Cargo: Representations and Transport Dynamics

• Cargo is defined as a transported load whose representation varies from a physical body to an abstract planning entity across scales and domains.
• Research reveals that cargo actively influences transport through stochastic force balance, elastic interactions, and density-based modeling.
• Engineered systems and logistics optimize cargo handling by integrating advanced sensing, cooperative control, and environmental adaptations.

Cargo denotes a transported load or object whose scientific treatment depends on scale, carrier, and operational environment. In the cited literature, cargo ranges from intracellular vesicles, organelles, endosomes, mRNA particles, viruses, and multivalent particles, to spherical microparticles, parcels, coal stockpiles, lunar payloads, and radiographically inspected freight. Across these settings, cargo is not merely the passive endpoint of transport. It is represented as a coupled dynamical body, a geometric or probabilistic state, a planning entity in a logistics network, or a monitored asset whose movement, concealment, damage, and delivery all enter the model explicitly (Miles et al., 2016, Belov et al., 2015, Jaccard et al., 2016).

1. Representations of cargo across domains

A recurrent distinction in the literature is between cargo as a physical body and cargo as an abstract planning or inference object. In multivalent transport, the cargo center is defined as the average of the currently bound leg positions,

$x_a(t)=\frac{1}{n}\sum_{l=1}^{n}x_l,$

with an equivalent force-balance form for spring-like linkers (Mosby et al., 2021). In mean-field intracellular transport, cargo can instead be reduced to a stochastic degree of freedom, or even to a single “characteristic distance” that proxies net force and mean velocity (Miles et al., 2016).

In robotic transport without prior object knowledge, a detected cargo is not represented by a precomputed geometric model. It is represented by an evolving density field $\phi(\boldsymbol q,t)$ built from the positions of agents that have locally detected the object, and the swarm minimizes a density-weighted locational cost over Voronoi cells (Song et al., 22 Feb 2026). In a reconfigurable parcel drone, by contrast, the parcel becomes the drone’s body, while propulsion modules and a central computation module are attached directly to the parcel perimeter (Schiano et al., 2022). In lunar logistics, the rover is required only to deliver its load within a tight relative tolerance because the payload is assumed to be “smart cargo,” with its own actuation and sensing for final placement (Krawciw et al., 6 Jan 2026).

In freight systems, cargo is often an allocative object rather than a mechanically modeled body. In the Hunter Valley Coal Chain, cargoes are customer-specific blended stockpiles assembled in a stockyard from coal delivered by train and then reclaimed in a prescribed order onto vessels (Belov et al., 2015). In urban logistics, parcel cargo becomes a request stream inserted into passenger Mobility-on-Demand schedules under quality-of-service constraints (Alho et al., 2020). A plausible implication is that “cargo” functions as a unifying term for transported value, but the mathematically relevant state variables vary sharply across biophysics, robotics, and logistics.

Domain	Cargo representation	Representative work
Intracellular transport	Center of bound legs; characteristic distance; elastic body	(Mosby et al., 2021, Miles et al., 2016)
Robotics and autonomy	Density field; parcel-as-body; smart cargo	(Song et al., 22 Feb 2026, Schiano et al., 2022, Krawciw et al., 6 Jan 2026)
Logistics and inspection	Stockpile, parcel request, monitored shipment	(Belov et al., 2015, Alho et al., 2020, Jaccard et al., 2016)

2. Cargo as an active dynamical element in intracellular transport

Several papers reject the notion that cargo is merely a passive load. In a mean-field tug-of-war model with oppositely directed motors, bidirectional switching can arise from cargo diffusion alone rather than from discrete motor-number fluctuations. The cargo obeys a stochastic force balance with drag $\gamma$, thermal forcing, and motor forces, and the reduced dynamics become metastable with switching between distinct directional transport states driven by thermal cargo diffusion (Miles et al., 2016). The same study predicts a non-monotonic dependence of switching time on cargo drag and reports switching times on the order of $\sim 0.5\,\mathrm{s}$.

