Drone Aerial Photography

Summary

This experiment investigates drone aerial photography. Full factorial of altitude, gimbal angle, flight speed, and overlap percentage to maximize ground resolution and minimize motion blur.

The design varies 4 factors: altitude m (m), ranging from 30 to 120, gimbal angle (deg), ranging from -90 to -45, flight speed (m/s), ranging from 2 to 12, and overlap pct (%), ranging from 60 to 85. The goal is to optimize 2 responses: gsd cm (cm/px) (minimize) and blur score (pts) (minimize). Fixed conditions held constant across all runs include camera = 1inch_sensor, wind = light.

A full factorial design was used to explore all 16 possible combinations of the 4 factors at two levels. This guarantees that every main effect and interaction can be estimated independently, at the cost of a larger experiment (16 runs).

Quadratic response surface models were fitted to capture potential curvature and factor interactions. The RSM contour plots below visualize how pairs of factors jointly affect each response.

Key Findings

For gsd cm, the most influential factors were altitude m (47.6%), flight speed (26.0%), overlap pct (24.4%). The best observed value was 0.3 (at altitude m = 30, gimbal angle = -90, flight speed = 12).

For blur score, the most influential factors were gimbal angle (36.8%), flight speed (31.6%), altitude m (30.7%). The best observed value was 1.1 (at altitude m = 120, gimbal angle = -45, flight speed = 2).

Recommended Next Steps

Consider whether any fixed factors should be varied in a future study.

Experimental Setup

Factors

Factor	Low	High	Unit
`altitude_m`	30	120	m
`gimbal_angle`	-90	-45	deg
`flight_speed`	2	12	m/s
`overlap_pct`	60	85	%

Fixed: camera = 1inch_sensor, wind = light

Responses

Response	Direction	Unit
`gsd_cm`	↓ minimize	cm/px
`blur_score`	↓ minimize	pts

Configuration

use_cases/154_drone_aerial_photo/config.json

{
  "metadata": {
    "name": "Drone Aerial Photography",
    "description": "Full factorial of altitude, gimbal angle, flight speed, and overlap percentage to maximize ground resolution and minimize motion blur"
  },
  "factors": [
    {
      "name": "altitude_m",
      "levels": [
        "30",
        "120"
      ],
      "type": "continuous",
      "unit": "m"
    },
    {
      "name": "gimbal_angle",
      "levels": [
        "-90",
        "-45"
      ],
      "type": "continuous",
      "unit": "deg"
    },
    {
      "name": "flight_speed",
      "levels": [
        "2",
        "12"
      ],
      "type": "continuous",
      "unit": "m/s"
    },
    {
      "name": "overlap_pct",
      "levels": [
        "60",
        "85"
      ],
      "type": "continuous",
      "unit": "%"
    }
  ],
  "fixed_factors": {
    "camera": "1inch_sensor",
    "wind": "light"
  },
  "responses": [
    {
      "name": "gsd_cm",
      "optimize": "minimize",
      "unit": "cm/px"
    },
    {
      "name": "blur_score",
      "optimize": "minimize",
      "unit": "pts"
    }
  ],
  "settings": {
    "operation": "full_factorial",
    "test_script": "use_cases/154_drone_aerial_photo/sim.sh"
  }
}

Experimental Matrix

The Full Factorial Design produces 16 runs. Each row is one experiment with specific factor settings.

Run	`altitude_m`	`gimbal_angle`	`flight_speed`	`overlap_pct`
1	30	-45	12	85
2	120	-90	2	85
3	30	-45	2	85
4	30	-45	12	60
5	120	-45	12	60
6	120	-90	12	60
7	120	-45	2	60
8	120	-90	2	60
9	30	-90	2	85
10	30	-90	12	60
11	120	-45	2	85
12	120	-45	12	85
13	30	-45	2	60
14	120	-90	12	85
15	30	-90	2	60
16	30	-90	12	85

Step-by-Step Workflow

1

Preview the design

Terminal

$ doe info --config use_cases/154_drone_aerial_photo/config.json

2

Generate the runner script

Terminal

$ doe generate --config use_cases/154_drone_aerial_photo/config.json \
    --output use_cases/154_drone_aerial_photo/results/run.sh --seed 42

3

Execute the experiments

Terminal

$ bash use_cases/154_drone_aerial_photo/results/run.sh

4

Analyze results

Terminal

$ doe analyze --config use_cases/154_drone_aerial_photo/config.json

5

Get optimization recommendations

Terminal

$ doe optimize --config use_cases/154_drone_aerial_photo/config.json

6

Multi-objective optimization

With 2 competing responses, use --multi to find the best compromise via Derringer–Suich desirability.

