Sports & Health Lab · Automat Labs

Performance,
quantified.

Four signals of the body — motion, sleep, temperature and biometrics — measured with sensors, pulled together by automated pipelines, and analysed with the same metrics used to score surgical skill. The goal: know what actually makes you faster and healthier, and how much of it is the athlete, the equipment or the conditions.

Motion analysis The sports

Motion Sleep Temperature Biometrics

01Motion analysis

Motion, scored like surgical skill.

In a study published with KU Leuven in Scientific Reports (Nature Portfolio), we tracked a fetal surgeon’s instruments in 6D and computed 39 motion metrics to test whether 3D vision improves skill. The same mathematics reads a badminton stroke, a running stride or a pedal stroke: how far, how fast, how smooth, how consistent.

Origin · fetal surgery

Method published in Scientific Reports (Nature Portfolio) with KU Leuven, 2023 — 3D vs. 2D simulated fetoscopy for spina bifida repair: a quantitative motion analysis. Ahmad, Weiler, Joyeux et al.

Read on nature.com → · doi:10.1038/s41598-023-47531-9

1.1

Three sports, three kinds of load.

Where the sensors go, what counts as one movement, and which metrics matter most.

01 · Segment · stroke

Badminton

Explosive, intermittent, and decided by technique. Measure the racket and the feet, not just the heart.

IMU in the racket handle and on the wrist. The non-racket arm plays the part of the study’s assistant hand: it stabilises, and its motion counts too.

Measure

Racket IMU — swing speed, stroke type & count
Insole pressure — footwork, split-step timing
Heart rate — rally load & recovery

Key metrics

S_max at contact · stroke time T
LDLJ & SPARC per stroke type
NSP — hesitation in the swing
SPARC on ω(t) — pronation

02 · Segment · stride

Running — trail & marathon

Long efforts where pacing, economy and heat decide the result. Trail adds climbing and technical ground.

IMU on the shoe or ankle and at the sacrum. One stride from foot strike to foot strike; a marathon is thousands of repetitions of the same segment.

Measure

HR / HRV · pace · cadence · ground contact
Running power · VAM on climbs (trail)
Pacing drift & fuelling (marathon)

Key metrics

σ_S stride to stride
LDLJ drift with fatigue
D along the vertical — oscillation
TOR on technical trail descents

03 · Segment · revolution

Cycling — gravel, MTB & road

Power is the headline number, but the terrain decides how much of it reaches the road.

IMU on the crank or pedal and at the knee. One crank revolution per segment, for gravel, MTB and road alike.

Measure

Power · cadence · HR · speed
Vibration & suspension travel (gravel, MTB)
Aero position & pacing (road)

Key metrics

σ_S of pedal speed — uniformity
NAP — dead spots
κ & TOR of the knee path
Bike sway out of the saddle

1.2

A movement is a curve in space.

Every sample is a point p(t). Its path, bounding volume and speed along the way are the raw material of every metric below.

Badminton · overhead clear

IMU at the racket head. One stroke from backswing to follow-through: the arc sets the path length, the speed peaks at contact.

colour: speed v(t), blue → ochre
box: extent Δx · Δy · Δz
shadow: floor projection
data: simulated, seeded, 200 Hz

Simulated signal — metrics are computed live

1.3

From raw sensor to clean segments.

The preprocessing pipeline of the study, unchanged. Only the reference frames and the segment boundaries change with the sport.

Format

Raw logs — EM-tracker files in the study, FIT/IMU logs here — into one table per sensor on one clock.

Transform

All sensors into one reference frame: the operating-table corner there; court, pelvis or bike frame here.

Prune

Gaps > 1 s removed, shorter gaps bridged with a quadratic spline, then report how much is real data:

v_{i} ≜ \frac{T_{motion, i}}{T_{i}}

Smooth

Butterworth low-pass, f_c = 10 Hz, n = 5, then an exponential filter:

y_{k} = α x_{k} + (1 - α) y_{k - 1}, α = 0.05

Annotate & debug

Segments marked from video: surgical steps there; strokes, strides, revolutions here. Interpolated stretches beyond physical limits (6 m/s² at a surgeon’s hand) are rejected; the limit is set per sensor.