A distinct minimal model introduces “least memory,” in which cargo remembers only the direction of its immediately previous step. At each lattice location the cargo occupies a plus-state $n^+$ or minus-state $n^-$, and this directional persistence produces long runs under constant load and oscillation in a fixed optical trap (Zhang, 2012). In the trap, the oscillation period decreases and the oscillation amplitude increases with the motor forward step rates, whereas both decrease with trap stiffness. The most likely cargo location may coincide with the trap center, differ from it, or bifurcate into two most likely locations when motors are sufficiently robust.

Elastic multi-motor models add a further layer of cargo-mediated interaction. In the “spider-like” model, each motor is a bead-spring system attached tightly to the cargo, the cargo position is set by force balance, and motors therefore do not share external load equally (Zhang, 2010). The paper concludes that the stall force of cargo usually decreases with interactions between motors. For several motors of the same species, the cargo stall force is bigger than that of the single motor but usually smaller than their sum; for opposite-direction motors it can be bigger or smaller than the difference of the two single-motor stall forces.

Environmental control also acts through the cargo. A stochastic mechanochemical model with explicit elastic coupling shows that cargo bias can be controlled or even reversed by varying the effective external load through viscosity or by changing ATP concentration (Klein et al., 2014). Under the baseline parameter set, short-time cargo variance is superdiffusive, with $\mathrm{var}[x_C(t)] \sim t^{1.5}$, indicating time-correlated motion induced by cargo-mediated motor cooperation. This complements the result that the widely used constant-force approximation can substantially overestimate the variance of motor progress: with explicit diffusive cargo, the low-diffusivity regime yields a more permissive precision law,

$\frac{\sigma_n^2}{\mu_n}=\frac{2}{\Delta G},$

independent of the number of stages in the motor cycle (Brown et al., 2018). A common misconception is therefore that replacing cargo by a constant opposing force is generically innocuous; the cited work argues that this approximation may be misapplied when cargo diffusion and elastic relaxation dominate the fluctuation structure.

3. Cargo under binding landscapes, confinement, and crowding

Another line of work studies cargo motion as an emergent drift–diffusion process produced by binding and unbinding asymmetries. For multivalent cargo with $N$ transient interaction sites, position-dependent binding and unbinding rates generate an effective diffusivity $D_{\mathrm{eff}}(x)$ and drift velocity $\phi(\boldsymbol q,t)$0. The central result is that cargo moves in the direction of increasing binding rate and decreasing unbinding rate (Mosby et al., 2021). In the continuum description,

$\phi(\boldsymbol q,t)$1

and for small cargo the leading binding-driven contribution scales as $\phi(\boldsymbol q,t)$2. The same framework extends to two dimensions, where the effective velocity retains the same directional dependence.

Confinement changes the same transport cycle in a qualitatively different way. In a corrugated channel model, a motor-cargo complex alternates between an active bound state moving with constant velocity $\phi(\boldsymbol q,t)$3 and a passive unbound state that feels an entropic barrier through a Fick–Jacobs reduction (Dey et al., 2017). Confinement generally reduces effective diffusivity and average velocity, produces an intermediate subdiffusive regime in the mean-squared displacement, and can sharpen a locked-to-running transition. However, the paper also identifies an exception: if confinement increases the average rebinding rate, then the average cargo velocity can exceed the unconfined mean-field value. This suggests that geometry can either hinder or enhance transport depending on how it modulates switching kinetics.

Crowding can likewise be ambivalent. A cargo that can associate at most $\phi(\boldsymbol q,t)$4 free motors already present on the track experiences two competing effects: crowded sites obstruct forward motion, but occupied sites can also be converted into additional cargo-bound motors (Mukherji et al., 2023). For $\phi(\boldsymbol q,t)$5 and $\phi(\boldsymbol q,t)$6, the peak in run-length with free motor density is governed by the largest eigenvalue of the transition matrix describing cargo dynamics. When free motors are processive and also bind and unbind from the microtubule, the same non-monotonic run-length pattern persists, though the peak height and location shift. A plausible implication is that “traffic” is not purely inhibitory when cargos can recruit motors during translocation.

