modelica_models

This project badge reports repository CI; it is not a Modelica Association certification. The checked rules and their MSL rationale are documented in CONTRIBUTING.md.

Reusable Modelica building blocks for rigid-body simulation, estimation, control, and verification.

This repository is the aerospace engineering workspace for CogniPilot vehicle development. Vehicle physics, flight-control source models, named vehicle parameterizations, avionics-facing plant interfaces, missions, and qualification criteria live here. Firmware repositories consume exported artifacts; they do not own alternate copies of these models.

Layout

• Avionics/: transport-independent sensor, navigation, and estimator lifecycle contracts shared by drivers, estimation, and control.
• Estimation/: structured estimator prediction and correction functions, including the replaceable StrapdownINS ESKF and manifold UKF.
• LinearAlgebra/: dimension-generic matrix algorithms used by estimation and control code.
• Polynomials/: dimension-generic Hermite construction, derivative evaluation, and integrated derivative-cost matrices.
• LieGroups/: Lie groups including SO(2), SO(3), SE(2), SE(3), and SE_2(3), with replaceable quaternion, DCM, MRP, and Euler rotation representations. All 12 axis sequences are available in both body-fixed and space-fixed form, including B232 and S123.
• Geodesy/: reusable local-frame and geodetic conversion helpers, including the East-North-Up projection and its inverse about a GeodeticOrigin used to turn global lat/lon/alt waypoints into local-frame references.
• RigidBody/: reusable six-degree-of-freedom rigid-body dynamics.
• MathUtilities/: shared clipping, filtering, angle, rate, and norm helpers.
• Control/: reusable control laws and sampled controller building blocks, including the multirotor SE_2(3)/SO(3) log-linear controller and the Multirotor.RateLoop and Multirotor.Allocation inner-loop building blocks.
• Planning/: forward-only bounded-curvature path planning, including all six classical Dubins path families.
• Vehicles/Templates/: parameterized fixed-wing and quadrotor plants.
• Vehicles/Cubs2/ and Vehicles/Rdd2/: named parameterizations, flight-control models, avionics plant interfaces, and qualification missions. RDD2 includes both its cascaded sampled controller and a thin vehicle parameterization of the reusable log-linear controller.
• tools/: non-library Python orchestration for validation, qualification, export, CI caching, and reports. Nothing under this directory is part of the Modelica package API.

The repository keeps automation outside its Modelica package trees, following the same separation used by the Modelica Standard Library. The structure check validates within declarations, package.order coverage, and package metadata without requiring Nix.

Navigation estimator boundary

Avionics is the pure-Modelica boundary between sensor drivers, navigation algorithms, and control. Its IMU, motion-capture, GPS, and optical- flow records use physical quantities with explicit ENU-world and FLU-body frame conventions; transport adapters may map Synapse/FlatBuffers messages into these records, but this library has no dependency on those message definitions.

Every estimator publishes Avionics.NavigationEstimate. It contains only algorithm-independent physical state: position, velocity, acceleration, body and world angular velocity, and mutually consistent quaternion, direction-cosine-matrix, and roll-pitch-yaw attitude forms. Internal bias states, tangent ordering, and covariance stay private because they are not comparable across arbitrary filter implementations.

Estimation.StrapdownINS.PartialEstimator is the common aided inertial- navigation interface. StrapdownINS.ESKF implements a 15-state local right-error ESKF, while StrapdownINS.UKF implements a 31-point manifold UKF over the same position, velocity, attitude, and IMU-bias state. The ESKF name is intentional: additive bias states mean that calling it an invariant Kalman filter would overstate its mathematics. Both filters accept identical sensor, noise, initialization, and terrain-plane assumptions so their closed-loop comparison is meaningful.

Sensor timestamp_s is capture time. valid may remain true while a usable sample is held; fresh pulses for one estimator tick when a new sample arrives, preventing a slow sensor value from being fused repeatedly. Latency compensation belongs in a reusable fixed-lag wrapper over a private estimator-backend contract: the wrapper buffers backend snapshots and IMU increments, corrects at the capture time, and replays prediction to the present. This keeps replay logic shared while allowing each backend to retain its own opaque state and uncertainty model.

