cs.LGOct 26, 2026
SaveHigh-resolution tactile observation makes hidden racket-control mechanisms learnable
Organizations: Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China · School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China
Abstract
Experts can master fine hand-object manipulation skills, yet limited conscious perception of rapid tactile interactions hinders their ability to articulate the underlying control mechanisms. Badminton racket control requires rapid, fine hand-force coordination, providing a demanding testbed for uncovering these mechanisms. An 864-node tactile-inertial glove with synchronized 100-Hz acquisition recorded over 14,000 strokes from more than 70 participants across five skills. Inspired by sensorimotor control, our mechanics-grounded two-layer framework inferred object-driving and grip-stabilizing control from tactile history, while resolving their spatiotemporal force realization. We found that higher proficiency was associated with selective rather than extensive control: greater skill specificity, anticipatory regulation, focal distal modulation and lower geometric torque cancellation, while spatiotemporal coordination showed a non-monotonic acquire-refine pattern. We translated these mechanisms into personalized guidance targeting force control and force-motion coordination. In a randomized cohort, mechanism-guided learners gained 0.72 expert-rated skill levels versus 0.05 with level-only feedback, making control mechanisms actionable.
Figures & tables
Fig. 1: From high-resolution contact evidence to interpretable control knowledge and learning. a, Distributed contact interactions during rapid action are difficult to consciously resolve. b, An 864-node glove records full-hand contact at a synchronized tactile–inertial rate of 100 Hz. c, Hand–racket reconstruction provides a common mechanical basis for the two layers. The control-organization layer (left) describes drive–grip regulation, while the spatiotemporal-realization layer (right) resolves local force modulation and regional coordination and assesses their mechanical effects. d, The control-organization layer reveals greater skill specificity, earlier preparation and shorter model-estimated perception-to-control intervals with expertise. The spatiotemporal-realization layer reveals focal distal modulation, lower geometric torque cancellation and acquire–refine coordination. e, Interactive learning with mechanism-guided feedback (left) and expert-rated skill gains after 10 min of practice under mechanism-guided or level-only feedback (right; per group). Dots show participant gains averaged across three raters and five skills. Full comparison and learning trajectories are shown in Fig. 5 .
Fig. 2: High-density tactile glove and sensor characterization. a, Dorsal electronics (left) and palmar view of the 864-node tactile array (right), with synchronized tactile–inertial acquisition at 100 Hz. b, Normal-force calibration (left) and the optical sensing principle in uncompressed and compressed states (right). c, Automated 0–3 N loading–unloading characterization. Pale curves show 1,968 cycles with complete synchronized records; dark curves show across-cycle summaries. Loading and unloading fits use available measured points within 0–3 N. At right, force-adjusted, detrended residuals span 2,000 mechanical cycles; the dark line and shaded band show the rolling median and 5th–95th percentiles. Confidence intervals for the force-conditioned coefficient of variation (CV) use a segmented moving-block bootstrap. d, Loading slopes at ten sampled sites, normalized to the ten-site mean (left), and within-site CVs of the 3-N response (right). Rows are paired and sorted by slope; dashed lines mark 100% and the median within-site CV. Each site contributed 29–30 quality-controlled presses, with 27–30 valid 3-N response bins. NRMSE, normalized root-mean-square error. Calibration, normalization and detrending procedures are detailed in Supplementary Methods S1.
Fig. 3: Task-specific functional organization and regional contact structure. a, Within-participant angular range of drive–grip recruitment, defined as the maximum minus minimum angle across recorded skills. Pale points show individuals; connected large circles show group means (Low, ; Advanced, ; Expert, ). Mean ranges are 42.6, 46.1 and 56.0 degrees, respectively. The one-sided ordered permutation trend test uses these participant-level ranges ( ). b, Pairwise distances between skill-specific spatial force bases, with level medians. c, Skill identity explains 3.25%, 15.32% and 17.89% of regional recruitment-timing variance. Pale points show leave-one-participant jackknife estimates; solid points show full-data (participants with at least two recorded skills). d, Impact-aligned drive and grip-gate proxies. Thin lines summarize skills; pale points are participant–skill observations; thick lines and bands show pooled medians and 95% confidence intervals. Trend tests use skill-adjusted ordered-level regression with participant-clustered errors; displayed values are adjusted across the three d outcomes (raw values in Supplementary Methods S4). e, Selected consensus partitions contain 16 Low and 23 pooled High co-activation regions. Matching shades identify corresponding regional families. f, Expected lag and normalized entropy of the learned temporal weighting profile. Points show participants; group summaries are means SEM (Low, ; Advanced, ; Expert, ). Different letters denote unadjusted two-sided Mann–Whitney ; denotes the Spearman ordered-group trend. Expected lag summarizes the model-estimated perception-to-control interval within the study cohort. Metric definitions are given in Methods and Supplementary Methods S4.
