EPDS: Energy-Predictive Drone Service

• EPDS is a predictive drone delivery framework that integrates energy forecasting with route planning, recharge scheduling, and service composition on directed skyway graphs.
• It leverages adaptive Bi-LSTM models to estimate per-segment energy use, enabling proactive management of charging pad reservations and reduced node congestion.
• Empirical studies demonstrate that EPDS can reduce average delivery times by up to 16% compared to traditional A* and Dijkstra-based routing methods.

Energy-Predictive Drone Service (EPDS) is a drone-delivery framework in which routing, recharge scheduling, and service composition are driven by explicit prediction of energy use and node availability rather than by geometric shortest paths alone. In its formalized form, the operating environment is a directed skyway graph $G=(V,E)$ whose nodes are rooftop takeoff, landing, and recharging points; a single-segment EPDS is composed into an EPDS Composite Service (ECS) for longer requests; and a central smart control center uses telemetry-derived prediction to estimate per-segment energy consumption, recharging demand, and the arrival-related states of other drones so as to reduce recharging station congestion and total delivery time (Ren et al., 3 Aug 2025).

1. Conceptual lineage and scope

EPDS emerges from a convergence of three research strands: energy-aware mission planning, service composition in skyway networks, and predictive congestion management. Earlier work on autonomous drone mission planning modeled energy expenditure with a machine-learning predictor and cast flight planning with recharging as a multi-criteria Asymmetric Traveling Salesman Problem, where the objective was the time-optimal, energy-feasible tour with refueling decisions and real-time re-computation (Alyassi et al., 2017). A later line of work introduced a two-level, constraint-aware service-composition framework for swarm-based delivery with in-flight wireless energy sharing, explicitly treating energy as a non-functional attribute and composing both Swarm-based Drone Services and Energy-as-a-Service within each route segment (Alkouz et al., 2022).

Study	Core capability	Relevance to EPDS
"Autonomous Recharging and Flight Mission Planning for Battery-operated Autonomous Drones" (Alyassi et al., 2017)	ML-based energy estimation, recharging optimization, real-time replanning	Prefigures energy-feasible mission planning
"In-Flight Energy-Driven Composition of Drone Swarm Services" (Alkouz et al., 2022)	Two-level service composition with in-flight energy sharing	Establishes energy as a first-class service constraint
"Energy-Predictive Planning for Optimizing Drone Service Delivery" (Ren et al., 3 Aug 2025)	Formal EPDS model, adaptive Bi-LSTM prediction, proactive pad reservation	Canonical EPDS formulation

Within this lineage, EPDS denotes more than an energy estimator attached to a route planner. It is a service architecture in which prediction is operationalized: forecasts alter takeoff times, reserve charging pads through pred_recharging states, and reshape composite services online. This distinguishes EPDS from classical shortest-path routing and from static recharge-planning formulations.

2. Formal service model and state representation

The canonical EPDS formulation models the skyway network as a directed graph $G=(V,E)$. Each node is represented as

$N=\langle N_{id}, N_{status}, Neighbors \rangle,$

where

$$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$

pred_recharging denotes proactive reservation based on predicted energy and recharge needs. An individual segment-level service is defined as

$EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$

where $EPDS_f$ includes $\langle Loc_{src}, Loc_{des}\rangle$, a voltage sequence $\langle V_0,\ldots,V_n\rangle$ sampled every $100$ ms, and time attributes $\langle T_{src}, T_{flight}, T_{des}\rangle$. A delivery request is

$G=(V,E)$0

with source $G=(V,E)$1, destination $G=(V,E)$2, and payload weight $G=(V,E)$3. Longer missions are represented as

$G=(V,E)$4

where Path is the node chain $G=(V,E)$5, and each $G=(V,E)$6 corresponds to one segment $G=(V,E)$7 (Ren et al., 3 Aug 2025).

The drone state is explicitly energy-centric. For drone $G=(V,E)$8 at time $G=(V,E)$9,

$N=\langle N_{id}, N_{status}, Neighbors \rangle,$0

where $N=\langle N_{id}, N_{status}, Neighbors \rangle,$1 is current node or edge position, $N=\langle N_{id}, N_{status}, Neighbors \rangle,$2 is battery state represented via voltage $N=\langle N_{id}, N_{status}, Neighbors \rangle,$3, $N=\langle N_{id}, N_{status}, Neighbors \rangle,$4 is payload mass, $N=\langle N_{id}, N_{status}, Neighbors \rangle,$5 captures remaining segments, $N=\langle N_{id}, N_{status}, Neighbors \rangle,$6 is station queue state, $N=\langle N_{id}, N_{status}, Neighbors \rangle,$7 is the fixed cruise speed and current altitude setting, and $N=\langle N_{id}, N_{status}, Neighbors \rangle,$8 denotes wind speed and direction. Recharging-station congestion is separately encoded as

$N=\langle N_{id}, N_{status}, Neighbors \rangle,$9

capturing overlapping requests, their energy predictions, and full recharge time. In the experiments associated with the canonical EPDS paper, drones use a fixed cruise speed $$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$0, altitude is set according to the rooftop elevation of the next node, vertical ascent and descent occur only at nodes, and intermediate-node charging is modeled as full recharge rather than partial charging (Ren et al., 3 Aug 2025).