The CUBS2 deployment boundary is intentionally narrower than the closed-loop test model. Vehicles.Cubs2.OuterLoop is the deployable Modelica controller; it sends pilot-style commands to an onboard inner-loop stabilizer whose proprietary implementation is unavailable to this project. Closed-loop CUBS2 tests use OnboardStabilizerSurrogate only as an explicit simulation fixture. Those tests verify the open outer loop and its assumed boundary behavior; they do not establish equivalence to, or qualify, the unseen stabilizer.

The vehicle library is execution-neutral. Its names describe physical or control meaning only. Tooling outside the library decides whether a model is executed directly or exported for another runtime.

Control.Multirotor.LogLinear contains the alternate controller as one documented package. It exposes the left-invariant state error, bounded position integral, SE_2(3) outer loop, SO(3) attitude loop, and sampled controller model. Vehicles.Rdd2.LogLinearController supplies only the RDD2 parameters. A differentially flat trajectory connects directly through its world-frame position, velocity, acceleration, and yaw-reference quaternion.

GPS waypoint navigation runs entirely on this local-frame controller. The reusable Planning.Bezier.waypointTrajectory builds a piecewise-septic differentially flat trajectory that passes through each waypoint at a commanded velocity (zero for rest-to-rest), feeding world-frame position, velocity, and acceleration to the log-linear controller; its collective thrust and body-rate command pass through Control.Multirotor.RateLoop and Control.Multirotor.Allocation onto the four rotors. Vehicles.Rdd2.Test.TruthWaypointMission flies a truth-feedback comparison baseline. Vehicles.Rdd2.Test.WaypointMission takes off, flies a box, and lands in the local East-North-Up frame using the optical-flow-aided ESKF, and Vehicles.Rdd2.Test.GlobalWaypointMission authors the same box in latitude/longitude/altitude, projects it back through a fixed mission origin, and flies it using the GPS-aided ESKF. Parallel UkfWaypointMission and UkfGlobalWaypointMission models fly the same missions with the UKF. All four aided tracks are compared with the truth-feedback baseline so controller/plant failures can be distinguished from estimator or aiding failures.

The optical-flow sensor traces a normalized image feature grid against the configured plane n' p = d; it therefore does not require that the observed surface be aligned with local vertical. Raw line-of-sight flow contains both translation and camera rotation. The compensated velocity and slant-range measurement use the same plane geometry as each filter's observation model. The default plane is horizontal because that is a common local-terrain approximation, and an inclined-plane regression prevents that default from becoming a hidden assumption.

Vehicle development

An aerospace change follows one source path:

1. Edit a reusable plant under Vehicles/Templates/, or a named vehicle, controller, and mission under Vehicles/Cubs2/ or Vehicles/Rdd2/.
2. Run the named vehicle qualification. Each mission exercises the controller and plant together and writes reviewable traces and reports beneath artifacts/vehicles/.
3. Export the same controller source as eFMI Production Code.
4. Export the same avionics plant interface as FMI 3 Co-Simulation.
5. Let the consuming firmware repository integrate those generated artifacts.

Landing-gear contact is intentionally eventful. Direct simulation preserves the touchdown relations. The current source-FMU profile rejects plant exports that contain event/action partitions; it must continue to fail closed until the FMI execution kernel preserves those partitions and its conformance tests cover them.

Install the cross-platform repository command from the checkout:

python -m pip install -e .
modelica-models doctor

Python owns the task definitions and process orchestration. Run qualifications and exports with the same command on Linux, macOS, or Windows:

modelica-models qualify cubs2
modelica-models qualify rdd2
modelica-models qualify all

modelica-models export cubs2-controller
modelica-models export cubs2-plant
modelica-models export rdd2-controller
modelica-models export rdd2-estimator
modelica-models export rdd2-plant

Rumoca's CLI and matching Python bindings are required for qualification; OpenModelica or a working Docker installation is required for the full test suite. Tool locations can be overridden with MODELICA_MODELS_RUMOCA, MODELICA_MODELS_OMC, and MODELICA_MODELS_DOCKER. Set MODELICA_MODELS_ROOT when running outside the checkout.