Fig. 4: Focal residual contact and acquire–refine spatiotemporal coordination. a, Positive residual maps relative to the low-proficiency spatial basis. b, Residual magnitude, spatial coverage, geometric cancellation per unit residual ( ) and cumulative geometric torque cancellation ( ). Here, is cumulative retained residual magnitude; accumulates the difference between summed local torque magnitudes and the resultant magnitude (Supplementary Methods S5). Coverage counts nodes reaching the 10% threshold in any frame of the 100-frame skill-by-group mean field. Large points and lines show means of five skill-specific estimates per group; error bars show 95% intervals across skills. Smaller points show skill estimates. Faint participant–skill points in the magnitude panel are ratio-centred to the corresponding skill estimate. Annotations give descriptive counts of decreasing adjacent-level skill contrasts. c, TE-derived regional ordering evaluated with equal-magnitude unit-torque proxies from two-dimensional regional centres, using pooled-Low, Advanced and Expert maps with 16, 20 and 17 regions ( , 11 and 8 participants, respectively). Points and bars show means and bootstrap 95% confidence intervals. Pooled High–Low comparisons use Welch tests; denotes Benjamini–Hochberg-adjusted , and denotes Hedges’ effect size. d, Inferred regional sequence duration and co-activation region count across ten algorithm initializations. Small points and thin lines show paired initialization results, with horizontal offsets for visibility; black points and thick lines show their means. Duration is the mean over 1,000 participant-bootstrap reconstructions at the original group sizes, then averaged equally across five skills within each initialization. Annotations count initializations with a strict Advanced peak. Initialization variability describes algorithmic repeatability. Skill-specific results and fixed-count spatial controls are reported in Supplementary Note 8.
Fig. 5: Mechanism-based guidance, level-only feedback and cumulative skill-level gains. a, Real-world training setup combining tactile–inertial measurement with interactive feedback. b, Reconstructed interface linking a skill-level summary to contact guidance and personalized motion suggestions. Displayed percentages are representative learner-facing outputs. Spatial and timing differences from a task-matched Expert-group reference were ranked separately. The three largest discrepancies of each type identified locations for force adjustment and regions for earlier/later recruitment (Supplementary Methods S6). c,d, Before/after exemplars contrast a proximal-dominant pattern with distal modulation across the stroke. Pale-grey arrows indicate earlier-to-later frame order; the lower row shows corresponding racket motion. All six tactile maps use the same intensity normalization. e, Participant-level changes in skill level after the first session. Skill level denotes the expert-rated 1–4 proficiency level assigned from observed task performance. Grey points and dark circles show mechanism-group expert-rated changes and means ( ). Teal points and the diamond show expert-rated skill-level changes and the mean in the separate level-only group ( ). Each group comprised four beginners, four intermediate players and four advanced players. Practice duration and raters were matched. Intervals are participant-bootstrap 95% confidence intervals. Other outcome dimensions refer to the mechanism-feedback group. Force-release control is a stroke-specific composite: the four net-spinning skills use the formal hand-action/spin item and the rear-court transition uses release speed. Whole-body coordination is omitted from this panel. f, Trajectories of six mechanism-group participants (two per proficiency level) across three sessions separated by 1-day intervals, expressed as changes in expert-rated skill level from each participant’s S1-pre value. Thin grey lines show individual trajectories; the dark line shows their mean. Dashed lines separate sessions. S2-pre and S3-pre describe maintenance between assessments, while S3-post is the cumulative endpoint. Confidence intervals are not drawn in f.
Appendix figures & tables37 assets
Supplementary material from the paper’s appendix.