This state design is significant because it collapses mission planning, queue prediction, and battery feasibility into a single control loop. A route is therefore not merely a sequence of edges but a coupled sequence of flight segments, recharge events, and queue interactions.

3. Predictive energy modeling and telemetry learning

The central predictive element in EPDS is an adaptive bidirectional Long Short-Term Memory model trained on high-frequency telemetry. Segment energy is obtained by predicting battery voltage, mapping voltage to current through a learned linear function, and integrating current over time: $$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$1 In continuous form the same quantity is written as

$$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$2

The predictive input vector includes time $$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$3, position $$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$4, flight dynamics $$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$5, voltage $$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$6, wind speed and direction, cumulative distance Dis, Loc_role (start, fly, destination), drone ID, node ID or name, and the input and prediction window sizes $$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$7 and $$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$8. The output is a predicted voltage sequence $$N_{status}=\langle T_{start}, T_{end}, Status \rangle,\quad Status\in\{recharging,\ pred\_recharging\}.$$9, subsequently converted to current and integrated into predicted energy consumption $EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$0 at the next node (Ren et al., 3 Aug 2025).

The recurrent model uses standard LSTM gating: $EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$1

$EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$2

$EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$3

with bidirectional hidden-state concatenation

$EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$4

Training uses MSE on voltage sequences, with RMSE as the main evaluation metric. Hyperparameters explored include hidden size $EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$5, learning rate $EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$6, input length $EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$7, and prediction length $EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$8. A model is trained “at each node” to capture local conditions and recharging context. Variable-length prediction is handled by chained prediction and clipping, and the controller delays prediction until a fraction of the segment, such as $EPDS=\langle EPDS_{id}, EPDS_f, EPDS_q\rangle,$9, has been flown so as to improve accuracy before updating $EPDS_f$0 (Ren et al., 3 Aug 2025).

Broader energy-modeling literature helps situate this predictive layer. A comparative study of five analytical drone-energy models and an LSTM predictor found that the LSTM attained $EPDS_f$1 and $EPDS_f$2, outperforming D’Andrea, Dorling, Stolaroff, Kirchstein, and Tseng models on the studied delivery dataset (Muli et al., 2022). A separate empirical model based on 187 quadcopter flights segmented missions into takeoff, cruise, and landing and reported approximately $EPDS_f$3, $EPDS_f$4, and $EPDS_f$5 of $EPDS_f$6 per package for a small electric quadcopter with a $EPDS_f$7 payload in the United States, showing that regime-specific prediction remains relevant when EPDS is extended beyond node-to-node congestion management (Rodrigues et al., 2021).

A common misconception is that EPDS is reducible to battery-voltage forecasting. In the formal framework, prediction is not an end in itself: forecasted energy is translated into recharge duration, pad occupancy intervals, and node-reservation states, and these predicted states are then used to alter takeoff schedules and path composition.

4. Optimization, composition, and scheduling logic

The optimization problem addressed by EPDS is to minimize average delivery time across active composite services by jointly accounting for flight, waiting, and recharge durations. For initial composition, the canonical planner uses an A*-like heuristic

$EPDS_f$8

where $EPDS_f$9 is Euclidean distance and $\langle Loc_{src}, Loc_{des}\rangle$0 is a coarse energy estimate without wind or payload. After path selection, the control center sorts ECS requests by FCFS priority, predicts energy over current segments, estimates recharge time at the next node, updates $\langle Loc_{src}, Loc_{des}\rangle$1 and $\langle Loc_{src}, Loc_{des}\rangle$2, and then reschedules waiting drones’ takeoff times to avoid overlapping arrivals (Ren et al., 3 Aug 2025).

In a related service-composition formulation, delivery is modeled as a nested optimization over path and in-flight energy support. The total delivery time is written as

$\langle Loc_{src}, Loc_{des}\rangle$3

with

$\langle Loc_{src}, Loc_{des}\rangle$4

An enhanced A* maintains a state

$\langle Loc_{src}, Loc_{des}\rangle$5

and expands actions that include movement to neighboring nodes, node charging under pad-capacity constraints, and local formation reordering for wireless transfer feasibility (Alkouz et al., 2022).