Nix is optional. It only provides pinned compilers, Python dependencies, and environment variables; it does not define tasks or task-specific wrappers:

nix develop
modelica-models qualify rdd2

# One command without entering the shell:
nix run . -- test

CI runs the CUBS2 and RDD2 qualifications as independent jobs. RDD2 flies the truth-feedback baseline plus optical-flow- and GPS-aided ESKF and UKF missions. Each job uploads its traces, PNG plots, and a self-contained HTML report, with a direct artifact link in the GitHub Actions job summary. The two jobs use fail-fast: false, so both vehicles are qualified even if one fails.

RDD2 sensor noise is deterministic and compiler-portable. Each Gaussian sample is produced by a Box-Muller transform of indexed uniform fixtures, then scaled from the exact measurement covariance or continuous IMU/bias-walk spectral density supplied to the selected filter. This is deliberately not the stateful Modelica Standard Library/OpenModelica Xorshift sequence. Qualification checks the empirical variance and cross-correlation against the declared assumptions; enableSensorNoise=false provides a noiseless diagnostic run.

Arguments after -- are forwarded to the selected qualification, exporter, or report implementation.

RDD2 optical-flow and GPS mission trace reports

These commands render the explicit optical-flow and GPS mission models and write a PNG, self-contained HTML report, JSON observation report, and selected CSV under artifacts/vehicles/rdd2/mission-plots/<mode>/. They report model traces; they do not qualify a physical aircraft or issue a flight-acceptance verdict.

Invoke the reporter through the Python orchestration command:

modelica-models mission-report optical -- --engine omc
modelica-models mission-report gps -- --engine omc

Live simulation refuses tracked modifications or untracked files among Modelica sources, scenario TOML, Resources/, and package.order, and checks again after simulation so a report cannot label dirty inputs with the clean revision. Provenance records resolved compiler and Python paths and their SHA-256 digests. Exact receipted compiler and model revisions are mandatory whether the tools came from Nix or a native installation.

The optical command always selects Vehicles.Rdd2.Test.WaypointMission; the GPS command always selects Vehicles.Rdd2.Test.GlobalWaypointMission. Defaults match the collected model evidence: 45 seconds with a 5 ms output step. The GPS report shows the existing 0.5 m model navigation-error criterion as a diagnostic. The optical report shows absolute-position drift without applying a threshold because velocity-only optical aiding does not observe absolute position.

The frozen Rumoca flight compiler revision 9860c307 is not available from the current optional environment, so live Rumoca reporting fails closed instead of silently using a different compiler. A receipted Rumoca CSV can still be replayed:

modelica-models mission-report optical -- \
  --engine rumoca --rumoca-csv /path/to/trace.csv \
  --rumoca-receipt /path/to/trace.receipt.json
modelica-models mission-report gps -- \
  --engine rumoca --rumoca-csv /path/to/trace.csv \
  --rumoca-receipt /path/to/trace.receipt.json

Replay refuses a CSV without a sidecar whose JSON fields exactly identify its mode, model, compiler, model revision, duration, cadence, and SHA-256 digest. The receipt schema is:

{
  "schema": "rdd2-mission-trace-receipt-v1",
  "engine": "rumoca",
  "mode": "gps",
  "model": "Vehicles.Rdd2.Test.GlobalWaypointMission",
  "compiler": {
    "name": "Rumoca",
    "identity": "rdd2-flight-freeze-2-9860c307",
    "revision": "9860c30781242ff65dfcf47b136385ac5ecf4350"
  },
  "model_revision": "a9e5037ab3e57b3fac6ca783c0bdbfdd2b6dd98e",
  "stop_time_s": 45.0,
  "step_s": 0.005,
  "csv_sha256": "<exactly 64 lowercase hexadecimal characters>"
}

