Space logistics and transportation

Physical AI for Space Logistics and Transportation: Composing the Velocity Budget with One Estimation-and-Control Stack

A Δv-composition framework, an on-orbit non-cooperative capture, and a headless physics core the whole chain runs on.

David Jean Charlot, PhD

Dean of Physical AI · The Charlot Lab, Institute for Physical AI @ JBI

Correspondence: contact@physicalai-bmi.org · physicalai-bmi.org
Interactive companion: physicalai-bmi.org/research/charlot-lab/space-logistics · Code: github.com/dcharlot-physicalai-bmi/orbital-logistics

1. Can a whole transport chain be written as one velocity budget?

It can, and that is what makes it one problem rather than seven. Launch, orbital transfer, rendezvous, capture, servicing, assembly and return compose into a single continuous chain. Space logistics is usually pictured as launch, the moment a vehicle leaves the ground. But moving materiel to and around space is a chain with many links: ascent to orbit, transfer between orbits, rendezvous with another object, capture of that object, servicing or assembly, and, increasingly, return. Each link moves mass through a change in velocity, and the currency that unifies the chain is therefore the velocity budget, Δv. Reaching low Earth orbit costs on the order of 9.4 km/s of Δv: ~7.8 km/s of orbital velocity at a 200 km circular orbit (√(μ/r) with μ = 3.986 × 10¹⁴ m³/s² and r = 6,578 km), plus ~1.5–2.0 km/s of gravity, drag and steering losses, less ~0.4 km/s of credit from Earth's rotation at a low-latitude site. A geostationary slot, the lunar surface, or the surface of Mars cost successively more. Every link in the logistics chain is, at bottom, a Δv to be paid.

The reason that budget is hard is the rocket equation, which makes the propellant a vehicle must carry grow exponentially with the Δv it must supply on its own. This report takes as its subject the two ways that AI, Physical AI, and embodied AI change the shape of the problem. The first is composition: reusable, shared infrastructure and autonomous in-space transport can supply parts of the budget so the vehicle does not carry all of it, and the exponential works in the payload's favor as soon as the onboard share falls. The second is that the infrastructure and transport that do this are, without exception, autonomy problems: a momentum-exchange tether catch, an electromagnetic launch handoff, an on-orbit rendezvous with a body that neither holds still nor cooperates. The capability that opens the chain is estimation and control carried on the vehicle. The report's thesis is that this capability is one capability: the same estimation-and-control primitive recurs at every link, so a single autonomy stack, priced in Δv and joules and run at the edge, serves the whole chain.

The aim is practical. Efficiencies, new materials, and new optimizations from this direction expand what space transportation and the management of space logistics can do, and they do so in a way that many actors can build on rather than a few: a path toward an open and decentralized space economy. The remainder of the report develops the budget bookkeeping (Section 3), the shared estimation-and-control shape (Section 4), the on-orbit case that is hardest and most clearly Physical AI (Section 5), and the open instruments and core that make the whole argument runnable (Section 6).

2. What is in scope, and how was it measured?

This is a position and methodology report, not an experimental one. It proposes a framework and a set of instruments; it reports no original measurements and claims no benchmark result for any system it describes. Two categories of quantity appear, and the report is explicit about which is which. The mathematics of Sections 3–5 (the rocket equation and the payload-fraction composition, the constant-stress tether taper, the vis-viva and escape relations, and the constant-velocity Kalman filter) is exact standard astronautics and estimation, and it is implemented and regression-checked in the released code[11]. The velocity budgets attached to destinations, and the per-segment Δv contributions attributed to each transport mode, are representative mission values used to make the composition legible; they are not predictions for a specific vehicle. The dynamics shown in the on-orbit capture instrument are illustrative, driven by the exact filter but not a validated flight simulation. Every empirical claim about the state of practice (that autonomous rendezvous and proximity operations, and non-cooperative inspection, already run in orbit) is attributed to the cited primary sources. Where this report proposes that one autonomy stack spans the chain, that is an organizing position offered for test, not a demonstrated result.