Under varying wind, a complementary formulation models the mission as a cycle on a time-dependent cost graph $\langle Loc_{src}, Loc_{des}\rangle$6, where edge energies are revealed only when a drone reaches a new vertex. The actual cost of a path $\langle Loc_{src}, Loc_{des}\rangle$7 starting at $\langle Loc_{src}, Loc_{des}\rangle$8 is

$\langle Loc_{src}, Loc_{des}\rangle$9

and mission outcomes are categorized as Success, Delivered-only, Failure, or Canceled depending on whether outbound and return costs fit within battery budget $\langle V_0,\ldots,V_n\rangle$0. This formulation is directly relevant to EPDS because it formalizes online replanning under incomplete knowledge of future edge costs (Sorbelli et al., 2020).

The practical significance of these formulations is that EPDS is not equivalent to shortest-path planning. The canonical experiments explicitly compare EPDS against A* and Dijkstra baselines and treat station contention as a first-order scheduling variable rather than as a post hoc delay.

5. In-flight energy support and emergency replenishment

A broader EPDS literature extends predictive planning with explicit in-flight energy support. In the swarm-composition framework, delivery drones $\langle V_0,\ldots,V_n\rangle$1 are assisted by support drones $\langle V_0,\ldots,V_n\rangle$2 whose sole purpose is to recharge other drones during flight. The skyway graph is $\langle V_0,\ldots,V_n\rangle$3; delivery drones in the reported experiments use $\langle V_0,\ldots,V_n\rangle$4 batteries; support drones carry extra batteries with capacity approximately $\langle V_0,\ldots,V_n\rangle$5; the wireless power-transfer rate is $\langle V_0,\ldots,V_n\rangle$6; and transfer is feasible only when inter-drone separation is within $\langle V_0,\ldots,V_n\rangle$7. Two sharing policies are defined. The Priority-based method orders requests by earliest start time and then by larger requested energy, whereas the Fairness-based method allocates fixed slices $\langle V_0,\ldots,V_n\rangle$8 in round-robin order. The same framework also defines two positioning settings: location-aware, which places heavier delivery drones in energy-favorable positions and support drones in worse positions, and energy-aware, which instead places support drones in energy-favorable positions to maximize the available energy budget for sharing (Alkouz et al., 2022).

Within that model, in-flight transfer obeys

$\langle V_0,\ldots,V_n\rangle$9

and in discrete form

$100$0

These constraints make clear that in-flight replenishment is highly structured: one provider serves one consumer at a time, proximity must be maintained, and local reordering may be required to bring the requesting drone within range.

A distinct but related line of work replaces wireless transfer with physical mid-air battery exchange. In the AeroBridge Emergency Battery Service, an EBS drone receives an “emergency energy” request, flies to the receiver’s GPS waypoint, switches to Cross Marker Position localization within about $100$1, and performs a diagonal docking with approximately $100$2 vertical separation. The validated system uses a D455 depth camera, CMP fiducials, 45° slides, and diagonal alignment to minimize downwash. CFD and experiments support the choice of diagonal rather than perpendicular alignment, and the reported system achieves position lock with up to $100$3 accuracy, orientation deviation below $100$4, and successful mid-air transfer in $100$5, with outdoor trials reported at winds up to $100$6 (Seth et al., 2024).

These two replenishment mechanisms serve different operational roles. Wireless energy sharing is tightly integrated with route composition and formation control, whereas emergency battery handoff functions as a field-service layer that can rescue or extend a mission outside the fixed node-and-pad infrastructure. The available evidence suggests that both can be treated as EPDS-compatible service primitives rather than mutually exclusive architectures.

6. Empirical evidence, performance, and tooling

The main empirical EPDS study evaluates the framework on 70 flights using three Crazyflie 2.1 nano quadcopters in an indoor 3D-modeled CBD skyway network with rooftops as nodes. Telemetry is sampled every $100$7; wind conditions include none, $100$8, and $100$9 with directions N/S/E; recharging is wireless; a full recharge threshold of $\langle T_{src}, T_{flight}, T_{des}\rangle$0 is used; and the empirical 7-node network is augmented to 36 nodes by cosine-similarity mapping and distance scaling. On this setup, Bi-LSTM with Vbat achieved $\langle T_{src}, T_{flight}, T_{des}\rangle$1, outperforming RNN with Vbat ($\langle T_{src}, T_{flight}, T_{des}\rangle$2), Bi-LSTM with all features ($\langle T_{src}, T_{flight}, T_{des}\rangle$3), and Bi-LSTM with all features (PCA) ($\langle T_{src}, T_{flight}, T_{des}\rangle$4). The planner reduced average delivery time by approximately $\langle T_{src}, T_{flight}, T_{des}\rangle$5 over A* and Dijkstra baselines, and by approximately $\langle T_{src}, T_{flight}, T_{des}\rangle$6 in long-distance and fast-recharge scenarios (Ren et al., 3 Aug 2025).