Appendix
Supplementary Fig. 1: Tactile–inertial glove hardware. a, Worn prototype. b, Dorsal acquisition board. c, Layered sensing unit with structured elastic contact layer. d, Six-axis inertial measurement unit. e, Sensing-circuit principle. f, Eight arrays of three types: four Type I arrays for the non-thumb fingers (96 nodes each), one Type II thumb array (96 nodes), and three Type III palm arrays (128 nodes each).
| System | Number of sensing nodes | Acquisition rate (Hz) |
|---|---|---|
| Fabric-based tactile dataglove 5 | 54 | 1000 |
| Prior badminton glove 1 | 48 | 50 |
| Tekscan TactileGlove 2 | 18 | 500 |
| Scalable tactile glove (STAG) 3 | 548 | 7.3 |
| Capacitive pressure-array tactile glove 6 | 137 | Not explicitly reported |
| Stretchable tactile glove for forceful interaction 4 | 1,152 | 13 |
Supplementary Table 1: Representative tactile-glove and finger-worn sensing capacity. Node counts and system-level acquisition rates are listed as reported by the corresponding studies or product pages. “Not explicitly reported” means that the source did not provide a system-level tactile acquisition rate. Element response time was not converted into acquisition frequency.
Supplementary Fig. 2: Spatiotemporal comparison of representative tactile-glove systems. Node count and nominal acquisition rate are shown on logarithmic axes. Prior systems are grey and this work is dark coral; dashed curves indicate constant sensing-node frames per second. The 137-node capacitive array is omitted because its reported 90-ms element response time does not establish a system-level acquisition rate. Supplementary Table 1 includes systems without a verified acquisition rate.
Supplementary Fig. 3: Normal-force calibration apparatus. A motor-driven stage loads the tactile specimen while a reference force sensor measures applied force. Synchronized loading and unloading records provide the calibration pairs.
| Measure | Complete input | Regional omission |
|---|---|---|
| Participants | 40 | 40 |
| Valid contact frames | 120 | 118 |
| Weighted median distance / | 0.652 | 1.100 |
| Weighted mean distance / | 0.837 (0.750–0.931) | 1.274 (1.059–1.519) |
| Weighted 90th-percentile distance / | 1.695 | 2.772 |
| Participants with mean distance below | 32/40 | 16/40 |
Supplementary Table 2: Contact geometry in the temporal-refinement benchmark. All distances are normalized by the fixed handle inradius . Complete-input contact distances cover all active nodes; regional-omission distances cover active nodes in the omitted regions. Tactile-response weights were normalized within each valid frame; frames were weighted equally within participants, and participants equally. Medians and 90th percentiles use this same weighted distribution. Parentheses in the mean-distance row give 95% participant-bootstrap confidence intervals for the mean. Two regional-omission frames had no above-threshold omitted-region response and supplied no contact-distance value. Penetration summaries include all 864 nodes in all 120 evaluated frames in each condition.
Supplementary Fig. 4: From tactile history to hand–racket contact mechanics. Left, full-hand tactile input. Middle, pose estimation with a graph neural network and long short-term memory model (GNN + LSTM). Right, contact geometry after physical refinement. Grey straight arrows represent grip stabilization ( ); red curved arrows represent racket-driving torque ( ). These model variables describe the mechanical roles of contact. The example matches Supplementary Video 1.
Supplementary Fig. 5: Drive–grip responses during movement and posture holding. a,b, Empirical cumulative distributions of sequence-mean drive norm and drive-to-total norm ratio. c,d, Signed Pearson correlation and maximum absolute lagged correlation between drive and grip norms within dynamic validation sequences. Dashed lines mark distribution means. Each observation is a sequence; sequences from the same participant are repeated observations.
| Fixed rank | Low | Advanced | Expert | Strictly increasing initializations |
|---|---|---|---|---|
| 4 | 0.4885 | 0.7318 | 0.7121 | 0/3 |
| 5 | 0.5454 | 0.6397 | 0.6922 | 3/3 |
| 6 | 0.5576 | 0.6686 | 0.6706 | 3/3 |
| 7 | 0.5352 | 0.6569 | 0.6497 | 1/3 |
| 8 | 0.5551 | 0.6604 | 0.6835 | 3/3 |
| 9 | 0.5574 | 0.6713 | 0.6669 | 0/3 |
Supplementary Table 3: Fixed-rank sensitivity of spatial force-basis distances. Distances are medians over the ten skill pairs for the primary initialization. The final column counts initializations with the strict ordering Low Advanced Expert, out of three.