3. How does the budget compose?

A vehicle that supplies a velocity change Δv from its own propellant, with effective exhaust velocity v_e, obeys the rocket equation of Tsiolkovsky[1], which fixes the ratio of wet to dry mass:

Because the mass ratio is exponential in Δv, the deliverable payload fraction collapses as the required Δv rises. Writing the inert (structure) mass fraction as ε, the fraction of launch mass delivered as payload for a single stage supplying the whole budget T is λ₀ = 1/exp(T/v_e) − ε, which for a large enough T is negative, meaning no single vehicle of that class reaches the destination at all.

Composition changes the exponent. Suppose reusable, shared infrastructure and autonomous in-space transport supply a set of segment contributions {δ_k}: a launch handoff, a tether boost, an orbital-transfer stage, an aerocapture at arrival. The vehicle then supplies only the remainder, and its payload fraction follows from the reduced onboard budget:

The accounting is to report λ directly, as a physical mass fraction, rather than a ratio against a single-vehicle baseline: when that baseline is itself infeasible (λ₀ ≤ 0), a ratio is meaningless and inflates without bound. The composition instrument therefore states, for each destination, the share of the budget carried by shared infrastructure, the resulting payload fraction, and (only when a single vehicle could reach the destination at all) the multiple over that baseline. A destination a lone vehicle cannot reach is labelled as such, not scored. Figure 1 shows the composition against representative budgets.

4. What shape do all these problems share?

The transport modes that supply the offload segments of Section 3 are not, at bottom, materials problems. A momentum-exchange tether (the rotating skyhook of Moravec[2] and the later boost-tether studies[3]) must catch a payload at a closing speed of kilometers per second in a window measured in a second, which is a non-cooperative rendezvous under a hard deadline. A launch loop[4] is an elevated structure held in an unstable equilibrium by a fast internal rotor: it stands not because any material is stiff enough but because a distributed controller damps every span, and it buckles the instant that control is lost. An electromagnetic launch track[5] ends in a guidance-and-control handoff at hypersonic speed. In each case the estimation-and-control problem must be solved before the mode can fly at all, but which constraint binds today differs by mode. For the momentum-exchange tether it is materials: at a 3 km/s tip the constant-stress mass ratio is 13.6× in aramid against 0.26× in carbon nanotube, a factor of 52 in tether mass set entirely by σ/ρ with the control problem unchanged. For the launch loop it is the distributed controller and the rotor power that sustains the unstable equilibrium. For on-orbit rendezvous, where the hardware already flies, it is estimation and control. This report's subject is the last of these; the claim is that the primitive is shared across the chain, not that materials never bind.

Stated as control, the modes share a shape. In each, an estimator resolves the state of the world from noisy, delayed measurements, and a controller holds that state inside a proven corridor to a deadline. The value of naming the shape is that the estimator and the certified controller are then one stack, developed once and specialized per link. Certification here is the companion to this lab's work on provable control[10]: a controller that can carry a certificate of the region in which it will hold its corridor is a controller a vehicle can trust to run without a human in the loop, which (as Section 5 shows) is the only way the tightest links close at all.

Table 1. Links in the transport chain and the estimation-and-control primitive each reduces to. The gate in every row is autonomy carried on the vehicle; the material or power figure is downstream of it.

5. How do you catch something that is not cooperating?

The clearest instance of the shared shape, and the one furthest from the launch pad, is on-orbit rendezvous with a body that neither holds still nor helps. This is no longer hypothetical. Astroscale's ADRAS-J spacecraft approached a spent, tumbling rocket upper stage (a non-cooperative object of several tonnes), held station within tens of meters, flew around it under autonomous guidance, and validated autonomous collision avoidance[6]. Northrop Grumman's SpaceLogistics Mission Extension Vehicles docked with client satellites in geostationary orbit to extend their operational lives[7]. These are the first operational links of an in-space logistics layer, and the capability under them is exactly the estimator-and-certified-controller of Section 4.

