{"id":"57122309-5312-41dd-a503-66ea760da98c","arxiv_id":"2504.12854","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A trunk-rotation-aware spring template model plus quaternion-based planning and control lets a compliant quadruped jump farther and handle rougher terrain than the same robot without springs.","lead":"This paper introduces a spring-loaded pendulum model that adds trunk rotation to a leg template for quadrupeds with parallel elastic springs, together with a planning and control pipeline. On a Go1 robot with and without springs, the compliant version jumps up to 25% farther and tolerates twice the ground height variation.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Headline quantitative gains rest on single hardware trials, and the 50 cm froggy result uses an asymmetric spring configuration (RR calf spring removed, Remark 4); without repeated trials and a non-confounded comparison, the claimed 25–100% benefits are not yet established.","rationale":"The reader's conditional verdict is reasonable and I would keep it. The paper presents a coherent model, a clear planning and control pipeline, simulation support, open-source hardware designs, and hardware demonstrations with shared control gains, so there is no internal inconsistency that would justify rejection. However, the central claim's quantitative support is fragile exactly where the abstract states specific percentages. The most load-bearing concern is not the ignored centroidal angular momentum, which the authors acknowledge and which primarily explains tracking degradation rather than undermining the compliance comparison; it is that the headline gains come from single-trial maxima and that the strongest froggy-jumping result is obtained with an asymmetric spring configuration that is not the modeled symmetric one. These issues directly affect whether 'parallel elasticity improves explosive motion by at least 25%' and 'allowable height variation increases by 100%' are credible quantitative statements. The proposed repeated-trials protocol, including the RR-spring-removed control condition, would settle whether the concern lands: if the symmetric compliant robot cannot reproduce the gains, or if the asymmetric configuration performs no better than rigid, the quantitative claims should be softened, while the qualitative demonstration of versatile explosive motion on a compliant quadruped would remain.","tokens_in":28779,"tokens_out":6423,"duration_ms":77164,"concrete_test":"Run at least five trials per condition on E-Go-V2 for (a) rigid, (b) symmetric springs, and (c) RR-spring-removed, for 50 cm froggy jumping plus the 40/50 cm pronking and 125/145° hop-turn comparisons, measuring landing distance and yaw angle with the same marker protocol and reporting median and range. If condition (b) cannot achieve 50 cm, or if the performance of (c) overlaps with (a), the froggy-specific claim is confounded; if median gains for symmetric conditions do not exceed rigid by the claimed margins, the quantitative headline should be downgraded to a qualitative demonstration.","verdict_should_be":"UNCHANGED","load_bearing_attack":"To support the central claim, the spring-engaged configuration must be the cause of the reported gains, and those gains must be reliable. Two linked weaknesses are load-bearing. First, Table 2 and the robustness results are single-trial maxima: 'maximal pronking distance', '145° vs 125°', and '10 cm vs 5 cm' carry no repetitions, ranges, or uncertainty, so the abstract's 'at least 25%, 15%, 25%, 100%' are not established as typical or reproducible effects. Second, the froggy-jumping gain, one of the three explosive-motion percentages, is confounded: for jumps longer than 40 cm the authors remove the RR calf spring (Remark 4), so the 50 cm compliant result is achieved by an asymmetric compliant robot, not by the symmetric TD-aSLIP configuration used in planning. Since the Discussion notes that unidirectional springs demand extra flight-phase torque, the RR-spring removal may improve the result by removing a disturbance rather than by demonstrating the modeled parallel compliance. The angular-momentum limitation is real and self-acknowledged, but it limits tracking (e.g., 70° vs 90° yaw) rather than directly invalidating the compliance comparison; the single-trial and asymmetric-spring issues strike at the headline numbers.