Supplementary Fig. 6: Regional granularity under common search rules. Left and centre, held-out scores over the same resolution grid at a common normal-to-tactile weight of 0.6. Open circles mark the selected resolution. Right, final Low and High ROI counts for every archived consensus seed. Search scores and final consensus counts describe different stages of the partitioning procedure.
| Seed | Regions | BH transition | BH in | BH out | FH in | FH out |
|---|---|---|---|---|---|---|
| 63 | 16/19/17 | 60.77/76.46/72.09 | 66.38/76.67/67.51 | 64.83/78.39/64.93 | 63.78/75.72/64.13 | 67.17/75.91/73.01 |
| 64 | 16/18/17 | 61.41/72.65/72.18 | 66.57/73.50/67.09 | 64.91/76.10/64.61 | 64.54/73.35/64.48 | 67.25/74.28/72.86 |
| 65 | 16/19/17 | 64.41/76.40/72.18 | 66.97/77.23/67.09 | 67.45/78.66/64.61 | 65.56/75.63/64.48 | 66.43/76.40/72.86 |
| 66 | 16/19/17 | 61.33/76.13/72.03 | 64.98/77.40/64.79 | 66.28/77.91/63.47 | 64.27/75.85/63.37 | 67.08/76.18/75.46 |
| 67 | 16/17/17 | 61.14/71.45/69.71 | 66.46/70.17/67.28 | 64.33/70.38/64.97 | 63.67/67.96/63.41 | 67.43/68.92/73.16 |
| 68 | 16/19/17 | 60.57/76.40/68.91 | 66.41/77.23/66.30 | 64.89/78.66/64.77 | 63.35/75.63/63.68 | 67.24/76.40/73.97 |
Supplementary Table 4: Regional counts and skill-specific sequence durations across ten initializations. Entries list Low/Advanced/Expert. Region counts refer to each learned partition; durations (ms) are means of 1,000 participant-bootstrap reconstructions at the original group sizes. BH and FH denote backhand and forehand; in and out denote inward and outward spinning. The BH transition is the rear-court transition. Main Fig. 4d averages the five duration estimates within each initialization.
| Spatial representation | Bootstrap-mean peaks / 5 | Mean peak margin (ms) |
|---|---|---|
| Adaptive, proficiency-specific (16/20/17) | 5 | |
| Fixed-count, level-specific ( – ) | 2–4 | |
| Fixed-count, pooled ( – ) | 2–4 | |
| Anatomical (15 regions) | 4 | |
| Shared, Low-derived (16 regions) | 3 | |
| Shared, Advanced-derived (20 regions) | 5 |
Supplementary Table 5: Matched spatial-representation comparisons and fixed-count sensitivity. The upper section compares all representations under the same 1,000 whole-participant bootstrap samples. Bootstrap-mean peaks count skills with Advanced strictly above both Low and Expert; ties do not count. Mean peak margin is Advanced minus the larger of Low and Expert, calculated from bootstrap-mean durations within each skill and averaged across all five skills. For fixed-count summaries, peak counts are ranges across and margins average equally over these 11 counts. In the lower section, each paired cell reports level-specific pooled maps at the same fixed region count, with boundaries learned separately by level or jointly across levels. Boot denotes the mean over bootstrap graphs. The last two columns report participant-level High minus Low differences, where High pools Advanced and Expert. Chain advantage is standardized against shuffled orders; alignment is a mean cosine. Counts summarize descriptive peak recovery.
| Endpoint | Effect | 95% CI | ||
| Fixed-count, pooled maps: all 11 counts | ||||
| Sequence duration (ms) | 0.652 | 1.000 | ||
| Chain advantage ( ) | 0.857 | 1.000 | ||
| Step alignment | 0.223 | 0.892 | ||
| Fixed anatomical map, 15 regions | ||||
| Sequence duration (ms) | 0.822 | 0.880 | ||
Supplementary Table 6: Effect sizes and uncertainty under alternative regional representations. For duration, the effect is Advanced minus the larger of Low and Expert, calculated within skill before averaging across the five skills. For the geometric endpoints, the effect is High minus Low after averaging available skills within participant. Fixed-count pooled-map effects and level-specific-minus-pooled differences additionally average over ; the anatomical map has . Intervals are 95% participant-bootstrap percentile intervals conditional on fixed maps. Permutation tests are one-sided for duration and two-sided for geometric effects; Holm-adjusted values retain the original four-endpoint family within each map analysis. Paired level-specific-minus-pooled contrasts use bootstrap intervals. For duration, these inferential comparisons use complete-sample graph estimates; bootstrap-mean duration sensitivity is summarized in Supplementary Table 5 .