Terminal

$ doe optimize --config use_cases/154_drone_aerial_photo/config.json --multi

7

Generate the HTML report

Terminal

$ doe report --config use_cases/154_drone_aerial_photo/config.json \
    --output use_cases/154_drone_aerial_photo/results/report.html

Features Exercised

Feature	Value
Design type	`full_factorial`
Factor types	`continuous` (all 4)
Arg style	`double-dash`
Responses	2 (gsd_cm ↓, blur_score ↓)
Total runs	16

Analysis Results

Generated from actual experiment runs using the DOE Helper Tool.

Response: gsd_cm

Top factors: altitude_m (47.6%), flight_speed (26.0%), overlap_pct (24.4%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
altitude_m	1	8.8506	8.8506	5.958	0.0586
gimbal_angle	1	0.0156	0.0156	0.011	0.9223
flight_speed	1	2.6406	2.6406	1.777	0.2400
overlap_pct	1	2.3256	2.3256	1.565	0.2662
altitude_m*gimbal_angle	1	0.0156	0.0156	0.011	0.9223
altitude_m*flight_speed	1	2.4806	2.4806	1.670	0.2528
altitude_m*overlap_pct	1	0.3306	0.3306	0.223	0.6570
gimbal_angle*flight_speed	1	2.6406	2.6406	1.777	0.2400
gimbal_angle*overlap_pct	1	3.1506	3.1506	2.121	0.2051
flight_speed*overlap_pct	1	10.7256	10.7256	7.220	0.0435
Error	5	7.4281	1.4856
Total	15	40.6044	2.7070

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Half-Normal Plot of Effects

Model Diagnostics

Response: blur_score

Top factors: gimbal_angle (36.8%), flight_speed (31.6%), altitude_m (30.7%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
altitude_m	1	3.0625	3.0625	1.205	0.3224
gimbal_angle	1	4.4100	4.4100	1.735	0.2449
flight_speed	1	3.2400	3.2400	1.275	0.3101
overlap_pct	1	0.0025	0.0025	0.001	0.9762
altitude_m*gimbal_angle	1	1.6900	1.6900	0.665	0.4519
altitude_m*flight_speed	1	1.0000	1.0000	0.393	0.5580
altitude_m*overlap_pct	1	0.0225	0.0225	0.009	0.9287
gimbal_angle*flight_speed	1	9.9225	9.9225	3.904	0.1051
gimbal_angle*overlap_pct	1	4.0000	4.0000	1.574	0.2651
flight_speed*overlap_pct	1	1.4400	1.4400	0.567	0.4855
Error	5	12.7075	2.5415
Total	15	41.4975	2.7665

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Half-Normal Plot of Effects

Model Diagnostics

Response Surface Plots

3D surfaces fitted with quadratic RSM. Red dots are observed data points.

blur score altitude m vs flight speed

blur score altitude m vs gimbal angle

blur score altitude m vs overlap pct

blur score flight speed vs overlap pct

blur score gimbal angle vs flight speed

blur score gimbal angle vs overlap pct

gsd cm altitude m vs flight speed

gsd cm altitude m vs gimbal angle

gsd cm altitude m vs overlap pct

gsd cm flight speed vs overlap pct

gsd cm gimbal angle vs flight speed

gsd cm gimbal angle vs overlap pct

Multi-Objective Optimization

When responses compete, Derringer–Suich desirability finds the best compromise. Each response is scaled to a 0–1 desirability, then combined via a weighted geometric mean.

Overall Desirability

D = 0.8923

Per-Response Desirability

Response	Weight	Desirability	Predicted	Dir
`gsd_cm`	1.0	0.8066	1.00 0.8066 1.00 cm/px	↓
`blur_score`	1.5	0.9545	1.10 0.9545 1.10 pts	↓

Recommended Settings

Factor	Value
`altitude_m`	30 m
`gimbal_angle`	-45 deg
`flight_speed`	2 m/s
`overlap_pct`	85 %

Source: from observed run #3

Trade-off Summary

Sacrifice = how much worse than single-objective best.