Relative translation near a target on a circular orbit is governed by the Clohessy–Wiltshire equations[8]; the estimation problem is to recover the target's relative position, velocity, and (for a tumbling body) attitude and angular rate, from noisy and latency-bearing returns. The lab's instrument runs a per-axis constant-velocity Kalman filter[9] for the relative position. Writing the per-axis state as position and velocity (x, ẋ) with covariance P, the filter predicts and then corrects on each measurement z of noise variance r:

The controller then holds the chaser inside a certified approach corridor about the rotating capture axis, shrinking its standoff only as the pose covariance falls and the corridor is held: an estimator gating a certified maneuver. Capture succeeds when relative position, closing velocity, and the corridor condition are simultaneously inside tolerance. The instrument makes the reason for autonomy legible by offering a human-in-the-loop mode: at a coarse control rate and a quarter-second lag, the estimator never even converges inside the window that a real catch allows, and the approach misses. Autonomy is not an optimization of this link; it is its precondition.

6. What instruments does this need?

The argument is made runnable rather than only asserted. Each transport mode is realized as a self-contained instrument that executes in the browser, on the device, on its governing equations: a Δv-architecture composer, the on-orbit capture of Section 5, a momentum-exchange tether on real orbital mechanics and the constant-stress taper, an electromagnetic sled, and a launch loop on a distributed-instability model. The load-bearing equations are additionally extracted into a headless core that runs parameter sweeps without a display and is checked against independently re-derived values[11]. Those checks pin, among others, that a maglev sled reaching 2.9 km/s at 10 g needs 42.9 km of track; that a constant-stress tether at a 3 km/s tip has a mass ratio M_t/M_p = √π · x · e^{x²} · erf(x), where x = v_tip/v_c and v_c = √(2σ/ρ) is the material's characteristic velocity: 13.6× in aramid (σ = 3.6 GPa, ρ = 1,440 kg/m³, safety factor 1, so v_c = 2.24 km/s and x = 1.34) and 0.26× in carbon nanotube (σ = 50 GPa, ρ = 1,350 kg/m³, so v_c = 8.61 km/s and x = 0.35). Substitute σ, ρ and a safety factor for any other candidate material and recompute.; and (a correction the checks caught) that a rotovator's release must be compared against escape velocity at the tether tip radius, not at the station, which is where the 10.56 km/s release of a 600 km, 400 km-arm hook correctly exceeds the 10.40 km/s escape at the ≈1000 km tip. The instruments and core are released openly[11] so the capabilities can be tested, applied, and extended by others: a working expression of the open, decentralized aim.

7. Optimal, learned, or benchmarked?

Sections 4 and 5 describe the shape; the 2026 frontier fixes how that shape is best realized, and this section reports the lab's implementation of it on the same open, on-device terms. Two directions define the frontier. In control, learned and optimal policies now fly proximity operations: reinforcement learning has flown as the control law for a free-flyer in orbit, reported by the Naval Research Laboratory as the first such demonstration [13]; this review did not locate an earlier one.[13], and receding-horizon path-integral and tube-based model-predictive control give the certified corridor a rigorous form. In perception, monocular six-degree pose estimation of a non-cooperative target is benchmarked on shared datasets such as SPEED[14].

The lab implements all three, runnable in a browser. For control, the hand-tuned loop of Section 5 is replaced by a Model Predictive Path Integral controller[12]: it samples control sequences, rolls each out on the Clohessy–Wiltshire dynamics, and takes the cost-weighted average as the plan (reach, soft berth, corridor, effort), re-solved every step. From that optimal controller a policy is then distilled by behavior cloning: a 1,282-parameter multilayer perceptron that flies the approach as a plain forward pass, released openly[15] and run on the device with no framework. For perception, the target's tumble is integrated as a torque-free rigid body (Euler's equations with a quaternion, so the motion wanders as a real tumble does rather than spinning about a fixed axis), and its six-degree pose is recovered from one camera's noisy keypoints by perspective-n-point, scored against the truth with the SPEED metric at roughly one to two degrees of rotation and a few centimetres of translation. The score is fixed by four inputs, held at the RPO-Bench scenario values: range to target, focal length in pixels, keypoint count, and keypoint noise in pixels. Keypoint noise and range dominate; change either in the scenario file [11] and the score moves with them..