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes TD-aSLIP, a reduced-order quadruped template model with two massless legs, a trunk rotation state, and explicitly modeled parallel compliance obtained by decoupling motor actuation from spring forces. A configuration-aware stiffness mapping is introduced, and a dual-layer trajectory optimization (SLIP-level coarse planning followed by quaternion-based kinodynamic refinement) is combined with a quaternion MPC and a whole-body controller with parallel-compliance compensation. The pipeline is evaluated in PyBullet simulation and on hardware: a rigid Unitree Go1 and a new compliant variant E-Go-V2 with thigh and calf springs. The central claims are that the model enables versatile explosive motions (pronking, hop-turn, froggy jumping), that parallel elasticity improves explosive performance (at least 25%, 15%, and 25% gains in maximum pronking distance, hop-turn yaw, and froggy-jump distance), and that it improves robustness, including a 100% increase in allowable support-surface height variation.","tokens_in":29009,"tokens_out":5310,"duration_ms":58759,"significance":"If the central claims hold, this is a useful contribution to model-based dynamic legged locomotion: it extends the authors' prior aSLIP line to include trunk rotation, uses a singularity-free quaternion formulation in both planning and control, provides a reproducible compliant quadruped platform with open-source CAD, and offers an external baseline (springs disengaged on the same robot) rather than only comparing against the authors' previous model. The simulation comparison against dual-aSLIP is a genuine incremental validation, and the statement that all control tasks share the same gains is a strength. The main significance risk is that the headline experimental gains rest on very thin evidence: single trials, no error bars, and a froggy-jump comparison performed with an asymmetric spring configuration.","major_comments":[{"comment":"The headline quantitative claims are not established as reproducible effects. Table 2 reports single maximum values for pronking distance (40 cm vs 50 cm), hop-turn yaw (125 vs 145 degrees), and froggy-jump distance (40 cm vs 50 cm), and the robustness section reports 5 cm vs 10 cm allowable height variation, all without repeated trials, ranges, medians, or success rates. As written, the abstract's 'at least 25%, 15%, 25%, 100%' statements are maxima from single trials and could reflect trial-to-trial variation or favorable conditions rather than a systematic benefit of parallel elasticity. Please provide repeated trials with spread or success counts for each extreme-motion comparison.","section":"Section VIII, Table 2 and the 'Robustness' subsection"},{"comment":"The froggy-jumping gain, one of the three explosive-motion percentages, is confounded. Remark 4 states that for jumps longer than 40 cm the RR calf spring is removed, so the 50 cm compliant result is achieved by an asymmetric compliant robot, not by the symmetric TD-aSLIP configuration used in planning. The Discussion also notes that unidirectional springs require extra flight-phase torque, so removing the RR spring may improve the result by removing a disturbance rather than by demonstrating the modeled parallel compliance. At minimum, the 25% froggy-jump gain in Table 2 should be separated from the symmetric-compliance claims, or the experiment should be repeated in a configuration that matches the planning model.","section":"Section VIII, Remark 4 (Enhanced froggy jumping)"},{"comment":"The configuration-aware stiffness is obtained as a cubic polynomial fitted to sampled data (Fig. 4), but no fit error, cross-validation, or comparison against the direct Jacobian-based stiffness is reported. Since this polynomial is the mechanism by which 'configuration-aware' compliance enters the planner, its accuracy is load-bearing for the claim of improved model accuracy. In addition, Eq. (9) defines the scalar spring constant as the Euclidean norm of the diagonal of the equivalent stiffness matrix; this does not obviously equal the leg-direction stiffness used in Eq. (4), so the mapping needs a derivation or numerical validation.","section":"Section IV-B2 (Configuration-aware stiffness mapping)"},{"comment":"The paper states in Contribution 1 that the model captures 'the varying angular momentum' and uses this as part of its novelty relative to prior SLIP models, but the TD-aSLIP dynamics assume massless legs and only model trunk inertia, so the centroidal angular momentum is not captured. The Discussion explicitly acknowledges that this limits tracking, e.g., the rigid robot lands at about 70 degrees in a 90-degree hop-turn. This does not invalidate the compliant-vs-rigid comparison, but the contribution statement overstates what the model captures; the claim should be reformulated to 'trunk angular momentum' or