Response	Predicted	Best Observed	Sacrifice
`blur_score`	1.10	1.10	+0.00

Top 3 Runs by Desirability

Run	D	Factor Settings
#9	0.8459	altitude_m=120, gimbal_angle=-90, flight_speed=2, overlap_pct=60
#13	0.8424	altitude_m=120, gimbal_angle=-45, flight_speed=2, overlap_pct=60

Model Quality

Response	R²	Type
`blur_score`	0.3544	linear

Full Multi-Objective Output

doe optimize --multi
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================

Overall desirability: D = 0.8923

Response                  Weight Desirability    Predicted  Direction
---------------------------------------------------------------------
gsd_cm                       1.0       0.8066        1.00 cm/px   ↓
blur_score                   1.5       0.9545        1.10 pts   ↓

Recommended settings:
  altitude_m = 30 m
  gimbal_angle = -45 deg
  flight_speed = 2 m/s
  overlap_pct = 85 %
  (from observed run #3)

Trade-off summary:
  gsd_cm: 1.00 (best observed: 0.30, sacrifice: +0.70)
  blur_score: 1.10 (best observed: 1.10, sacrifice: +0.00)

Model quality:
  gsd_cm: R² = 0.7937 (linear)
  blur_score: R² = 0.3544 (linear)

Top 3 observed runs by overall desirability:
  1. Run #3 (D=0.8923): altitude_m=30, gimbal_angle=-45, flight_speed=2, overlap_pct=85
  2. Run #9 (D=0.8459): altitude_m=120, gimbal_angle=-90, flight_speed=2, overlap_pct=60
  3. Run #13 (D=0.8424): altitude_m=120, gimbal_angle=-45, flight_speed=2, overlap_pct=60

Full Analysis Output

doe analyze
=== Main Effects: gsd_cm ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
altitude_m              -1.4875       0.4113            47.6%
flight_speed            -0.8125       0.4113            26.0%
overlap_pct              0.7625       0.4113            24.4%
gimbal_angle             0.0625       0.4113             2.0%

=== ANOVA Table: gsd_cm ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
altitude_m                   1       8.8506       8.8506      5.958     0.0586
gimbal_angle                 1       0.0156       0.0156      0.011     0.9223
flight_speed                 1       2.6406       2.6406      1.777     0.2400
overlap_pct                  1       2.3256       2.3256      1.565     0.2662
altitude_m*gimbal_angle      1       0.0156       0.0156      0.011     0.9223
altitude_m*flight_speed      1       2.4806       2.4806      1.670     0.2528
altitude_m*overlap_pct       1       0.3306       0.3306      0.223     0.6570
gimbal_angle*flight_speed    1       2.6406       2.6406      1.777     0.2400
gimbal_angle*overlap_pct     1       3.1506       3.1506      2.121     0.2051
flight_speed*overlap_pct     1      10.7256      10.7256      7.220     0.0435
Error                        5       7.4281       1.4856
Total                       15      40.6044       2.7070

=== Interaction Effects: gsd_cm ===
Factor A             Factor B              Interaction   % Contribution
------------------------------------------------------------------------
flight_speed         overlap_pct               -1.6375            36.6%
gimbal_angle         overlap_pct                0.8875            19.8%
gimbal_angle         flight_speed               0.8125            18.2%
altitude_m           flight_speed              -0.7875            17.6%
altitude_m           overlap_pct                0.2875             6.4%
altitude_m           gimbal_angle              -0.0625             1.4%

=== Summary Statistics: gsd_cm ===

altitude_m:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  120                 8     3.2625     1.7361     0.3000     4.6000
  30                  8     1.7750     1.2338     0.7000     4.1000

gimbal_angle:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  -45                 8     2.4875     1.5189     0.7000     4.6000
  -90                 8     2.5500     1.8685     0.3000     4.5000

flight_speed:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  12                  8     2.9250     1.6342     0.3000     4.6000
  2                   8     2.1125     1.6591     0.7000     4.3000

overlap_pct:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  60                  8     2.1375     1.5408     0.3000     4.3000
  85                  8     2.9000     1.7591     0.7000     4.6000

=== Main Effects: blur_score ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
gimbal_angle            -1.0500       0.4158            36.8%
flight_speed             0.9000       0.4158            31.6%
altitude_m              -0.8750       0.4158            30.7%
overlap_pct             -0.0250       0.4158             0.9%