Source: Scientific Reports (Nature Portfolio) 13:20951 (2023) — Methods · Motion data processing.

1.4

Position, then three derivatives.

Speed, acceleration and jerk are the first, second and third derivative of position. Smoothness metrics live in the third.

position · x y z

𝒑 (t) = {(x y z)}^{⊤}, p = \sqrt{x^{2} + y^{2} + z^{2}}

speed

𝒗 (t) = \frac{d 𝒑}{d t}, v = \sqrt{{\dot{x}}^{2} + {\dot{y}}^{2} + {\dot{z}}^{2}}

acceleration

𝒂 (t) = \frac{d^{2} 𝒑}{d t^{2}}, a = ‖ 𝒂 (t) ‖

jerk

𝒋 (t) = \frac{d^{3} 𝒑}{d t^{3}}, j = ‖ 𝒋 (t) ‖

1.5

Metric bench: smooth vs intermittent.

Slide from one fluent movement to one built from hesitant sub-movements with tremor. The speed peaks, the spectrum and the metrics respond as they did between 2D and 3D surgery.

smooth intermittent k = 0.40 Simulated

P2.45mvs smooth ±0 %

S_max11.57m/svs smooth −5 %

S̄5.39m/svs smooth +1 %

σ_S3.73m/svs smooth −15 %

NSP_α=12vs smooth +100 %

MAPR_α=1077%vs smooth +8 %

LDLJ7.68vs smooth +3 %

SPARC−1.53vs smooth −9 %

TOR1.000vs smooth ±0 %

NSP counts speed maxima above α·S̄ (α = 1). MAPR: share of time above 10 % of S_max. LDLJ as in the paper, ln|DLJ| — higher means jerkier. SPARC closer to 0 means smoother. Change shown vs the smooth (k = 0) movement.

1.6

The metric atlas.

Every definition used in the study (Scientific Reports (Nature Portfolio) 13:20951, Table 1), plus curvature, turning angle and tortuosity. Index i is a movement segment — a surgical step there, a stroke, stride or crank revolution here.

T · P · V · D · TOR

Time & space

How long, how far, how much room. → stroke arc · stride loop · pedal circle, and how much the envelope wanders.

Total time

T_{i} ≜ \int_{t_{i, start}}^{t_{i, end}} d t

Shorter in experts; the primary outcome of the study.

Path length

P_{i} ≜ \int_{0}^{T_{i}} v_{i} (t) d t

Distance travelled. Significant 3D vs 2D.

Volume

V_{i} = convhull (𝒑_{i} (t))

Convex hull of all positions: the space a movement claims.

Depth perception

D_{i} ≜ \int_{0}^{T_{i}} \sqrt{{(\frac{d z^{'}}{d t})}^{2}} d t

Path along the tool axis z′ — here the racket shaft or the tibia.

Tortuosity

{TOR}_{i} = 1 + a, a = - \frac{d \ln L (s)}{d \ln s}

Divider method: path length L vs divider step s. 1 = straight, 2 = maximally convoluted.

S · NSP · SPR · MAPR

Speed

How fast, how even, how often it surges. → racket speed at contact · ankle swing speed · crank uniformity (σ → 0 = even pedalling).

Max · mean · consistency

S_{i, \max} ≜ \max (v_{i}), {\bar{S}}_{i} ≜ mean (v_{i}), σ_{S_{i}} ≜ std (v_{i})

Peak, average and spread of the speed profile.

Number of speed peaks

{NSP}_{i, α} ≜ | {v_{i} (t) ∣ \frac{d v_{i}}{d t} = 0, \frac{d^{2} v_{i}}{d t^{2}} < 0, v_{i} > α {\bar{S}}_{i}} |

Each peak is a sub-movement or a correction. Significant 3D vs 2D.