the model should be extended with leg inertia.","section":"Section I (Contribution 1) and Discussion ('Momentum-aware motion planning and control')"}],"minor_comments":[{"comment":"The last row of the matrix T(Q) appears to be [-qz, qx, qw] as printed; for consistency with Eq. (34) and the quaternion derivative it should be [-qy, qx, qw].","section":"Eq. (35)"},{"comment":"The caption refers to blue, green, and purple curves, but the figure appears in grayscale; please use distinguishable line styles or annotate the curves directly.","section":"Fig. 4"},{"comment":"The manual landmark-based distance measurement is described, but it is not stated whether measurements were taken by a single observer, whether images were processed automatically, or whether any inter-rater variability was considered; a brief statement would improve reproducibility.","section":"Section VIII (System setting)"},{"comment":"The use of Euclidean distance with the min over Q and -Q is an acknowledged approximation to the quaternion distance; this is acceptable, but please state explicitly in the text that this is a heuristic rather than the geodesic metric, since it affects the cost landscape.","section":"Eq. (24)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope for a robotics journal and the modeling/planning pipeline is a credible extension of the authors' prior aSLIP work. The main concern is experimental: the central 'parallel elasticity improves explosive performance' claim currently rests on single trials, and the froggy-jump comparison is confounded by asymmetry. These issues are fixable with additional experiments and rephrasing, so I recommend major revision rather than rejection. Please also ask the authors to be precise about what the TD-aSLIP model does and does not capture regarding angular momentum, as the current contribution statement overreaches."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the two things to know: this is a legitimate extension of the authors' earlier dual-aSLIP model rather than a brand-new paradigm, and the hardware results are real but the headline numbers are weaker than they look. I'd send it to peer review, but I'd push hard for repeated trials and a clean compliance comparison.\n\nThe new bits are TD-aSLIP with trunk rotation and a configuration-aware stiffness map, and the dual-layer quaternion TO. The model is sensible: they decouple parallel spring forces from actuation, map joint-space stiffness to a leg-length-dependent equivalent stiffness via a fitted cubic, and integrate that into planning. The quaternion TO avoids singularity for large rotations, and their simulation comparison against their own dual-aSLIP shows better landing error. The hardware platform, E-Go-V2, is open-sourced, which is a real plus. The experiments do show the compliant robot pronking further, hop-turning more, and jumping more robustly from uneven surfaces. The paper is also honest: it flags the centroidal angular momentum issue and Remark 4 mentions the RR spring removal.\n\nWhere it gets soft: Table 2 and the robustness section give single-trial maxima — 50 cm vs 40 cm pronk, 145° vs 125° hop-turn, 50 cm vs 40 cm froggy, 10 cm vs 5 cm terrain. No repetitions, no error bars, no sense of typical or worst-case performance. Since these are 'maximal' results, the abstract's 'at least 25%' language overstates the evidence. The froggy comparison is also confounded: the 50 cm jump is done with the RR calf spring removed, so the compliant configuration is asymmetric. That means the improvement over the rigid case could come from removing a spring that causes control trouble, not from the modeled parallel compliance. The cubic stiffness fit error isn't quantified, and the model ignores leg mass — which they concede and which shows up in the 70° vs 90° yaw tracking.\n\nNone of this sinks the paper. The modeling and control pipeline is a genuine contribution, and the open hardware and video make it checkable. But the evidence doesn't yet support the strength of the claims. The right fix is straightforward: repeat each condition several times, report distributions, and either do froggy with symmetric springs or explain why the asymmetric result is a fair test.