=== ANOVA Table: blur_score ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
altitude_m                   1       3.0625       3.0625      1.205     0.3224
gimbal_angle                 1       4.4100       4.4100      1.735     0.2449
flight_speed                 1       3.2400       3.2400      1.275     0.3101
overlap_pct                  1       0.0025       0.0025      0.001     0.9762
altitude_m*gimbal_angle      1       1.6900       1.6900      0.665     0.4519
altitude_m*flight_speed      1       1.0000       1.0000      0.393     0.5580
altitude_m*overlap_pct       1       0.0225       0.0225      0.009     0.9287
gimbal_angle*flight_speed    1       9.9225       9.9225      3.904     0.1051
gimbal_angle*overlap_pct     1       4.0000       4.0000      1.574     0.2651
flight_speed*overlap_pct     1       1.4400       1.4400      0.567     0.4855
Error                        5      12.7075       2.5415
Total                       15      41.4975       2.7665

=== Interaction Effects: blur_score ===
Factor A             Factor B              Interaction   % Contribution
------------------------------------------------------------------------
gimbal_angle         flight_speed               1.5750            35.8%
gimbal_angle         overlap_pct                1.0000            22.7%
altitude_m           gimbal_angle              -0.6500            14.8%
flight_speed         overlap_pct                0.6000            13.6%
altitude_m           flight_speed               0.5000            11.4%
altitude_m           overlap_pct               -0.0750             1.7%

=== Summary Statistics: blur_score ===

altitude_m:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  120                 8     3.7250     1.6909     1.6000     5.8000
  30                  8     2.8500     1.6222     1.1000     5.2000

gimbal_angle:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  -45                 8     3.8125     1.3174     2.1000     5.3000
  -90                 8     2.7625     1.8875     1.1000     5.8000

flight_speed:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  12                  8     2.8375     1.7246     1.2000     5.3000
  2                   8     3.7375     1.5784     1.1000     5.8000

overlap_pct:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  60                  8     3.3000     1.7254     1.1000     5.3000
  85                  8     3.2750     1.7178     1.2000     5.8000

Optimization Recommendations

doe optimize
=== Optimization: gsd_cm ===
Direction: minimize

Best observed run: #9
  altitude_m = 30
  gimbal_angle = -90
  flight_speed = 12
  overlap_pct = 85
  Value: 0.3

RSM Model (linear, R² = 0.0427, Adj R² = -0.3055):
  Coefficients:
    intercept                      +2.5188
    altitude_m                     +0.1688
    gimbal_angle                   +0.0813
    flight_speed                   -0.0312
    overlap_pct                    +0.2688

RSM Model (quadratic, R² = 0.3102, Adj R² = -9.3467):
  Coefficients:
    intercept                      +0.5038
    altitude_m                     +0.1687
    gimbal_angle                   +0.0813
    flight_speed                   -0.0312
    overlap_pct                    +0.2688
    altitude_m*gimbal_angle        -0.0688
    altitude_m*flight_speed        +0.0938
    altitude_m*overlap_pct         +0.5938
    gimbal_angle*flight_speed      +0.0563
    gimbal_angle*overlap_pct       +0.2313
    flight_speed*overlap_pct       -0.5062
    altitude_m^2                   +0.5038
    gimbal_angle^2                 +0.5038
    flight_speed^2                 +0.5038
    overlap_pct^2                  +0.5038

  Curvature analysis:
    altitude_m                     coef=+0.5038  convex (has a minimum)
    gimbal_angle                   coef=+0.5038  convex (has a minimum)
    flight_speed                   coef=+0.5038  convex (has a minimum)
    overlap_pct                    coef=+0.5038  convex (has a minimum)

  Notable interactions:
    altitude_m*overlap_pct         coef=+0.5938  (synergistic)
    flight_speed*overlap_pct       coef=-0.5062  (antagonistic)

  Predicted optimum (from linear model, at observed points):
    altitude_m = 120
    gimbal_angle = -45
    flight_speed = 2
    overlap_pct = 85
    Predicted value: 3.0688

  Surface optimum (via L-BFGS-B, linear model):
    altitude_m = 30
    gimbal_angle = -90
    flight_speed = 12
    overlap_pct = 60
    Predicted value: 1.9688

  Model quality: Weak fit — consider adding center points or using a different design.

