Mapping DO-361A Content to Sample Algorithm Code
RTCA’s DO-361A contains two appendices which document algorithms and models associated with the research for Interval Management.
- Appendix C: SAMPLE ALGORITHM provides detailed technical documentation of a “sample” algorithm that meets the requirements in DO-361A. The software in this git repo is our own implementation of Appendix C.
- Appendix H: MOPS Aircraft and Control Model is an overview of a 3-degree-of-freedom aircraft dynamics & control model which we’ve used for our research.
- Detailed documentation is found in this published paper.
- An implementation of Appendix H is also available
These appendices have been written by MITRE and are the copyright of RTCA. In this git repo, and our related FIM MOPS Aircraft & Control Model, are provided our software implementations of the algorithms and models. Below is a general mapping between each section of DO-361A Appendix C/H and our open source code.
(If any mistakes are noticed in this mapping, please open an issue to notify us of the mistake.)
| Appendix Section | Appendix Title | Public Implementation |
|---|---|---|
| C | SAMPLE ALGORITHM | im_sample_algorithm |
| C.1 | Overview | No Applicable URL |
| C.2 | Generation of the Reference Trajectories | Not Available |
| C.2.1 | Calculation of the Horizontal Path | HorizontalPath.cpp |
| C.2.1.1 | Determining the Waypoint Sequence | AircraftIntent.cpp |
| C.2.1.2 | Conversion of Waypoint Latitudes and Longitudes to x;y Coordinates | TangentPlaneSequence.cpp |
| C.2.1.3 | Determine Course Change Between Waypoints | Not Available |
| C.2.1.4 | Calculate Turn Radius | Not Available |
| C.2.1.5 | Calculate the Start; End; and Center of the Turn | Not Available |
| C.2.1.6 | Determine Horizontal Path Transitions and Distance-To-Go (DTG) | Not Available |
| C.2.1.7 | Data Format for the Horizontal Path | HorizontalPath.cpp |
| C.2.2 | Ground Speed Assembly | KinematicTrajectoryPredictor.cpp |
| C.2.2.1 | Trajectory Segments | KinematicDescent4DPredictor.cpp |
| C.2.2.1.1 | Constant Calibrated Airspeed descent | KinematicDescent4DPredictor.cpp |
| C.2.2.1.2 | Constant Mach Descent | KinematicDescent4DPredictor.cpp |
| C.2.2.1.3 | Deceleration and Descent | KinematicDescent4DPredictor.cpp |
| C.2.2.1.4 | Constant Geometric Flight-Path Angle Descent; Maintain Constant Airspeed | KinematicDescent4DPredictor.cpp |
| C.2.2.1.5 | Constant Geometric Flight-Path Angle Descent; Decelerate Airspeed | KinematicDescent4DPredictor.cpp |
| C.2.2.1.6 | Level Flight; Maintain Constant Airspeed | KinematicDescent4DPredictor.cpp |
| C.2.2.1.7 | Level Flight; Decelerate Airspeed | KinematicDescent4DPredictor.cpp |
| C.2.2.2 | Calculation of the Mach/CAS Crossover Altitude | Atmosphere.cpp |
| C.2.2.3 | Wind Information | No Applicable URL |
| C.2.2.3.1 | Format for Forecast and Sensed Wind Information | Wind.cpp |
| C.2.2.3.2 | Spline-Fit Algorithms to Calculate Predicted Winds | Wind.cpp |
| C.2.2.4 | Temperature Information | StandardAtmosphere.cpp |
| C.2.2.5 | Updating Wind and Temperature Information and Recalculating Predicted Trajectories | MOPSPredictedWindEvaluatorVersion2.cpp; Public/Wind.cpp |
| C.2.2.6 | Use of Procedural and Default Limits | KinematicDescent4DPredictor.cpp |
| C.2.2.7 | Logic for Combining Trajectory Segments | KinematicDescent4DPredictor.cpp |
| C.2.2.8 | Calculating Along-path Positions from Current Position | AircraftCalculations.cpp; AircraftCalculations.cpp |
| C.2.2.8.1 | Cross-Track Error Calculation | AircraftCalculations.cpp |
| C.2.2.8.2 | Along-path Position Calculation | AircraftCalculations.cpp; AlongPathDistanceCalculator.cpp |