\n\nWho this is for: groups working on elastic quadrupeds or SLIP-based planning. It deserves peer review with mandatory experimental revisions.","headline":"Solid modeling/control pipeline for compliant quadrupeds, but the headline performance numbers rest on single trials and a confounded froggy jump; still worth refereeing.","tokens_in":29579,"tokens_out":3312,"would_cite":true,"duration_ms":33450,"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":"Parallel springs let a quadruped jump 25% farther and turn 15% wider","keywords":["quadrupedal locomotion","parallel compliance","spring-loaded inverted pendulum","trajectory optimization","quaternion singularity-free control","whole-body control","explosive motion","robust locomotion"],"falsifier":"Run the same 90-degree hop-turn plan under motion capture that reconstructs whole-body angular momentum, then re-plan with a centroidal-dynamics model that includes leg inertia; if the yaw error stays around 20 degrees and the rigid-versus-compliant gap persists, the single-rigid-body assumption is not the limiting factor and the paper's explanation would need revision.","tokens_in":28547,"feed_emoji":"🤖","tokens_out":7186,"duration_ms":70869,"temperature":0.7,"pith_summary":"This paper claims that adding parallel springs to a quadruped's legs and explicitly modeling those springs in planning and control turns a rigid robot into one that can jump farther, rotate further, and tolerate rougher terrain. The authors introduce the trunk dual actuated spring-loaded inverted pendulum (TD-aSLIP), a reduced-order model with two massless spring legs and a rotating trunk, and pair it with a dual-layer trajectory optimizer and a whole-body controller. In hardware, the spring-equipped robot increased maximal pronking distance by at least 25%, hop-turn yaw angle by at least 15%, and froggy-jumping distance by at least 25% compared with the same robot without springs, and it survived a 10 cm terrain height variation where the rigid version managed 5 cm. The paper's claim is that these gains come not from the springs alone, but from the springs plus a planner and controller built around configuration-aware compliance.","feed_headline":"Parallel springs let a quadruped jump 25% farther and turn 15% wider","feed_subtitle":"A new template model plans pronking, froggy jumps, and hop-turns; the springs also double the terrain error the robot survives.","key_machinery":"The central object is the TD-aSLIP, or trunk dual actuated spring-loaded inverted pendulum: a reduced-order model with a single rigid trunk, two massless legs, and, on each leg, an actuation force and a parallel spring force acting in parallel. Its load-bearing move is a configuration-aware stiffness mapping that converts joint-space spring constants into an equivalent Cartesian leg stiffness through the leg Jacobian, then captures how that stiffness changes with leg length by sampling the robot's workspace and fitting a cubic polynomial. This makes the model's spring term match the actual hardware configuration rather than assuming a fixed constant. Around this model the paper builds a two-layer planner, first SLIP-based trajectory optimization and then quaternion kinodynamics optimization, and a controller made of a quaternion single-rigid-body MPC feeding a whole-body quadratic program that compensates spring torques and enforces safety constraints.","core_discovery":"The central claim is that explosive quadruped motion with large trunk rotation can be planned and tracked using a two-legged, one-trunk template model that separates spring forces from motor forces, and that this explicit separation is what unlocks the benefits of parallel compliance. Concretely, the paper claims that the TD-aSLIP model, where each of two massless legs couples an actuation force with a unidirectional spring force whose stiffness varies with configuration, generates pronking, froggy jumping, and hop-turns without a hand-tuned reference trajectory. A dual-layer trajectory optimizer first solves a coarse SLIP problem and then refines it with quaternion kinematics and dynamics, avoiding Gimbal-lock singularities during large rotations. A quaternion-based model-predictive controller and a whole-body controller with explicit spring compensation track the plan in hardware. Comparison between a rigid quadruped and the same robot with parallel thigh and calf springs shows that the compliant version reaches larger pronks, larger yaw turns, and longer froggy jumps, and tolerates twice the terrain height variation when jumping from unknown uneven surfaces.","pith_inferences":["I would expect the configuration-aware stiffness mapping to matter most in deeply crouched stances like froggy jumping, where the leg Jacobian changes substantially; rerunning the planner with a fixed stiffness constant should produce visibly worse landing tracking on those motions.","The four legs are symmetrically paired into two SLIP legs; I would expect an asymmetric front/rear version with different spring constants or rest