Supplementary Fig. 7: Whole-hand contact redistribution relative to impact. Left, average timing of contact redistribution. Right, fraction of redistribution occurring before impact. Grey lines show skills; coloured points and bars show participant-weighted means and bootstrap 95% intervals (31 Low, 11 Advanced and 8 Expert).
| Condition / dimension / seed | Epoch | Expert–Low lag (ms), 95% CI |
|---|---|---|
| matched100_d8_s41 | 31 | -0.95 [-1.69, -0.37] |
| matched100_d8_s42 | 32 | -0.76 [-1.33, -0.28] |
| matched100_d8_s43 | 32 | -1.00 [-1.81, -0.35] |
| native_d16_s41 | 32 | -0.75 [-1.38, -0.27] |
| native_d16_s42 | 32 | -0.96 [-1.74, -0.38] |
| native_d16_s43 | 32 | -1.13 [-1.89, -0.51] |
Supplementary Table 7: Capacity and sampling sensitivity. Each row is a separately trained projection/control model followed by attention fitting. Native conditions use lags 3–8 at 100 Hz; matched sampling conditions use 40, 60 and 80 ms. Epoch denotes the selected attention epoch. All rows use the same 50 dynamic participants for lag summaries.
| Metric | Anatomical 15 | Learned 15 | Adaptive | Change [95% CI] | |
| Original split: 24 fitting participants, 26 evaluation participants; adaptive | |||||
| Waveform error | 0.24069 | 0.23563 | 0.23025 | [-0.01156, -0.00930] | |
| Timing dispersion (ms) | 118.56 | 110.11 | 108.52 | [-11.01, -9.14] | |
| Force coherence (%) | 70.53 | 87.54 | 89.63 | [+15.78, +22.62] | |
| Reversed split: 26 fitting participants, 24 evaluation participants; adaptive | |||||
| Waveform error | 0.23904 | 0.23090 | 0.22702 | [-0.01438, -0.00982] | |
Supplementary Table 8: Anatomical, count-matched learned and adaptive learned representations. Entries are participant means after averaging available skills within each participant. The change and its 95% participant-bootstrap interval compare adaptive with anatomical regions. Coherence and its change are expressed in percent and percentage points, respectively. Lower error and dispersion, and higher coherence, indicate greater within-region fidelity or consistency. Two-sided sign-flip tests use the joint Holm correction specified in Supplementary Methods S11.
Supplementary Fig. 8: Regional force representation with anatomical and learned partitions. a, Whole-hand normalized waveform reconstruction error. b, Within-region dispersion of palm-node force-activity time centroids. c, Within-region coherence of reconstructed palm contact-force directions. Anatomical and count-matched learned maps contain 15 regions; native adaptive maps contain 18 in this split. Pale lines connect the same held-out participants across maps; dark lines and coloured points show means ( ). Maps were fitted on the other 24 participants. All pairwise comparisons passed the joint Holm-adjusted tests ( ). Reversed-split results and paired intervals are reported in Supplementary Table 8 .
Supplementary Fig. 9: Local palm dynamics obscured by whole-palm averaging. a, Anatomical and data-derived 15-region maps. Colours identify regions within each map. The anatomical map treats the palm as one region. b, Two adjacent palm subregions selected separately for each proficiency group using training trials of backhand inward spinning. Selection maximized the training waveform contrast among adjacent pairs containing at least 16 palm nodes each. c, Corresponding held-out waveforms and the whole-palm mean (Low, ; Advanced, ; Expert, ). Each curve was normalized to its own peak within participant before averaging. Blue and orange curves correspond to the subregions in b; grey shows the separately normalized whole-palm mean. Lines and shading show participant means and SEM; zero marks impact. Comparisons concern waveform shape within each group: selected locations differ across groups, and amplitudes do not represent absolute force.