Speed peak rate

{SPR}_{α, i} = \frac{{NSP}_{i, α}}{T_{i}}

Peaks per second, less dependent on duration.

Movement arrest period ratio

{MAPR}_{i, α} ≜ \frac{T_{i, v_{i} > (α / 100) S_{i, \max}}}{T_{i}}

Share of time actually moving vs pausing.

A · NAP · APR · IAV

Acceleration

Force in disguise: starts, stops, impacts. → lunges and split-steps · foot strike · dead spots at 12 and 6 o’clock.

Max · mean · consistency

A_{i, \max} ≜ \max (a_{i}), {\bar{A}}_{i} ≜ mean (a_{i}), σ_{A_{i}} ≜ std (a_{i})

Peak, average and spread of acceleration.

Number of acceleration peaks

{NAP}_{i, α} ≜ | {a_{i} (t) ∣ \frac{d a_{i}}{d t} = 0, \frac{d^{2} a_{i}}{d t^{2}} < 0, a_{i} > α {\bar{A}}_{i}} |

Bursts of force. Significant 3D vs 2D.

Acceleration peak rate

{APR}_{i, α} = \frac{{NAP}_{i, α}}{T_{i}}

Bursts per second.

Integral of acceleration

{IAV}_{i} ≜ \int_{0}^{T_{i}} a_{i} (t) d t

Total “effort” of changing velocity.

Sm · SAL · SPARC · LDLJ

Smoothness

Where skill shows: the third derivative and the spectrum. → the fluency of a stroke · form breaking down in the last 10 km · a round pedal stroke.

Smoothness

{Sm}_{i} ≜ \frac{1}{T_{i}} \sqrt{\frac{1}{2} \int_{0}^{T_{i}} [{(\frac{d^{3} x}{d t^{3}})}^{2} + {(\frac{d^{3} y}{d t^{3}})}^{2} + {(\frac{d^{3} z}{d t^{3}})}^{2}] d t}

Root jerk; not dimensionless, so it scales with amplitude and duration.

Spectral arc length

{SAL}_{i} ≜ - \int_{0}^{ω_{c}} \sqrt{{(\frac{1}{ω_{c}})}^{2} + {(\frac{d {\hat{V}}_{i} (ω)}{d ω})}^{2}} d ω, {\hat{V}}_{i} (ω) = \frac{V_{i} (ω)}{V_{i} (0)}

Arc length of the normalised speed spectrum: a smooth movement has a short, simple spectrum.

SPARC · adaptive cut-off

ω_{c} ≜ \min {ω_{c}^{\max}, \min {ω ∣ {\hat{V}}_{i} (r) < \bar{V}, \forall r > ω}}

SAL with a cut-off chosen per movement; independent of temporal scaling. Closer to 0 = smoother.

Dimensionless · log jerk

{DLJ}_{i} ≜ \frac{{(T_{i})}^{3}}{v_{i, peak}^{2}} \int_{0}^{T_{i}} j_{i} {(t)}^{2} d t

{LDLJ}_{i} ≜ \ln | {DLJ}_{i} |

Jerk made dimensionless. Significant 3D vs 2D.

κ · TA

Shape

How straight, how sharply it turns. → the arc of a smash vs a drive · knee tracking in the frontal plane · cornering lines.

Curvature

κ_{i} (t) ≜ \frac{‖ 𝒗_{i} (t) \times 𝒂_{i} (t) ‖}{v_{i}^{3} (t)}

≈ 0 for straight movements; summarised by mean, max or spread.

Turning angle

{TA}_{i} (t) ≜ \arccos (\frac{𝒖_{i, t - 1} \cdot 𝒖_{i, t + 1}}{‖ 𝒖_{i, t - 1} ‖ ‖ 𝒖_{i, t + 1} ‖})

With u_t−1 = p(t) − p(t−1): angle between consecutive steps.

q · ω

Orientation

The study’s open lead: the tracker also logs rotation, and almost no study uses it. → forearm pronation and racket-face angle · foot-strike angle · ankling through the pedal stroke.

