SpaceTech AcademyMISSION FL-RPO-17 · AURORARENDEZVOUS OPERATIONS LAB
CW / Hill guidance20 MIN / 12 S

CW / Hill guidance · Proximity geometry visually amplified

Autonomous rendezvous—in real time.

A chaser CubeSat closes from 300 metres through a constrained approach corridor. Hill-frame relative motion, closed-loop thrust commands, keep-out geometry, closing speed, and delta-v remain visible throughout the maneuver.
CW / Hill guidanceTARGET VEHICLE
Drag anywhere to take camera control · Scroll to zoom
Click a vehicle to inspect
Jump to phase
Flight profile
Playback rate
RELATIVE RANGE
300.7 m
CLOSING RATE
0.000 m/s
POINTING ERROR
8.39°
DELTA-V USED
0.000 m/s
MISSION PHASE
Far-range phasing
MODEL CLOHESSY–WILTSHIRET+ 0.0 minacmd 1200 μm/s²CORRIDOR 3.93°PROPELLANT 0.00 g
SPACE play/pause · 1/2/3/4 cameras · R restart · F full screen
FLIGHTLAB LIVE12.0 s · 300 samples · COUPLED 3-DOF · QUATERNION
OUTPUT / 02

Spacecraft pointing response

Angle deviation from trim · degrees

60 μN·m
Normalized environmental torque5°3°0°-3°-5°0s3s6s9s12s0.0s
TIME (SECONDS)
Live CubeSat attitude stateLQR
PITCH
4.20°
ROLL
6.40°
YAW
2.80°
Simulation time0.00 s
Drag the timeline to inspect any moment
Playback speed
ORBITAL TELEMETRY / 04

Orbital mission console

Coupled quaternion propagation, body rate, reaction-wheel momentum, guidance mode, and orbit-state telemetry for the tracked controller.

Guidance frame: Sun pointingTruth-driven educational control loop
Accelerated orbit previewT+0.00 s
Subsatellite latitude
N 17.07°
Subsatellite longitude
E 56.09°
Orbital velocity
7.658 km/s
Body-rate magnitude0.080 °/s
Commanded torque7.117 mN·m
Wheel momentum0.0003 N·m·s
Estimator residual0.028°
Attitude quaternionq = [0.9975, 0.0549, 0.0379, 0.0223]
Body-rate magnitudeω = [-0.062, -0.044, -0.026] °/s
Wheel momentum vectorhw = [0.0002, 0.0001, 0.0001] N·m·s
Wheel momentumLQR
Momentum capacity
1.3%
Simulated ADCS sensors
GyroscopeNominalSun sensorNominalMagnetometerNominal
Mission event sequenceT+0.00 s
  1. 01
    Initialize stateT+0.0 s
  2. 02
    Disturbance injectionT+2.0 s
  3. 03
    Closed-loop recoveryT+5.2 s
  4. 04
    Performance assessmentT+9.2 s

Controller comparison

UncontrolledMarginal
RMS error
4.20°
Peak deviation
4.2°
Settle time
>12 s
PIDStable
RMS error
2.33°
Peak deviation
4.2°
Settle time
9.8 s
LQRStable
RMS error
2.05°
Peak deviation
4.2°
Settle time
8.2 s
ANALYSIS / 03

Mission analysis

A composite score combines RMS error, peak deviation, and settling performance across pitch, roll, and yaw.

Best overall responseLQR · 80.7/100
Engineering run summaryObjective achieved
Attitude-error suppression
53.0%
RMS · LQR
Peak wheel capacity
52.0%
max |hw,axis|
Maximum body rate
3.137°/s
max |ω|
Sample integrity
301/301
Δt = 0.04 s
VERIFICATION / 05

ADCS verification matrix

IDRequirementMeasured resultStatus
ADCS-RQ-01Final pointing error ≤ 5°2.427°PASS
ADCS-RQ-02Per-axis wheel momentum < 100%52.04%PASS
ADCS-RQ-03Quaternion norm error ≤ 10⁻⁵2.22e-16PASS
ADCS-RQ-04301 state samples at 25 Hz301 @ 25 HzPASS
ADCS-RQ-05Identical disturbance for all controllersSOLAR · deterministic profilePASS
OPTIMIZATION / 06

Multi-objective ADCS gain optimizer

Evaluates 81 authority/gain designs across solar, magnetic, and slew missions, rejects infeasible wheel or pointing outcomes, and identifies the best weighted design and Pareto frontier.

ROBUSTNESS / 07

Design-envelope robustness campaign

A seeded 48-case campaign perturbs spacecraft mass, orbit altitude, environmental torque, wheel authority, gain calibration, inclination, and disturbance scenario.

#1LQR80.7

Stability score

#2PID79.7

Stability score

#3Uncontrolled67.3

Stability score

The score is a transparent educational index, not a certification or safety rating.

MODEL TRANSPARENCY / 03

Know what the simulator is calculating

FlightLab keeps the mathematics visible. It uses three independent rotational channels to isolate the effect of feedback on pitch, roll, and yaw.
01

Rigid-body attitude dynamics

q̇ = ½ q ⊗ [0, ω]Iω̇ + ω×(Iω) = τrw + τenv + τgg

The spacecraft branch propagates a normalized attitude quaternion and a coupled three-component body-rate vector using the diagonal inertia tensor, gyroscopic cross-coupling, environmental torque, gravity-gradient torque, and saturated reaction wheels.