lengths to handle the 50 cm froggy jump even better than the authors' workaround of removing the right-rear calf spring, because the rear legs carry much more load during the rear-leg stance phase.","Since the paper's stated limitation is the ignored centroidal angular momentum, I would expect that replacing the single-rigid-body MPC with a momentum-aware or centroidal-dynamics controller would reduce the yaw tracking error in hop-turns, potentially pushing the compliant robot beyond the reported 145-degree limit."],"forward_implications":["The same dual-layer planner, with only waypoints and contact sequence changed, should generate further flight-phase maneuvers such as sideways jumps or larger rotations without hand-tuned references; the paper demonstrates pronking, froggy jumping, and hop-turn from one formulation.","If parallel compliance is doing the work, the robustness gain should persist under modest spring mistuning or surface uncertainty, and the paper reports the allowable support-surface height variation doubles from 5 cm to 10 cm for froggy jumping.","The singularity-free quaternion formulation means the planned motions transfer across platforms without Gimbal-lock issues during large rotation, and the paper reports the same control gains work for both the rigid and spring-equipped versions.","The modeling principle of decoupling spring force from actuation force in a reduced-order template should extend to other explosive motions, such as consecutive jumps, because the dynamics equations do not depend on a particular contact schedule."],"supporting_citations":[{"why":"Proposed the actuated SLIP with decoupled parallel compliance and impact-aware landing control that TD-aSLIP generalizes to trunk rotation.","marker":"Ding et al. (2024a)"},{"why":"Introduced the dual-leg aSLIP and the original E-Go hardware and control that this paper's E-Go-V2 and TD-aSLIP extend.","marker":"Ding et al. (2024b)"},{"why":"Source of the time-varying quaternion MPC whose dynamics and linearization the SRB MPC in Section VI-A follows.","marker":"García et al. (2021)"},{"why":"Formulation that the whole-body controller with parallel-compliance compensation and safety constraints is explicitly inspired by.","marker":"Kim et al. (2019)"},{"why":"Prior singularity-free rotation-matrix MPC for explosive quadruped motion, cited as the representation approach this work continues via quaternions.","marker":"Ding et al. (2021)"},{"why":"Established the compliant-leg SLIP template that the aSLIP and TD-aSLIP family builds on.","marker":"Geyer et al. (2006)"}],"fun_headline_variants":["Parallel springs boost quadruped jump distance by 25% and turn angle by 15%","New template model enables 25% longer pronks and 2x terrain error tolerance","Compliant quadrupeds jump 25% farther, turn 15% wider, and handle rougher ground","Springs double terrain robustness and increase jump distance by a quarter","Explosive locomotion: springs add 25% jump distance and 100% terrain tolerance"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire pipeline treats the robot as a single rigid body with massless legs, so it assumes leg swing and body-shape changes do not carry significant angular momentum; the authors concede this is why the rigid robot undershoots a 90-degree hop-turn by about 20 degrees.","fun_headline_variants_meta":{"raw":{"variants":["Parallel springs boost quadruped jump distance by 25% and turn angle by 15%","New template model enables 25% longer pronks and 2x terrain error tolerance","Compliant quadrupeds jump 25% farther, turn 15% wider, and handle rougher ground","Springs double terrain robustness and increase jump distance by a quarter","Explosive locomotion: springs add 25% jump distance and 100% terrain tolerance"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000328,"raw_usage":{"total_tokens":1882,"prompt_tokens":1043,"completion_tokens":839,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":659,"completion_tokens_details":{"reasoning_tokens":724}},"tokens_in":659,"tokens_out":839,"duration_ms":8281,"temperature":1.0,"reasoning_tokens":724,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T12:20:27.268793+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same 90-degree hop-turn plan under motion capture that reconstructs whole-body angular momentum, then re-plan with a centroidal-dynamics model that includes leg inertia; if the yaw error stays around 20 degrees and the rigid-versus-compliant gap persists, the single-rigid-body assumption is not the limiting factor and the paper's explanation would need revision.","supporting_citations":[],"review_version":1}