Quaternion

𝒒 (t) ≜ {(q_{4} q_{1} q_{2} q_{3})}^{⊤}, ‖ 𝒒 ‖ = 1

Orientation without gimbal lock, straight from the sensor.

Angular speed

ω (t) = 2 ‖ \dot{𝒒} (t) \otimes 𝒒^{*} (t) ‖

Feed ω(t) instead of v(t) into NSP, SPARC or LDLJ: rotation gets its own smoothness score.

Scroll or drag the strip · hover a formula for its name and meaning.

02Sleep

Recovery is where training pays off.

Sleep stages from a wrist or ring sensor, nocturnal heart-rate variability, and movement during the night — scored with the same peak detection as the motion toolbox.

Sleep efficiency

SE = \frac{TST}{TIB} \times 100 %

Total sleep time over time in bed.

Wake after sleep onset

WASO = \sum_{e > SOL} Δ t_{e} [s_{e} = wake]

Minutes awake after sleep-onset latency SOL; 30-second epochs e.

Night movement

{NAP}_{α} (a_{wrist}), {MAPR}_{α} (v_{wrist})

Restlessness, counted with the motion metrics above.

Hypnogram · 23:00–07:00 · 30-s epochsSimulated

03Body temperature

Heat is a hidden load.

Core and skin temperature drive fatigue. How do layers, fabrics and fit change skin and core temperature, sweat rate and heart-rate drift — in heat and in cold?

Mean skin temperature · Ramanathan

{\bar{T}}_{sk} = 0.3 T_{chest} + 0.3 T_{arm} + 0.2 T_{thigh} + 0.2 T_{leg}

Four skin sensors, one weighted number.

Physiological strain index · Moran

PSI = 5 \frac{T_{c, t} - T_{c, 0}}{39.5 - T_{c, 0}} + 5 \frac{{HR}_{t} - {HR}_{0}}{180 - {HR}_{0}}

Heat strain on a 0–10 scale from core temperature and heart rate.

Cardiac drift

Δ {HR}_{drift} = \frac{{\bar{HR}}_{2nd half} - {\bar{HR}}_{1st half}}{{\bar{HR}}_{1st half}} | \bar{P} = const

Heart-rate rise at constant power or pace: the price of heat.

60-min run in the heat · core, skin, HRSimulated

04Biometrics

Heart, load and energy.

The classic numbers — heart rate, heart-rate variability, training load and energy expenditure — computed the same way every time, so sessions compare across weeks, sports and equipment.

Heart-rate reserve · Karvonen

{HR}_{target} = {HR}_{rest} + x \cdot ({HR}_{max} - {HR}_{rest})

Zones as a fraction x of the reserve.

HRV · RMSSD

RMSSD = \sqrt{\frac{1}{N - 1} \sum_{i = 1}^{N - 1} {({RR}_{i + 1} - {RR}_{i})}^{2}}

Beat-to-beat variability: a recovery signal.

Training impulse · Banister

TRIMP = \sum_{t} Δ t \cdot h_{t} \cdot 0.64 e^{1.92 h_{t}}, h_{t} = \frac{{HR}_{t} - {HR}_{rest}}{{HR}_{max} - {HR}_{rest}}

Internal load, weighted towards high intensity (coefficients 0.86 and 1.67 for women).

Energy from power

E_{met} = \frac{1}{η} \int_{0}^{T} P (t) d t, η \approx 0.24 \Rightarrow kcal \approx {kJ}_{mech}

Gross efficiency turns power-meter work into energy burned.

ECG · R-R intervals · RMSSDSimulated

05Equipment & environment

How much is the athlete, and how much is the kit?

The research focus of the lab: isolating the effect of equipment, materials and conditions — with the same controlled 2D-vs-3D mindset, now applied to a racket, a shoe or a tyre.