Supplementary Fig. 10: Spatial retention of contact structure. Held-out co-activation modularity, boundary recall and fine-scale ROI preservation across node counts. Thin lines show the five subsampling repeats; points and bars show their means and standard deviations after averaging the 189 parameter settings within each repeat (Supplementary Table 9 ).
| Nodes | Modularity | Boundary recall | Fine-scale preservation |
|---|---|---|---|
| 27 | 0.438 0.028 | 0.016 0.004 | 0.027 0.027 |
| 54 | 0.602 0.014 | 0.053 0.003 | 0.096 0.047 |
| 108 | 0.663 0.018 | 0.123 0.010 | 0.348 0.026 |
| 216 | 0.706 0.006 | 0.266 0.025 | 0.568 0.056 |
| 432 | 0.723 0.004 | 0.574 0.028 | 0.945 0.007 |
| 864 | 0.749 0.002 | 1.000 0.000 | 1.000 0.000 |
Supplementary Table 9: Spatial retention summarized across five subsampling repeats. Entries are mean standard deviation of repeat-level means, each averaged over 189 parameter cells. These standard deviations describe subsampling-repeat variation.
Supplementary Fig. 11: Recovered decreasing contrasts across six spatial resolutions. Blue curves refit sparse tactile inputs under the original spatial and temporal smoothing pipeline; bands span three initialization seeds. Orange dashed curves subsample residual fields already inferred using all 864 nodes, without refitting. All curves use the ten planned contrasts as the denominator; annotations identify reductions in measurable contrasts. Straight segments connect evaluated resolutions.
| Metric | 864 | 432 | 216 | 108 | 54 | 27 |
|---|---|---|---|---|---|---|
| Sparse-input refit, with spatial smoothing | ||||||
| Residual magnitude | 10/10 | 10/10 | 8/10 | 8/10 | 5/10 | 4/10 |
| Residual spatial coverage | 8/10 | 7/10 | 8/10 | 7/10 | 5/10 | 4/10 |
| Geometric cancellation per unit residual | 8/10 | 8/10 | 7/10 (8) | 1/10 (4) | 1/10 (3) | 0/10 (1) |
| Cumulative geometric torque cancellation | 9/10 | 9/10 | 8/10 | 8/10 | 5/10 | 4/10 |
| Sparse-input refit, without spatial smoothing | ||||||
Supplementary Table 10: Recovered decreasing contrasts in residual metrics. Entries count decreasing adjacent-level contrasts among five skills (ten planned contrasts). Sparse-input refits average three seeds before taking differences; the third condition subsamples a field inferred at full resolution. Main Fig. 4b uses that full-resolution baseline, whereas each refit condition uses its own re-estimated 864-node baseline. Parentheses give the number of measurable contrasts when below ten. At 54 nodes under the original pipeline, all five Expert fields have zero residual magnitude, spatial coverage and cumulative cancellation; cancellation per unit residual is undefined (N/A). For this ratio, three of the ten planned adjacent contrasts remain measurable and one decreases, reported as 1/10 (3).
Supplementary Fig. 12: Signed residual reductions across spatial resolutions. Each skill’s two adjacent reductions are normalized by its Low estimate at 864 nodes, then averaged across contrasts and skills. Positive values favour the original decreasing direction. Lines are shown only where all five skill triplets are measurable; N/A denotes an unavailable five-skill summary. Measurable individual contrasts remain included in Supplementary Fig. 11 and Supplementary Table 10 . Colours and line styles match Supplementary Fig. 11 ; native baselines are specific to each refitting/postprocessing condition.
Supplementary Fig. 13: Sampling-rate effects on regional coordination. Top, participant-average High-minus-Low geometric ordering contrasts with percentile 95% participant-bootstrap intervals. Bottom, Advanced minus the larger Low or Expert value for sequence duration. Thin lines show skills and thick lines their mean. All tested rates are shown, including 90–60 Hz. Maps, candidate links and participants are fixed within comparisons; sampling changes the delay grid and effective sample count.
| Rate (Hz) | Duration margin (ms) | Skills with Advanced peak |
|---|---|---|
| 100 | 6.68 | 5/5 |
| 90 | 8.65 | 5/5 |
| 80 | 8.25 | 5/5 |
| 70 | 11.32 | 5/5 |
| 60 | 14.24 | 5/5 |
| 50 | 14.70 | 4/5 |
Supplementary Table 11: Descriptive temporal peak contrasts across sampling rates. Sequence duration uses the five-skill Advanced-minus-maximum-endpoint contrast. Counts give skills with an Advanced peak.