| C.2.2.9 | Calculating TTG from Along-path Distance | No Applicable URL |
| C.3 | Nomenclature | No Applicable URL |
| C.4 | Achieve Stage | IMAchieve.cpp |
| C.4.1 | Predicted Spacing Interval Calculation | No Applicable URL |
| C.4.1.1 | Time-based Predicted Spacing Interval | IMTimeBasedAchieve.cpp |
| C.4.1.2 | Distance-based Predicted Spacing Interval | IMDistBasedAchieve.cpp |
| C.4.2 | Default Traffic Reference Point | Not Available |
| C.4.3 | Time-to-Go Control Law for Time-based Assigned Spacing Goals | IMTimeBasedAchieve.cpp |
| C.4.4 | Time-to-Go Control Law for Distance-based Assigned Spacing Goals | IMDistBasedAchieve.cpp |
| C.4.5 | Error Thresholds | IMAchieve.cpp |
| C.4.6 | Hysteresis on New Speed Implementation | IMAlgorithm.cpp |
| C.4.7 | Discretization of the Control Law Speed | IMTimeBasedAchieve.cpp |
| C.5 | IM Turn Algorithm | No Applicable URL |
| C.5.1 | Calculation of the IM Turn Point | https://github.com/mitre/im_sample_algorithm/blob/master/IMTurn/calcPathShorteningTurnPointTTG.m |
| C.5.2 | IM Turn Leg Lengths | Not Available |
| C.5.3 | Reference TTG for Ownship | Not Available |
| C.5.4 | Assumed Vertical and Airspeed Profiles | Not Available |
| C.5.5 | Description of the IM Turn Point | Not Available |
| C.5.6 | Transition to the Achieve Stage | Not Available |
| C.6 | Final Approach Spacing Algorithm | No Applicable URL |
| C.6.1 | Determine Whether an Aircraft is on a Vector to Intercept | IMKinematicAchieve.cpp |
| C.6.2 | Calculate Merge Point | IMUtils.cpp |
| C.7 | Maintain Stage Algorithm | IMMaintain.cpp |
| C.7.1 | Measured Spacing Interval Calculation | No Applicable URL |
| C.7.1.1 | Traffic Alignment | Not Available |
| C.7.1.2 | Time-based Measured Spacing Interval | IMKinematicTimeBasedMaintain.cpp |
| C.7.1.3 | Distance-based Measured Spacing Interval | IMKinematicDistBasedMaintain.cpp |
| C.7.2 | Time-History Control Law for Time-based Assigned Spacing Goals | IMKinematicTimeBasedMaintain.cpp |
| C.7.3 | Station-Keeping Algorithm for Distance-based Assigned Spacing Goals | IMKinematicDistBasedMaintain.cpp |
| C.7.4 | Discretization of the Control Law Speed | IMKinematicTimeBasedMaintain.cpp |
| H | MOPS Aircraft and Control Model | FMACM |
| H.1 | Aircraft Equations | No Applicable URL |
| H.1.1 | Reference Frames | ThreeDOFDynamics.cpp |
| H.1.2 | Equations of Motion | ThreeDOFDynamics.cpp |
| H.2 | Guidance Control Laws | AircraftControl.cpp |
| H.2.1 | Lateral Control | AircraftControl.cpp |
| H.2.2 | Speed Control Using Thrust | SpeedOnThrustControl.cpp |
| H.2.3 | Speed Control Using Pitch | SpeedOnPitchControl.cpp |
| H.2.4 | Control Gains and Parameter Values | AircraftControl.cpp |
| H.3 | Aircraft-Specific Modeling | https://github.com/mitre/FMACM/blob/master/include/aaesim/BadaWithCalc.h |
In addition to the above model mappings, Appendix H documents the control law gain values we used in our simulations. The mapping between the gains and our code is below.
| Parameter/Control Gain | Value | Public Implementation |
|---|---|---|
| thrust | 0.352 s-1 | AircraftControl.cpp#L56 |
| phi | 0.400 s-1 | SpeedOnPitchControl.cpp#L23 |
| speed brake | 0.100 s-1 | SpeedOnThrustControl.cpp#L24 |
| psi | 3 | AircraftControl.cpp#L120 |
| gamma | 0.400 s-1 | SpeedOnPitchControl.cpp#L22 |
| cross-track | 5 × 10-4 m-1 | AircraftControl.cpp#L119 |
| IAS | 0.1136 s-1 | SpeedOnPitchControl.cpp#L36 |
| altitude | 0.20 s-1 | SpeedOnPitchControl.cpp#L21 |
| altitude threshold | 500 feet | TestFrameworkAircraft.cpp |
| IAS threshold | 20 knot | TestFrameworkAircraft.cpp |