Materials

Rackets, strings, shoes and shuttles. What do stiffness, weight balance and foam actually change in the data — and in the smoothness of the movement?

Racket frame layup & stiffness
String tension
Shoe foam & stack · shuttle type

Mechanics & terrain

The bike as a machine: geometry, tyres and drivetrain on asphalt, gravel and trail.

Tyre width & pressure vs rolling resistance
Compliance & vibration per terrain
Geometry · drivetrain efficiency

06Metrics

What gets measured.

Metric	Pillar	Sensor	Sports	What it quantifies
Path, speed & peaks	Motion	IMU	All	P, S_max, NSP per stroke, stride or revolution
Smoothness	Motion	IMU	All	LDLJ and SPARC — fluency, fatigue, technique
Orientation	Motion	IMU (quaternion)	Badminton, cycling	Pronation, racket face, ankling
Foot pressure	Motion	Pressure insoles	Badminton, running	Footwork, landing pattern, left/right balance
Sleep stages & efficiency	Sleep	Wrist / ring	All	TST, SE, WASO, night movement
Skin & core temperature	Temperature	Temperature sensors	All	Heat strain (PSI), clothing and material effects
Heart rate & HRV	Biometrics	Chest strap	All	Internal load, TRIMP, recovery, cardiac drift
Power & energy	Biometrics	Power meter	Cycling, running	External work, kcal — the reference for every comparison
Pace, speed & elevation	Biometrics	GPS · barometer	Running, cycling	Pacing, climbing rate (VAM), terrain sections
Vibration & tyre pressure	Equipment	Frame accelerometer · pressure	Gravel, MTB	Terrain roughness, rolling resistance vs grip

07Project log

Work in the open.

Planned

Motion-metrics toolbox: MATLAB → Python

motionPython

Tyre pressure vs terrain on gravel

cyclingmechanics

Clothing layers vs skin temperature

runningtemperature

Marathon pacing drift analysis

runningHR

In progress

Racket IMU — stroke detection

badmintonsensors

Automated FIT/GPX ingestion pipeline

Pythondata

Published

3D vs 2D fetoscopy: quantitative motion analysis — Scientific Reports 2023 ↗

motionsurgery

Train, test, compare.

Club, coach, equipment brand or curious athlete — questions, ideas or a sensor to test? Get in touch.

Email me yolan.weiler@automatx.eu Sensor builds → Robotics lab

Performance,
quantified.

Motion, scored like surgical skill.

Three sports, three kinds of load.

Badminton

Running — trail & marathon

Cycling — gravel, MTB & road

A movement is a curve in space.

Badminton · overhead clear

Running · two strides

Cycling · two crank revolutions

From raw sensor to clean segments.

Format

Transform

Prune

Smooth

Annotate & debug

Position, then three derivatives.

Metric bench: smooth vs intermittent.

The metric atlas.

Time & space

Speed

Acceleration

Smoothness

Shape

Orientation

Recovery is where training pays off.

Heat is a hidden load.

Heart, load and energy.

How much is the athlete, and how much is the kit?

Materials

Mechanics & terrain

What gets measured.

Work in the open.

Train, test, compare.

Performance,quantified.

Motion, scored like surgical skill.

Three sports, three kinds of load.

Badminton

Running — trail & marathon

Cycling — gravel, MTB & road

A movement is a curve in space.

Badminton · overhead clear

Running · two strides

Cycling · two crank revolutions

From raw sensor to clean segments.

Format

Transform

Prune

Smooth

Annotate & debug

Position, then three derivatives.

Metric bench: smooth vs intermittent.

The metric atlas.

Time & space

Speed

Acceleration

Smoothness

Shape

Orientation

Recovery is where training pays off.

Heat is a hidden load.

Heart, load and energy.

How much is the athlete, and how much is the kit?

Materials

Mechanics & terrain

What gets measured.

Work in the open.

Train, test, compare.

Performance,
quantified.