OpenModelica replay uses the same schema with engine omc, identity OpenModelica/a96aa1a682c463b0fd2d285b486c09a8b7fe496d, and revision a96aa1a682c463b0fd2d285b486c09a8b7fe496d. Trace validation also requires finite samples, time zero, strict ordering, exact cadence, and complete requested coverage. Use --stop-time and --step to match a shorter receipted trace. These commands are currently Linux-only.

Mission trajectory logs

Named vehicle missions write a canonical, execution-neutral trajectory log:

time_s,x_m,y_m,z_m,roll_rad,pitch_rad,yaw_rad

The trajectory comparison tool treats one such log as the gold standard, interpolates any number of named candidate logs at its timestamps, renders full trajectory/component/error plots, and enforces duration, position, altitude, and attitude limits. It intentionally knows nothing about the system that produced a log:

modelica-models trajectory-compare -- --help

Qualification artifacts remain ignored build outputs under artifacts/vehicles/. A downstream repository can compare generated, bench, or flight logs by adapting them to this seven-column contract; no downstream execution terminology or log decoder belongs in this library.

Testing

All mathematical test definitions are Modelica classes under Tests/. The suite uses Modelica assert equations for Lie-group identities, generic linear-algebra systems, geometric error-state filters, Dubins paths, and analytic rigid-body trajectories. No Python source generation or numerical oracle is involved.

Run the complete suite with the installed Python command:

modelica-models test

Individual checks are available through the same interface:

modelica-models check-structure
modelica-models test omc
modelica-models test rumoca
modelica-models test plots

From an uninstalled source checkout, replace modelica-models with python -m tools.modelica_models_cli. The runner uses the declared OpenModelica container when Docker is operational, then falls back to a local omc. It handles paths, temporary directories, process failures, and artifact validation without platform-specific scripts. Python does not compute test oracles: mathematical pass/fail checks remain Modelica assertions executed by OpenModelica and, where currently supported, Rumoca.

The CI command also simulates reproducible planning examples and writes CSV data plus PNG plots under artifacts/planning/. The primary aircraft figure is a closed figure eight whose two crossing headings share exactly one center position. Redundant identical poses are coalesced, leaving seven waypoint occurrences and six nonzero Dubins legs. The initial flight plan is overlaid with its flyable, continuous-curvature Dubins-polynomial smoothing. A separate plot checks curvature and curvature-derivative continuity across every leg and waypoint junction, and a mission-wide signed bank-angle plot shows the coordinated left/right command. Generated artifacts are ignored by Git and uploaded by the GitHub Actions workflow.

The Dubins-polynomial coefficients are obtained with a fixed-cost analytical procedure: one joint unconstrained quadratic solve over the free junction derivatives, followed by one closed-form true-spatial-derivative repair pass. The default derivative weights are {0.3, 1, 0, 50} through third order. The CI gallery also renders four paper-style comparisons with the Dubins reference, optimized path, and nominal segment junctions on common axes.

The plotted example also checks a stated aircraft flight envelope in Modelica: minimum turn radius, coordinated bank angle, and coordinated bank rate at the declared flight speed. Thus "flyable" means that those explicit assumptions pass assertions; it is not inferred from geometric smoothness alone.

To regenerate only the planning artifacts:

modelica-models test plots

CI uses the same Python commands. Its optional Nix layer pins compiler binaries and caches only the Rumoca runtime when that pin changes. OpenModelica runs the complete assertion simulation using the pinned container image, with a local omc as the fallback when Docker is unavailable. Rumoca independently parses, resolves, flattens, and lowers the same Tests.All model to DAE form, then executes SO(2) and SE(2) assertion smoke models with its simulation backend. The complete assertion model remains the OpenModelica simulation authority because Rumoca does not yet structurally lower every aggregate static assertion and array-valued dynamic equation.