A complementary swarm-composition study evaluates 10,000 synthetic delivery requests on an urban road-network subset used to mimic a skyway, with a largest connected subgraph of 195 nodes. Reported drone parameters include DJI Phantom 3, $\langle T_{src}, T_{flight}, T_{des}\rangle$7 battery, speed $\langle T_{src}, T_{flight}, T_{des}\rangle$8, $\langle T_{src}, T_{flight}, T_{des}\rangle$9 maximum package, wireless transfer rate $G=(V,E)$00, and support-drone capacity approximately $G=(V,E)$01 delivery capacity. Baseline success without in-flight sharing is $G=(V,E)$02, compared with $G=(V,E)$03 for Floyd–Warshall and $G=(V,E)$04 for Dijkstra. The study also reports that location-aware positioning generally yields higher success counts than energy-aware positioning, with one combined-scenario example of $G=(V,E)$05 versus $G=(V,E)$06 successful deliveries, while Priority-based sharing is faster than Fairness-based sharing (Alkouz et al., 2022).

Study	Experimental setting	Selected findings
(Ren et al., 3 Aug 2025)	70 flights; three Crazyflie 2.1; 7-node and 36-node skyway networks	Bi-LSTM with Vbat RMSE $G=(V,E)$07; average delivery time reduced by $G=(V,E)$08; $G=(V,E)$09 gain in long-distance fast-recharge scenarios
(Alkouz et al., 2022)	10,000 synthetic requests; 195-node connected subgraph; DJI Phantom 3 parameters	Baseline $G=(V,E)$10 successful; Floyd–Warshall $G=(V,E)$11; Dijkstra $G=(V,E)$12; PB faster than FB
(Seth et al., 2024)	Indoor and outdoor validation of battery handoff	$G=(V,E)$13 mid-air transfer; CMP accuracy $G=(V,E)$14; stable at $G=(V,E)$15 separation and up to $G=(V,E)$16 wind

The EPDS ecosystem also includes simulation and data-generation infrastructure. An immersive 3D Drone-as-a-Service simulator provides Edit Mode for constructing skyway networks with buildings, rooftop nodes, and waypoints, and Runtime Mode for executing non-deterministic scenarios while exchanging node-by-node updates between a Unity front end and a Python back end. The simulator uses a Kirschstein-based energy model, displays drone battery percentage and segment lengths in runtime, exports trip CSV logs containing energy consumption, battery levels, node dwell times, and segment travel times, and stores network configurations as JSON, making it suitable for EPDS benchmarking and dataset generation (Lin et al., 2023).

7. Assumptions, limitations, and contested points

EPDS research remains constrained by simplifying assumptions. In the canonical predictive-planning study, queueing is not modeled stochastically, FCFS allocation is assumed at stations, cruise speed is fixed, vertical flight occurs only at nodes, drones fully recharge at intermediate nodes, and stochasticity is represented primarily through prediction error and confidence intervals rather than through a fully stochastic queueing or airspace model (Ren et al., 3 Aug 2025). In the swarm energy-composition literature, environments are often deterministic after composition, swarm size is static, formation geometry is fixed globally, reordering is assumed to have negligible time and energy cost, transfer efficiency is treated as constant, and only one provider-to-one-consumer transfer is allowed at a time (Alkouz et al., 2022). Emergency battery handoff work adds further caveats: electrical hot-swap connectors were not implemented in the reported system, scaling beyond the tested battery sizes remains open, and marker detection can degrade under glare, rain, or occlusion (Seth et al., 2024).

Several recurring misconceptions follow from these assumptions. First, EPDS is not simply “A* plus a battery model.” The defining feature is proactive control over shared infrastructure: node states are predicted, pads are reserved as pred_recharging, and departures are staggered to avoid congestion. Second, EPDS is not synonymous with in-flight recharging. The canonical 2025 formulation uses predictive reservation and composite scheduling without requiring airborne energy transfer, whereas support-drone sharing and emergency battery replacement are extensions that broaden the service envelope. Third, the strong performance of voltage-only Bi-LSTM prediction in one study does not settle the question of universally optimal feature design. The same literature still treats wind, payload, formation, and station context as operationally essential, and outdoor generalization, mixed fleets, battery degradation, and regulatory constraints remain unresolved.

The stated future directions are correspondingly broad. Proposed extensions include richer optimization such as mixed-integer programming for time windows and pad capacities, federated learning across providers, robust or chance-constrained planning under uncertain wind, battery health and degradation models, dynamic replanning under deviations, adaptive formation selection, digital twins for aerodynamic validation, collision-aware reordering, and integration of outdoor weather feeds and broader regulatory constraints such as BVLOS and geofencing (Ren et al., 3 Aug 2025). This suggests that EPDS is best understood not as a closed algorithmic recipe but as a systems framework in which prediction, energy-aware optimization, infrastructure coordination, and contingency energy services are progressively being unified.