tokens":2011,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":648,"completion_tokens_details":{"reasoning_tokens":1930}},"tokens_in":648,"tokens_out":2011,"duration_ms":14236,"temperature":1.0,"reasoning_tokens":1930,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:07:09.739191+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run HapticRRT on a task whose governing physics include a contact mode intentionally omitted from the potential, such as dry friction or jamming between the inserted object and the shelf; if the planner yields a policy whose simulated force profile diverges from measured forces, or if the ODE drifts off $M_{\\mathrm{eq}}$ near a singularity, the claim that a single smooth potential suffices is falsified.","supporting_citations":[{"cited_title":"A geometric framework for quasi-static manipulation of a network of elastically connected rigid bodies,","cited_arxiv_id":null,"evidence_quote":"Supplies the potential-based quasi-static model and the Hessian Schur complement that defines the haptic metric used for edge lengths."},{"cited_title":"Quasi-static mechanical manipulation as an optimal process,","cited_arxiv_id":null,"evidence_quote":"Establishes the equilibrium-manifold view of quasi-static manipulation and the staircase branch for the pendulum task."},{"cited_title":"Planning for quasi- static manipulation tasks via an intrinsic haptic metric: A book insertion case study,","cited_arxiv_id":null,"evidence_quote":"Earlier work that introduced the adaptive ODE and the book-insertion and DMP-BBO baselines that HapticRRT extends and compares against."},{"cited_title":"Exploring implicit spaces for constrained sampling-based planning,","cited_arxiv_id":null,"evidence_quote":"Provides the AtlasRRT constrained-planning baseline used as the comparison for kinematic-only planners."},{"cited_title":"Spivak, Calculus on manifolds: a modern approach to classical theorems of advanced calculus","cited_arxiv_id":null,"evidence_quote":"The implicit function theorem whose application guarantees that $M_{\\mathrm{eq}}$ is a smooth embedded submanifold."}],"review_version":1}