4. Engineered cargo transport: swarms, cells, drones, and lunar rovers

Engineered systems often recast cargo handling as an autonomy problem with incomplete information. A decentralized cooperative-transport framework for $\phi(\boldsymbol q,t)$7 mobile agents in a bounded workspace $\phi(\boldsymbol q,t)$8 assumes no prior knowledge of cargo number, position, size, or shape (Song et al., 22 Feb 2026). Local detections activate Gaussian components in a density field, the swarm minimizes

$\phi(\boldsymbol q,t)$9

and nominal motion is given by $\gamma$0. A Control Barrier Function layer enforces pairwise spacing through $\gamma$1 and a quadratic program. In the main simulation, two cargos of different sizes are transported simultaneously, with five agents around the smaller cargo and seven around the larger one. The paper is explicit that symmetric enclosure is emergent from CVT balancing plus pairwise spacing constraints; there is no dedicated angular-spacing controller and no proof of optimal team size convergence.

At a smaller physical scale, a single Dictyostelium discoideum cell can act as a “cellular truck” for spherical cargo particles (Panah et al., 2023). For radii $\gamma$2, the mean transport speed is approximately constant for $\gamma$3,

$\gamma$4

while the mean inferred force rises from $\gamma$5 at $\gamma$6 to $\gamma$7 at $\gamma$8. A linear extrapolation of contact-point speed predicts a stall radius $\gamma$9 with $\sim 0.5\,\mathrm{s}$0 interval $\sim 0.5\,\mathrm{s}$1, and the polarization rate $\sim 0.5\,\mathrm{s}$2 extrapolates to zero at about $\sim 0.5\,\mathrm{s}$3. Under external flow, however, the same cell–cargo systems can resist a wall-corrected drag of about $\sim 0.5\,\mathrm{s}$4, indicating strong mechanoresponsive adaptation.

Aerial cargo transport can invert the usual payload–airframe relation. In a reconfigurable multicopter, the parcel itself becomes the drone’s body and propulsion modules are attached to its edges (Schiano et al., 2022). Configuration generation uses viability constraints $\sim 0.5\,\mathrm{s}$5 and $\sim 0.5\,\mathrm{s}$6, and scores feasible morphologies by

$\sim 0.5\,\mathrm{s}$7

Indoor trajectory tracking over four parcel morphologies yielded average RMSE of approximately $\sim 0.5\,\mathrm{s}$8 cm in $\sim 0.5\,\mathrm{s}$9, $n^+$0 cm in $n^+$1, and $n^+$2 cm in $n^+$3. The paper also identifies a limitation: elongated morphologies with fewer propulsion modules can have weak yaw authority and worse outdoor wind sensitivity.

Lunar cargo transport emphasizes repeatability over exploration. A one-tonne path-to-flight rover used Lidar Teach and Repeat to move a $n^+$4 kg cargo between known locations in a two-week field test (Krawciw et al., 6 Jan 2026). Cargo pickup required $n^+$5 cm longitudinal and $n^+$6 cm lateral positioning, with only 20 cm of cab-to-cargo clearance. At the habitat interface, the delivered cargo ended $n^+$7 m from the habitat with $n^+$8 m lateral offset. The semi-autonomous forward mission took $n^+$9, whereas the autonomous repeat of the same route took $n^-$0. Burnett et al. are cited in the localization stack for the robust ICP variant used during repeat traversals.

5. Cargo in logistics, distribution, and smart shipping

In large logistics systems, cargo becomes a unit of planning under spatial, temporal, and infrastructure constraints. In the Hunter Valley Coal Chain, each arriving vessel induces one or more customer-specific cargoes assembled as stockpiles in a stockyard, then reclaimed and loaded onto the vessel in a predetermined sequence (Belov et al., 2015). The stockyard is modeled as a one-dimensional spatial resource over time, and the objective is to minimize total vessel delay,

$n^-$1

The paper formulates pad occupancy, stacking throughput, reclaimer travel, berth capacity, shiploader concurrency, tidal departures, and channel usage in MiniZinc, and compares a rolling-horizon CP/LNS approach with adaptive greedy heuristics. It reports that the optional “ship loading capacity” constraint, modeled as $n^-$2, is one of the strongest experimentally.