Because a benchmark is what makes any of this checkable, the lab releases RPO-Bench: a fixed set of capture and pose scenarios with fixed seeds, bit-identical in Node or in a browser, with reference baselines[11]. On capture, the optimal and the distilled controllers trade fuel against reliability against the hand-tuned baseline; on pose, the perspective-n-point estimator scores S_pnp on the SPEED metric against S_centroid for the naive centroid baseline, a factor of about N. Both absolute scores, and the seed that fixes them, are printed by RPO-Bench so the ratio has a stated floor rather than only a multiple.. The point is not the numbers but that anyone can reproduce them and try to beat them. The frontier laboratories have stronger methods and flight hardware; the contribution here is delivery: the learned-control and monocular-pose frontier made open, on-device, and verifiable.

8. Where does this leave the field?

The position is that space logistics and transportation should be organized around autonomy carried on the vehicle, because the estimation-and-control primitive that opens the tightest links is a single capability that composes across the whole chain, and because Δv and joules are the right units in which to price it. The efficiencies this direction offers are not incremental: composing the velocity budget moves the exponential of the rocket equation in the payload's favor, and destinations a single vehicle cannot reach at all become reachable when infrastructure carries most of the budget. New materials (high-strength tethers, multifunctional surfaces) enter the framework as parameters that change where a mode becomes buildable, not as the thing that gates the chain. And the optimization that matters is at the level of the network: composing modes into a chain and managing the flow of mass through it.

The report is equally clear about what it does not claim. It does not claim a fielded system or flight results; the instruments are computational, and their dynamics, where not exact mathematics, are illustrative. The benchmark of Section 7 is synthetic and reproducible, not a flight dataset, and the released policy flies the approach on representative dynamics, not certified flight software. It does not claim the per-segment Δv contributions as design values; they are representative. It does not claim novelty for the underlying astronautics or estimation, which are standard and cited. What it claims is organizational: that the links of the transport chain reduce to one estimation-and-control shape, that the shape is where autonomy is the enabling capability, and that building the shape once (provable, physically grounded, priced in Δv and joules, and run at the edge) is the way the space economy opens to many actors rather than few. That last claim is a position offered for test, and the released instruments and core are the first move in testing it.

9. Conclusion

Every link in the space-logistics chain is a velocity budget to be paid, and the rocket equation makes paying it alone exponentially expensive. Reusable, shared infrastructure and autonomous in-space transport pay the budget down, and the modes that do so (momentum-exchange tethers, electromagnetic launch, launch loops, and the on-orbit links of rendezvous, capture, servicing, and assembly) are, without exception, estimation-and-control problems carried on the vehicle. Because they share that shape, one autonomy stack, provable and priced in Δv and joules, serves the whole chain. The non-cooperative capture that is already operational in orbit is the clearest case and the report's centerpiece: a Kalman filter resolving a tumbling body's pose, a certified corridor held to a deadline, a latch that a human in the loop cannot make. The instruments and the open core make the framework runnable today; what remains is the work the report does not shortcut: fielding the stack, certifying it link by link, and measuring it against the budgets it is built to pay.

10. What would move this?

The binding constraint is delta-v, and the rocket equation makes paying it alone exponentially expensive. Every link in the chain is a velocity budget, and that is the whole economics of the subject: a budget that does not refill, priced by an exponential. Reusable shared infrastructure and autonomous in-space transport are ways of paying it down rather than ways of avoiding it, and the modes that do so (momentum-exchange tethers, electromagnetic launch, launch loops, and the on-orbit links of rendezvous, capture, servicing and assembly) are, without exception, estimation-and-control problems carried on the vehicle.