Supplementary Fig. 14: Retention and similarity of temporal relationships. Left, fraction of each group’s 100-Hz stable directed links retained at lower rates. Right, Jaccard similarity between the lower-rate and matched 100-Hz stable directed edge sets. Lines average five skill-specific values per group. Both measures describe agreement with the native graph.
| Rate (Hz) | Low | Advanced | Expert |
|---|---|---|---|
| 100 | 1.000 | 1.000 | 1.000 |
| 90 | 0.988 | 0.989 | 0.981 |
| 80 | 0.986 | 0.983 | 0.975 |
| 70 | 0.973 | 0.968 | 0.960 |
| 60 | 0.968 | 0.952 | 0.952 |
| 50 | 0.952 | 0.932 | 0.938 |
Supplementary Table 12: Retention of native stable directed links. Entries are mean fractions across five skills. The same participant membership is used at every rate; eligibility requires at least 120 effective observations at 20 Hz.
Supplementary Fig. 15: Scoring force–motion coordination and selecting motion guidance. a, Reward model and candidate IMU trajectories. b,c, Recorded and generated trajectories for two predetermined validation participant–skill combinations: backhand rear-court transition and backhand inward spinning. Recorded trajectories average strokes within each combination. IMU-derived displacement is in arbitrary units. Tactile input is held fixed while the model ranks eight candidate inertial sequences. Validation is reported in Supplementary Note 14.
Supplementary Fig. 16: Mechanism-feedback learning gains across five racket-control skills. a, First-session pre-to-post changes in 12 participants. b, Cumulative changes from session-1 pre to session-3 post in six participants. Circles show expert-rated mean gains; bars show 95% percentile intervals from 20,000 participant bootstrap samples. Each contrast retains the paired assessment states and averages the three raters before estimating participant-level uncertainty.
Supplementary Fig. 17: Variation in learning gains across participants and skills. a, First-session expert-rated changes in 12 learners across five skills. b, Cumulative changes in the six-person three-session subset. Each cell is a paired endpoint difference averaged across three experts. Both panels use the same colour scale and participant identifiers. ZS, forehand inward spinning; ZZ, forehand outward spinning; FS, backhand inward spinning; FZ, backhand outward spinning; FH, backhand rear-court transition.
Supplementary Fig. 18: Expert-rating reliability and sensitivity to rater inclusion. a, Rating distributions for three experts over 240 unique video–skill targets. b, Mean skill level by skill. c, Pairwise quadratic-weighted . d, Participant-average first-session gain, within-session gain, between-session change and cumulative gain using all three experts or leaving one out. Error bars are participant-bootstrap 95% intervals from 20,000 resamples; the first-session contrast uses 12 participants and the three-session contrasts six. Rater abbreviations identify the same raters across panels.
| Feedback condition or contrast | Pre | Post | Change or difference [95% CI] |
|---|---|---|---|
| Mechanism guidance ( ) | 1.85 | 2.57 | 0.72 [0.44, 1.02] |
| Level-only feedback ( ) | 1.91 | 1.96 | 0.05 [ , 0.11] |
| Difference in gains | — | — | 0.67 [0.39, 0.98] |
| Baseline-adjusted group coefficient | — | — | 0.66 [0.29, 1.03] |
Supplementary Table 13: First-session skill-level comparison. Skill levels are on the 1–4 scale and are averaged across three experts and five skills for each participant. Brackets report 95% confidence intervals. Group gains and the difference in gains use participant percentile bootstraps; the baseline-adjusted coefficient uses an HC3-robust interval. Each group contains 12 different participants: four beginners, four intermediate players and four advanced players.
Supplementary Fig. 19: Expert-rated gains with mechanism guidance and level-only feedback. a, Participant-average pre/post ratings, with thin lines joining paired assessments and thick lines showing group means. b, Participant changes and group means with bootstrap 95% intervals. c, Mean changes per skill with bootstrap 95% intervals. Each condition contains 12 different participants; resampling retains each person’s skills and raters together. Grey denotes guidance and teal level-only feedback. Practice duration and experts were matched. Skill-specific intervals are descriptive and unadjusted for multiple comparisons.