For same-day parcel distribution, cargo-hitching uses spare capacity in passenger transport modes. A Singapore simulation of Mobility-on-Demand cargo-hitching evaluates a fleet of 17,900 MoD vehicles against 67,000 same-day parcel requests and 576,786 daily MoD passenger trips (Alho et al., 2020). In the Shared-only scenario about 34,000 parcel requests are fulfilled; in Shared+Idle and Shared+Restricted Idle, about 67,000 are fulfilled. Passenger impacts remain modest but measurable: shared-ride requests served fall by 1–2%, peak travel time rises from 22.5 min to 22.9–23.3 min, and total VKT decreases by about 2%. The main trade-off is that protecting passenger quality of service in peak periods can sharply worsen parcel waiting times, especially in the PM peak.

Large-scale cargo distribution can also be decomposed algorithmically. A graph-based approach for cross-border logistics represents infrastructure with OpenStreetMap-derived shortest-path graphs, partitions the graph by spectral clustering, and computes regional plans with Tabu search (Stopar et al., 2020). The method scales to 10,000 nodes and reports a 91% time saving on 10k-node graphs, while solution quality improves by 23% to 40% relative to the full-graph Tabu baseline. The stated drawback is that the regional decomposition does not generate inter-region routes.

A distinct recent use of the word appears as the acronym CARGO, “Carbon-Aware Gossip Orchestration,” in smart shipping (Kalafatelis et al., 29 Mar 2026). There, vessels train predictive-maintenance models without a central server, and a control plane decides each round’s active vessels, active edges, compression policy, and recovery flag:

$n^-$3

Activation scores

$n^-$4

combine learning utility, carbon-cost proxy, and fairness penalty. The data plane uses compressed gossip with error feedback, while the control plane adapts participation and connectivity under dropout, packet loss, and multiple connectivity regimes. The evaluation reports that CARGO remains in the high-accuracy regime while reducing carbon footprint and communication overheads compared with accuracy-competitive decentralized baselines.

6. Inspection, integrity monitoring, and concealed cargo

Cargo research also addresses whether freight has been misdeclared, concealed, mishandled, or damaged. In high-energy radiographic inspection, concealed-car detection is treated as a sliding-window image-classification problem over single-view cargo X-ray images from a Rapiscan Eagle R60 rail scanner with a 6 MV linear accelerator source (Jaccard et al., 2016). The dataset contains 79 car images with 192 individual cars, and image sizes range from $n^-$5 to $n^-$6 pixels. A trained-from-scratch 18-layer CNN using FC1 features and a Random Forest classifier achieves 100% car image classification at a false positive rate of 0.22%, or about 1 in 454 non-car images. Cars that were partially or completely obscured by other goods were correctly detected, and the paper argues that this performance is suitable for deployment in the field.

Damage detection in transit can be pushed into low-cost IoT monitoring. A scalable architecture for cargo-loss investigation divides the system into hardware, data, ingestion, and presentation layers, centered on an accelerometer-based tracking device with cellular backhaul (Gupta et al., 2022). The core calibration relation is

$n^-$7

where $n^-$8 is impact in g-force units, $n^-$9 is a case-specific calibration constant, and $\mathrm{var}[x_C(t)] \sim t^{1.5}$0 are raw accelerometer readings. Firmware records only threshold-crossing impact events, and scheduled cloud uploads extend battery life from a few days to up to a year; in the reported deployment, after about 4 months the device still had around 30% battery remaining. The case evidence indicated that land legs produced more severe impacts than sea transport. The paper cites estimates that the global financial impact of cargo loss exceeds $50 billion annually, framing visibility into transit conditions as a practical route to mitigation.

A plausible synthesis across inspection papers is that cargo integrity now spans two complementary observational regimes: non-intrusive sensing of hidden content and continuous sensing of in-transit handling. The former asks whether the declared object is present; the latter asks whether the object was subjected to damaging conditions.