Replaceable rotation representations

SE3.Generic and SE23.Generic accept any package implementing SO3.Interfaces.PartialRotation. Concrete quaternion, MRP, DCM, and Euler-B321 packages are provided. A specific Euler sequence can be selected directly:

package VehicleState = LieGroups.SE23.Generic(
  redeclare package Rotation = LieGroups.SO3.EulerSequences.B232);

Quaternion and DCM representations are generally preferable for global simulation. Euler representations are useful at interfaces where a named sequence is required. Proofs using local log coordinates should explicitly establish the chart-domain guard supplied by LieGroups.Analysis.

Verification-oriented APIs

The library keeps simulation equations and proof expressions aligned:

• RigidBody.stateDerivative is the pure vector field used by RigidBody6DOF.
• RigidBody.mechanicalEnergy, wrenchPower, and powerBalanceResidual expose the lossless passivity identity.
• LieGroups.Analysis supplies coordinate-independent attitude potential, principal-log domain checks, and dimension-generic tangent-space quadratic candidates.
• LinearAlgebra.contractionResidual, quadraticForm, and quadraticFormDerivative provide dimension-generic certificate expressions.
• The ESKF exposes its nominal discrete map, tangent transition, process covariance, measurement map, measurement covariance, and local residual as separate pure functions for reachable-set propagation.

These functions produce certificate quantities; they do not claim a proof by themselves. Bounds on chart validity, disturbances, numerical integration, and the sign of the resulting matrix inequalities remain explicit proof obligations.

Dubins path planning

Planning.Dubins computes the globally shortest member of the six classical forward-only, constant-turn-radius path families: LSL, RSR, LSR, RSL, RLR, and LRL. Positions are Cartesian x/y coordinates and headings are in radians.

The classical plan search includes RLR/LRL by default and accepts allowThreeTurnPaths=false when those reversal-heavy paths are inappropriate. Aircraft trajectory examples disable them by default and automatically select the shortest feasible LSL, RSR, LSR, or RSL path, so callers do not select a family manually.

Planning.Dubins.Path path;
Planning.Dubins.Pose midpoint;
equation
  path = Planning.Dubins.plan(
    {0.0, 0.0}, 0.0,
    {10.0, 10.0}, 0.5 * 2.0 * asin(1.0),
    5.0);
  midpoint = Planning.Dubins.evaluate(path, 0.5);

The path record exposes its selected family, physical length, turn radius, and three normalized segment lengths. Turn segment lengths are angles in radians; straight segment lengths are distance divided by turn radius. This makes the piecewise curvature and segment domains explicit for tracking and reachability analysis.

Smooth transverse-polynomial paths

Planning.DubinsPolynomial represents a smooth trajectory as a piecewise polynomial left-normal offset from an underlying Dubins path. Polynomial abscissas use physical nominal path distance rather than normalized segment coordinates, keeping derivative costs dimensionally consistent between arcs and straight segments.

The evaluator accepts any coefficient count and returns:

• position and heading;
• true unit-speed spatial derivatives through third order;
• signed curvature and curvature derivative;
• transverse offset and the offset-to-nominal metric scale.

smoothOffsets constructs a septic seed that fixes position and heading at the endpoints and segment junctions while making curvature and curvature rate continuous. derivativeCost and Polynomials.derivativeCostMatrix provide the quadratic objectives needed to penalize offset, curvature-related derivatives, and higher derivatives. The coordinated-flight helpers map curvature and its metric derivative to fixed-speed roll angle and roll rate.

The supplied smoothing seed constrains transverse offset and its first derivative to zero at nominal segment junctions. This makes its C3 continuity exact. An optimizer that permits nonzero junction offsets must additionally apply a nonlinear true-derivative repair iteration; use junctionContinuityResidual as the acceptance certificate. Every candidate must also retain a positive metricScale, since a zero value indicates a singular or locally reversed offset curve.