Rocket Landing GNC: Point-Mass Prototype

00Evidence status

Exploratory Point-mass model Single-run demo Private source

What is supported: a private Python prototype demonstrates a point-mass descent scenario and a basic closed-loop control concept.

What is not supported yet: 6-DOF rigid-body dynamics, aerodynamic or aerothermal validation, stochastic dispersion statistics, a 500-run campaign, and sub-2 m landing accuracy.

Evidence source: source inspection of the private FalconV5 prototype. No public repository, downloadable report, or result-plot set is currently available.

01Problem

Propulsive landing couples trajectory shaping, changing mass, limited thrust authority, and state-feedback control. A useful first step is to prove the software loop closes on a deliberately simple plant before adding rotational dynamics and uncertainty.

The prototype therefore asks a narrow question: can a point-mass vehicle follow one descent case under the implemented controller? The harder question—how it performs across realistic dispersions— remains the next phase, not a result of this one.

Prototype objective. Establish a reproducible point-mass descent baseline that can later be extended and verified without confusing planned fidelity with implemented fidelity.

01APlanned verification gates

Gate	Needed evidence	Current state	Disposition
RL-G1	Repeatable nominal point-mass run with saved inputs and outputs	Prototype demonstrated	Needs packaged evidence
RL-G2	Analytical sub-cases and time-step convergence	No visible test record	Pending
RL-G3	6-DOF model with frame, sign, conservation, and actuator-limit tests	Not implemented in reviewed prototype	Future work
RL-G4	Justified uncertainty model and seeded batch campaign	Not available	Future work
RL-G5	Landing-dispersion plots with reproducible data	Not available	No accuracy claim

01BPrototype scope

Represented

Translational descent. The plant is a point-mass approximation suitable for early controller experiments.
One nominal scenario. The visible implementation supports exploratory, single-run evaluation.
Closed-loop concept. A controller command is integrated with the simplified plant.

Not represented or evidenced

Rotational dynamics. Attitude, angular rate, inertia, and gimbal coupling need a verified 6-DOF extension.
Environment fidelity. Aerodynamics, heating, wind, and navigation-error models are not substantiated by the reviewed artifact.
Statistical performance. No seeded batch data or dispersion distribution is available.

02Prototype design

The implemented artifact is the smallest useful loop: a descent reference, a controller, and a point-mass plant integrated through one scenario. That decomposition is a useful scaffold, but the higher-fidelity blocks shown below remain a target architecture.

Target closed-loop architecture showing guidance, control, actuator, plant, navigation, environment, and uncertainty inputs. — **Fig. 1**Target architecture, not a diagram of fully verified functionality. The current prototype implements only a simplified subset of this loop.

Build sequence

Stage	Scope	Evidence needed	Status
Baseline	Point-mass plant and nominal controller run	Saved configuration, trace, and regression test	Prototype exists
Dynamics	Rigid-body attitude, changing inertia, and bounded actuation	Unit, conservation, and frame-convention tests	Pending
Uncertainty	Wind, initial state, sensor, and propulsion dispersions	Justified distributions and seeded repeatability	Pending
Campaign	Batch analysis and tail-case attribution	Versioned data, plots, and convergence study	Pending

03Model boundary

RoadmapNot current validation

The equations below document the intended progression from the point-mass baseline to a higher-fidelity simulator. They should not be read as evidence that each model is implemented, calibrated, or verified in the current prototype.

Planned rigid-body extension

m(t) v̇ = R{q}(T_gimbal) + F_aero + m(t) g − m(t) ω × v I(t) ω̇ = M_gimbal + M_aero − ω × (I(t) ω) q̇ = ½ q ⊗ [0, ω] ṁ = −T / (I_sp g₀) mass depletion couples straight back into m(t), I(t)

Planned aerodynamic extension

q̄ = ½ ρ(h) V² dynamic pressure, ρ from atmosphere model F_aero = q̄ S [C_D, C_Y, C_L]ᵀ coefficients functions of Mach and angle of attack M_aero = q̄ S L_ref [C_l, C_m, C_n]ᵀ

Planned aerothermal screening

q̇_stag ∝ ρ^0.5 V³ stagnation-point convective heating scaling Q = ∫ q̇ dt integrated heat load along the trajectory

A future heating model would not size thermal protection here; it would screen whether trajectories selected by the guidance law stay inside a sensible heating envelope rather than buying landing accuracy with an unflyable entry. No such aerothermal model exists in the reviewed prototype.