What would move it. That shared shape is the actionable part of this report: because the modes are one problem wearing different hardware, an autonomy stack that closes the loop for one is evidence about the others, and a demonstration should be read as buying down risk across the family rather than for a single mode. The quantity to publish per mode is therefore delta-v delivered per unit of mass carried, alongside the pointing and timing accuracy the control loop actually achieved. The second is what decides whether the first is repeatable.

References

1. K. E. Tsiolkovsky. Investigation of outer space by reaction devices (Изслѣдованіе мировыхъ пространствъ реактивными приборами). Nauchnoe Obozrenie, 1903. (The rocket equation.)
2. H. Moravec. A non-synchronous orbital skyhook. Journal of the Astronautical Sciences 25(4), 307–322, 1977.
3. R. P. Hoyt, C. Uphoff. Cislunar tether transport system. Journal of Spacecraft and Rockets 37(2), 177–186, 2000. doi:10.2514/2.3564. See also the HASTOL boost-tether study, Bogar et al., NASA Institute for Advanced Concepts, 2000.
4. K. H. Lofstrom. The launch loop: a low cost Earth-to-high-orbit launch system. AIAA/SAE/ASME/ASEE 21st Joint Propulsion Conference, AIAA-85-1368, 1985. doi:10.2514/6.1985-1368.
5. M. R. Doyle, D. J. Samuel, T. Conway, R. R. Klimowski. Electromagnetic aircraft launch system: EMALS. IEEE Transactions on Magnetics 31(1), 528–533, 1995. doi:10.1109/20.364638. (Electromagnetic launch feasibility.)
6. Astroscale Holdings. ADRAS-J: commercial rendezvous and proximity operations to a non-cooperative rocket upper stage (JAXA CRD2 Phase I). Mission reports, 2024–2025. astroscale.com/en/missions/adras-j.
7. Northrop Grumman / SpaceLogistics. Mission Extension Vehicle: on-orbit docking with client satellites in geostationary orbit (MEV-1, 2020; MEV-2, 2021). northropgrumman.com/what-we-do/space/space-logistics-services.
8. W. H. Clohessy, R. S. Wiltshire. Terminal guidance system for satellite rendezvous. Journal of the Aerospace Sciences 27(9), 653–658, 1960. doi:10.2514/8.8704.
9. R. E. Kalman. A new approach to linear filtering and prediction problems. Journal of Basic Engineering 82(1), 35–45, 1960. doi:10.1115/1.3662552.
10. Institute for Physical AI @ JBI, The Charlot Lab. Provable by Construction: on-device Lyapunov certificates for embodied control. Technical Report TR-2026-07, 2026.
11. Institute for Physical AI @ JBI, The Charlot Lab. Orbital Logistics: instrument suite, headless physics core, and RPO-Bench. github.com/dcharlot-physicalai-bmi/orbital-logistics, 2026.
12. G. Williams, A. Aldrich, E. A. Theodorou. Model predictive path integral control: from theory to parallel computation. Journal of Guidance, Control, and Dynamics 40(2), 344–357, 2017. doi:10.2514/1.G001921.
13. U.S. Naval Research Laboratory. Autonomous proximity operations by reinforcement learning: the first RL control of a free-flyer in space, demonstrated on the NASA Astrobee aboard the ISS, 2025.
14. M. Kisantal, S. Sharma, T. H. Park, D. Izzo, M. Märtens, S. D'Amico. Satellite pose estimation challenge: dataset, competition design, and results (SPEED). IEEE Transactions on Aerospace and Electronic Systems 56(5), 4083–4098, 2020. doi:10.1109/TAES.2020.2989063.
15. Institute for Physical AI @ JBI, The Charlot Lab. orbital-capture-bc: an on-device, behavior-cloned capture policy. Hugging Face, 2026. huggingface.co/physicalai-bmi/orbital-capture-bc.