Factor importance:
  1. overlap_pct  (effect: 0.5, contribution: 48.9%)
  2. altitude_m  (effect: -0.3, contribution: 30.7%)
  3. gimbal_angle  (effect: -0.2, contribution: 14.8%)
  4. flight_speed  (effect: 0.1, contribution: 5.7%)

=== Optimization: blur_score ===
Direction: minimize

Best observed run: #3
  altitude_m = 120
  gimbal_angle = -45
  flight_speed = 2
  overlap_pct = 60
  Value: 1.1

RSM Model (linear, R² = 0.2958, Adj R² = 0.0397):
  Coefficients:
    intercept                      +3.2875
    altitude_m                     +0.4000
    gimbal_angle                   -0.5125
    flight_speed                   +0.2625
    overlap_pct                    +0.5250

RSM Model (quadratic, R² = 0.8875, Adj R² = -0.6871):
  Coefficients:
    intercept                      +0.6575
    altitude_m                     +0.4000
    gimbal_angle                   -0.5125
    flight_speed                   +0.2625
    overlap_pct                    +0.5250
    altitude_m*gimbal_angle        -0.1750
    altitude_m*flight_speed        -0.2000
    altitude_m*overlap_pct         +0.5875
    gimbal_angle*flight_speed      -0.2375
    gimbal_angle*overlap_pct       +0.2500
    flight_speed*overlap_pct       -1.0000
    altitude_m^2                   +0.6575
    gimbal_angle^2                 +0.6575
    flight_speed^2                 +0.6575
    overlap_pct^2                  +0.6575

  Curvature analysis:
    altitude_m                     coef=+0.6575  convex (has a minimum)
    gimbal_angle                   coef=+0.6575  convex (has a minimum)
    overlap_pct                    coef=+0.6575  convex (has a minimum)
    flight_speed                   coef=+0.6575  convex (has a minimum)

  Notable interactions:
    flight_speed*overlap_pct       coef=-1.0000  (antagonistic)
    altitude_m*overlap_pct         coef=+0.5875  (synergistic)

  Predicted optimum (from linear model, at observed points):
    altitude_m = 120
    gimbal_angle = -90
    flight_speed = 12
    overlap_pct = 85
    Predicted value: 4.9875

  Surface optimum (via L-BFGS-B, linear model):
    altitude_m = 30
    gimbal_angle = -45
    flight_speed = 2
    overlap_pct = 60
    Predicted value: 1.5875

  Model quality: Weak fit — consider adding center points or using a different design.

Factor importance:
  1. overlap_pct  (effect: 1.0, contribution: 30.9%)
  2. gimbal_angle  (effect: 1.0, contribution: 30.1%)
  3. altitude_m  (effect: -0.8, contribution: 23.5%)
  4. flight_speed  (effect: -0.5, contribution: 15.4%)

Run	`altitude_m`	`gimbal_angle`	`flight_speed`	`overlap_pct`
1	30	-45	12	85
2	120	-90	2	85
3	30	-45	2	85
4	30	-45	12	60
5	120	-45	12	60
6	120	-90	12	60
7	120	-45	2	60
8	120	-90	2	60
9	30	-90	2	85
10	30	-90	12	60
11	120	-45	2	85
12	120	-45	12	85
13	30	-45	2	60
14	120	-90	12	85
15	30	-90	2	60
16	30	-90	12	85

Run	`altitude_m`	`gimbal_angle`	`flight_speed`	`overlap_pct`
1	30	-45	12	85
2	120	-90	2	85
3	30	-45	2	85
4	30	-45	12	60
5	120	-45	12	60
6	120	-90	12	60
7	120	-45	2	60
8	120	-90	2	60
9	30	-90	2	85
10	30	-90	12	60
11	120	-45	2	85
12	120	-45	12	85
13	30	-45	2	60
14	120	-90	12	85
15	30	-90	2	60
16	30	-90	12	85

Run	`altitude_m`	`gimbal_angle`	`flight_speed`	`overlap_pct`
1	30	-45	12	85
2	120	-90	2	85
3	30	-45	2	85
4	30	-45	12	60
5	120	-45	12	60
6	120	-90	12	60
7	120	-45	2	60
8	120	-90	2	60
9	30	-90	2	85
10	30	-90	12	60
11	120	-45	2	85
12	120	-45	12	85
13	30	-45	2	60
14	120	-90	12	85
15	30	-90	2	60
16	30	-90	12	85