I · inertia tensorτrw · wheel torqueτenv · disturbanceτgg · gravity gradient
02

Controller architecture

PIDu = −(Kpθ + Kdω + Ki∫θdt)

PID reacts to present error, motion rate, and accumulated error. It is intuitive to tune and can remove steady-state offset.

LQRu = −Kx

LQR applies state feedback to angle and angular rate. The gains represent a balance between attitude error and control effort.

03

Experiment protocol

12.0 shorizon
0.04 stime step
±6.5 mN·mactuator limit

Every controller receives the same initial condition and deterministic disturbance. This makes each comparison repeatable and fair.

How the inputs affect the model

InputEffect inside FlightLab
Spacecraft massScales the representative CubeSat principal moments of inertia.
Orbital altitudeSets orbital radius, mean motion, period, and the gravity-gradient coefficient.
Disturbance torqueSets environmental torque amplitude in micronewton-metres.
Reaction-wheel authorityScales feedback gains and available reaction-wheel command.
Orbital inclinationSets the latitude envelope and the orientation of the live orbital track.
PID gain multiplierAdjusts the PID gain set only, enabling controlled tuning experiments without changing LQR.
LQR gain multiplierAdjusts the LQR state-feedback gains only, enabling a fair side-by-side sensitivity test.

ASSUMPTIONS / 05

The assumptions behind the CubeSat branch

The astronautics model keeps physical units and orbital dependencies visible while isolating the controller comparison.
  1. 01

    Elliptical two-body low-Earth orbit with configurable inclination, RAAN, and eccentricity; Earth rotation, cylindrical eclipse, dipole magnetic-field magnitude, and secular J₂ RAAN drift are evaluated.

  2. 02

    A diagonal representative CubeSat inertia tensor with full three-axis gyroscopic coupling.

  3. 03

    Small pointing errors expressed in radians internally and reported in degrees.

  4. 04

    Deterministic solar, magnetic, and slew torques for repeatable experiments.

  5. 05

    Identical reaction-wheel saturation for PID and LQR control laws.

ASTRONAUTICS MODEL / 06

An orbital attitude-control laboratory—not an aircraft reskin

CubeSat mode uses a separate rotational model, orbital calculation, disturbance environment, actuator scale, and mission interpretation designed specifically for spacecraft ADCS education.
01 / DYNAMICS

Spacecraft rotational equation

Iω̇ + ω × (Iω)= τrw + τenv + τgg

Euler’s rigid-body equation balances angular-momentum rate against reaction-wheel, environmental, and gravity-gradient torques. FlightLab retains the ω×Iω coupling term and propagates a normalized quaternion at 25 Hz.

Solver
semi-implicit quaternion
Rate
25 Hz
State
q, ω, hw
02 / ORBIT

Low Earth orbit environment

n = √(μ / r³)T = 2π / n

A Kepler propagator advances an elliptical low-Earth orbit through ECI and Earth-fixed frames. The environment layer computes eclipse geometry, a dipole-field estimate, J₂ nodal drift, gravity-gradient torque, solar-pressure impulses, and residual magnetic interaction.

h
500 km
T
94.5 min
n
1.109e-3 rad/s
03 / GUIDANCE

ADCS control loop

ATTITUDE→ERROR→CONTROL→WHEELS

A mission ADCS estimates attitude, calculates error, commands actuators, and observes the new state. This laboratory focuses on control and rigid-body propagation.

04 / ACTUATION

Reaction-wheel actuation

PID and LQR command the same saturated wheel-torque envelope. Independent gain multipliers reveal overshoot, settling, and control-authority tradeoffs.

INTERPRETATION / 04

Read the result like a control engineer

RMS

RMS error

Average attitude error across the complete 12-second run. Lower values mean tighter regulation.

MAX

Peak deviation

The largest departure from trim. It shows the worst transient excursion.

Ts

Settle time

The final time the response remains outside the ±1.5° stability band.

Run a four-step experiment

A complete classroom or portfolio investigation takes only a few minutes.

  1. 01

    Choose a repeatable disturbance scenario.

  2. 02

    Set mass, airspeed, wind intensity, and control authority.

  3. 03

    Run once, then inspect pitch, roll, and yaw with identical conditions.

  4. 04

    Export the CSV and defend which controller performed better—and why.

Investigation prompts

  • When does added aircraft mass change the controller ranking?
  • Does higher control authority always improve the response?
  • Which axis is most sensitive to each disturbance profile?

01 / METHOD

What this demonstrates

A reproducible three-axis linearized model shows how feedback changes disturbance rejection. Every run is computed locally in your browser; no installation or account is required.

02 / SCOPE

Educational model

Designed for control-system intuition and classroom exploration—not aircraft design, certification, or operational use.

03 / 中文简介

航空与航天双域控制实验

SpaceTech FlightLab 将飞机飞行控制与 CubeSat 轨道姿态控制整合在同一平台中，可比较 PID、LQR 与无控制响应，并导出完整实验数据。