| Skill | Mechanism guidance | Level-only feedback | Difference in gains |
|---|---|---|---|
| Forehand inward spinning | 0.81 [0.42, 1.22] | 0.08 [0.00, 0.17] | 0.72 [0.31, 1.14] |
| Forehand outward spinning | 0.69 [0.42, 1.00] | 0.06 [ , 0.19] | 0.64 [0.33, 0.97] |
| Backhand inward spinning | 0.67 [0.36, 1.00] | 0.11 [0.03, 0.19] | 0.56 [0.22, 0.92] |
| Backhand outward spinning | 0.78 [0.42, 1.19] | [ , 0.03] | 0.89 [0.50, 1.33] |
| Backhand rear-court transition | 0.64 [0.28, 0.97] | 0.11 [0.03, 0.19] | 0.53 [0.17, 0.89] |
Supplementary Table 14: Expert-rated changes by skill in the two feedback conditions. Values are mean post-minus-pre changes [95% participant-bootstrap intervals], after averaging the three experts. The last column is mechanism minus level-only mean change; bootstrap draws are independent across groups. There are 12 participants per group. Skill-specific comparisons are descriptive.
| Metric | Signal-to-scalar definition | Unit and displayed summary |
|---|---|---|
| Angular spread (Fig. 3a) | For participant and skill , . Spread is . Each phase angle is the direction of the normalized trajectory. | Degrees per participant with at least two skills; group mean. |
| Spatial force-basis distance (Fig. 3b) | Centre each spatial basis vector over sensors and normalize its length. Match vectors one-to-one to maximize cosine similarity ; distance is . | Dimensionless distance per skill pair within group; median of ten pairs. |
| Temporal force-transfer variance (Fig. 3c) | Let be the person-centred, regional-standardized recruitment-time vector. Compute . | Percentage per proficiency group; full-data . Dots are participant-delete-one estimates. |
| Drive-peak time (Fig. 3d, left) | For each stroke, compute ; take the median across strokes for each participant and skill. | Milliseconds relative to impact; pooled median of participant–skill values. |
| Stabilization allocation (Fig. 3d, middle) | Compute the largest prominence of separately in frames 1–50 and 51–100. Take stroke medians , then . | Dimensionless fraction per participant–skill; pooled median. |
| Post-impact peak prominence (Fig. 3d, right) | Largest prominence of in frames 51–100 for each stroke, then median across strokes within participant and skill. | Model units per participant–skill; pooled median. |
Supplementary Table 15: Definitions of main reported metrics. Computational details below specify preprocessing and boundary rules. Group labels describe discovery-cohort proficiency; observations are aggregated only at the stated unit.
| Setting | Epoch | Lag contrast (ms) |
|---|---|---|
| Balanced; recent | 54 | -2.16 [-4.86, +0.82] |
| Balanced; no penalty | 63 | -2.21 [-5.22, +1.10] |
| Balanced; penalty 0.1 | 54 | -1.86 [-3.83, +0.33] |
| Balanced; remote | 54 | -2.16 [-4.83, +0.79] |
| Balanced; uniform | 54 | -2.16 [-4.85, +0.81] |
| Window sampling; recent | 63 | -3.57 [-5.93, -0.97] |
Supplementary Table 16: Frozen-backbone attention refits. Contrasts are Expert minus Low in nominal milliseconds; brackets show 95% participant-bootstrap intervals. Epoch is selected by the validation objective, without using proficiency contrasts.
| Level | Task-performance descriptor | Observable interpretation |
|---|---|---|
| 1 | Incomplete execution | Critical stroke elements are absent or repeatedly break down; the intended task action is not reliably produced. |
| 2 | Developing execution | The intended stroke is recognizable, but frequent errors or inconsistency remain in movement and shuttle control. |
| 3 | Consistent execution | The required stroke elements are generally coordinated and produce the intended task outcome reliably. |
| 4 | Refined execution | Execution is consistently controlled and fluent, with precise adjustment of the stroke to the task demands. |
Supplementary Table 17: Observable interpretation of skill levels. The descriptors apply the shared four-level proficiency framework to execution of the recorded task. They draw on the progression from incomplete execution to reliable, controlled performance in badminton assessment 9 ; the study’s five-task rating is not a direct administration of that publication’s full game-play rubric.
| ID | Proficiency | Playing experience (years) | Professional training (years) | Highest reported achievement / competitive background |
|---|---|---|---|---|
| P01 | Beginner | 0 | 0 | None reported |
| P02 | Beginner | 0 | 0 | None reported |
| P03 | Beginner | Not reported | 0 | None reported |
| P04 | Beginner | 0 | 0 | None reported |
| P05 | Beginner | 0 | 0 | None reported |
| P06 | Beginner | 0 | 0 | None reported |
Supplementary Table 18: Anonymized characteristics of the 50-participant dynamic-recording cohort.
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