Controller design form

e = x_ref − x̂ error against the estimated state δ_cmd = K_p e + K_i ∫e dt + K_d ė δ = clamp(δ_cmd, ±δ_max) deflection limit δ̇ = clamp(δ̇, ±δ̇_max) slew-rate limit

Planned dispersion model

per trial, drawn from seeded distributions initial position, velocity, attitude, rate errors wind profile: magnitude and shear, altitude dependent sensor bias and noise on the navigation solution thrust and I_sp variation

03AMethod roadmap

Current: numerical integration of the simplified translational descent state.
Next: quaternion attitude propagation with explicit frame-convention and normalization tests.
Next: bounded actuator dynamics and controller anti-windup verified under saturation.
Next: calibrated atmosphere, aerodynamic, and propulsion models with provenance.
Next: seeded batch sampling and data-backed dispersion post-processing.

04Implementation

Language	Python 3 with NumPy and SciPy
Plant	Exploratory point-mass descent model
Controller	Basic closed-loop demonstration for one nominal scenario
Execution	Single-run prototype; no published batch runner
Source	Private FalconV5 repository; no public release
Outputs	No curated, reproducible plot or data package published yet

05Verification status

The available prototype supports inspection and exploratory execution, but it does not include a visible verification record for the broader system described by the target architecture.

Package the baseline. Save the nominal input configuration, trajectory output, environment, and source revision.
Add analytical checks. Compare ballistic and constant-thrust sub-cases with closed-form solutions.
Run convergence tests. Demonstrate that the nominal answer is insensitive to integration step.
Verify the extended plant. Add frame, sign, conservation, mass-property, and actuator-limit tests before claiming 6-DOF fidelity.
Only then run dispersions. Publish seeded batch inputs, all outputs, convergence of statistics, and tail-case attribution.

05AClaim boundary

A plausible trajectory is evidence that the prototype runs, not that the physics are validated or that the controller is robust. Landing accuracy requires a defined touchdown metric, calibrated uncertainty distributions, repeated trials, and saved data that another reviewer can reproduce.

No Monte Carlo claim: no batch artifact was found in the reviewed source.
No accuracy claim: no auditable landing-dispersion dataset is published.
No 6-DOF claim: the reviewed plant is point-mass, not a verified rigid-body model.

06Demonstrated outcome

1

Nominal scenario

Point mass

Current plant

Private

Source access

Pending

Published data

The prototype closes a simplified controller-and-plant loop for a nominal descent case.
The code establishes a starting point for higher-fidelity dynamics and repeatable verification.
No statistical robustness, touchdown accuracy, aerothermal margin, or hardware result is claimed.

No public plotsNo downloadable report

This page intentionally does not draw a chart from unversioned or unavailable data.

06AEngineering tradeoffs

Tradeoff	Gained	Paid
Point-mass first	Fast iteration on the loop and numerical plumbing	Cannot establish attitude, gimbal, or rigid-body performance
Single scenario first	Simple debugging and a clear baseline	Cannot establish robustness or a probability distribution
Private development	Rapid iteration without packaging overhead	Reviewers cannot reproduce the result from this site
Roadmap before fidelity	Makes intended model growth explicit	Requires strict labeling so planned features are not read as implemented

06BRisks to resolve

Actuator realism

A point-mass command can imply control authority that a real gimbal, throttle system, or attitude controller cannot deliver. The next plant must impose deflection, slew, throttle, and engine timing limits before controller performance can be interpreted physically.

Coupled mass properties and frames

Mass, center of mass, and inertia change with propellant depletion. Extending the plant introduces moment arms, attitude conventions, and frame transformations that need explicit tests rather than a visually plausible trajectory.

Reproducible evidence

The most immediate gap is not speed; it is a versioned input, output, and plotting package. That package must exist before a larger campaign or an accuracy figure is useful to a reviewer.

06CLessons learned

A nominal run is a starting point. It exercises the loop but says little about robustness.
Model fidelity is a claim. Degrees of freedom and environmental effects must match the reviewed implementation.
Accuracy needs a dataset. A touchdown number without versioned inputs, outputs, and a defined statistic is not reviewable evidence.
Verify the plant before comparing controllers. Better control logic cannot repair an unverified physical model.

07Next evidence gates

Publish a reproducible nominal-run package with configuration, source revision, raw output, and plot-generation steps.
Add analytical sub-cases and time-step convergence tests to the point-mass plant.
Implement and verify 6-DOF dynamics, changing mass properties, and bounded actuation.
Add a navigation filter and justified atmosphere, wind, propulsion, and sensor uncertainty models.
Run a seeded campaign, publish every trial, and report statistical landing performance only after the distribution converges.

08Source status

Private repositoryArtifacts pending

The FalconV5 source is private and no public report, raw trajectory data, or generated plot set is linked from this portfolio. The page therefore presents the design intent and current prototype boundary without offering unavailable downloads.

Public evidence will be added only with a reproducible data package and clearly identified source revision.

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