Safe to Fly? Real-Time Flight Mission Feasibility Assessment for Drone Package Delivery Operations

Existing battery state prediction methods can be broadly categorized into two approaches: model-based and data-driven methods. Model-based approaches rely on physical models of the battery to predict key states, primarily future trajectories of terminal voltage and state of charge (SoC). These methods typically use either equivalent circuit models or electrochemical-based models, combined with estimators, to forecast battery states over time.

Equivalent circuit models represent the battery’s internal dynamics using electrical components such as resistors and capacitors. Common models include the Rint model, the RC model, and the Thévenin model [14]. These models simplify the battery’s behavior but still require parameter estimation and state estimation techniques for accurate predictions. In contrast, electrochemical-based models simulate the battery’s internal chemistry using porous electrode theory [15] and describe its dynamics through partial differential equations (PDEs). There are multiple versions of these models, varying in complexity depending on the target application, with the most widely used being [8] and [10]. While model-based methods offer high accuracy and interpretability, they require simulating complex, nonlinear battery models, making them computationally expensive and impractical for real-time in-flight applications.

To address this limitation, data-driven approaches have been developed. These methods use machine learning techniques to predict battery states with reduced computational cost. Among the most common are long short-term memory (LSTM) networks [5], support vector machines (SVM) [18], and fuzzy inference systems (FIS) [17]. Data-driven approaches are more computationally efficient [3], making them suitable for real-time applications such as in-flight battery state prediction. However, their accuracy tends to degrade as the prediction horizon increases, limiting their reliability for long-term planning applications.

The proposed framework aims to perform online battery state prediction for sUAS operations and assess mission feasibility. Several studies have explored similar goals. For instance, Shibl et al. [22] developed a battery management system for sUAS that employs deep neural networks (DNN) and LSTM networks to predict the SoC and the state of health (SoH). This system enhances battery monitoring and aids in mission planning based on the current battery state. Similarly, [4] proposed a method for assessing mission feasibility by considering battery performance and planning optimal routes to ensure successful mission completion. In another study, Shi et al. [20] introduced a cloud-based framework for the co-estimation of SoC and SoH, leveraging transformer-based deep learning techniques to provide accurate and real-time battery state predictions. Additionally, [21] explored a risk-aware approach for unmanned aerial vehicle and unmanned ground vehicle rendezvous planning using a chance-constrained Markov Decision Process. Their method accounts for the stochastic nature of energy consumption and optimizes rendezvous points to enhance mission feasibility and safety. Furthermore, Choudhry et al. [7] developed a deep energy model utilizing Temporal Convolutional Networks to predict energy consumption. They introduced a Conditional Value-at-Risk (CVaR) metric to assess the risk of battery depletion during flights, providing a framework for risk-aware mission planning and feasibility assessment.

However, none of these studies approach battery feasibility-based flight planning from the perspective of forecasting the future voltage trajectory. In contrast, our framework introduces a two-stage pipeline that first predicts the power consumption profile of the aircraft for the planned mission and then leverages a data-driven battery model to forecast the corresponding voltage trajectory. This approach enables a more realistic and forward-looking assessment of mission feasibility, unlike prior methods that rely solely on the current battery state or coarse approximations of future energy demands.

To determine the power required for future flight operations, the ideal approach would be to simulate the detailed aircraft dynamic model and collect the power required for future flight duration. However, since the detailed aircraft dynamic model is complex and highly nonlinear, doing so is computationally expensive. To address this challenge, we adopt a power consumption model for rotary-wing aircraft from [23]. This model is based on momentum theory and incorporates aerodynamic equations for each flight maneuver including, climb, hover, horizontal flight, and descent.

where $V_c$ and $V_d$ are vertical climb speed and vertical descent speed values, respectively. In addition, $\eta$ is the efficiency factor of the propulsion system, $\rho$ is the air density, $W$ is the total weight of the aircraft, and $A_t$ is the sum of the n-disc actuator areas. In addition, the instantaneous power for horizontal flight is given as:

where ${\alpha }_v$ is the angle of attack and ${\eta }_{\text{hor}}$ and the horizontal efficiency. In addition, the induced velocity in horizontal flight $v_{\text{hor}}$, is given by:

All the aircraft-related parameters mentioned in the equations above are given in Table 1.

The aircraft power consumption model outlined above provides the instantaneous power required by the aircraft during a given timestamp in a specific flight phase. However, to predict the power profile for each flight segment, we must also determine the duration of each segment. Here, we discuss the approach used to estimate the flight duration of each flight segment. During a climb or descent, the aircraft changes altitude at a constant speed, and the total time required to reach the desired attitude is given by:

where $h_{i+1}-h_i$ represents the altitude change and $V_{\text{climb}}$ or ($V_{\text{descend}}$) is the predefined climb (or descent) speed. Similarly, once the aircraft reaches cruising altitude, the aircraft moves with a constant horizontal velocity. The cruise time for a given segment is computed as:

where $d_i$ is the horizontal distance of the segment and $V_{\text{cruise}}$ is the predefined cruise speed. Finally, the overall flight power profile is obtained by concatenating the power profiles for the climb, cruise, and descent segments, each computed over its respective flight duration:

The current profile generation process produces two types of profiles: full-flight mission profiles and mid-flight constant profiles. Full-flight profiles capture both the takeoff and cruise phases of the aircraft operations, where the takeoff phase is characterized by a higher power demand, while the cruise phase exhibits a lower current draw. Mathematically, the generated current profile at time $t$, denoted as $I(t)$, is defined as:

where $I_{\text{takeoff}}\sim U(140,225)$ A and $I_{\text{cruise}}\sim U(50,70)$ A, with $U(a,b)$ denoting a uniform distribution. The takeoff duration, $T_{\text{takeoff}}$, is randomly sampled within the range $[1,10]$ seconds, ensuring variability in the generated profiles. Mid-flight profiles, on the other hand, are created by assigning the initial voltage at various points during a full-flight mission and applying a constant current profile from that point onward. This approach enables the evaluation of battery response under different initial conditions.

To simulate the voltage response corresponding to the generated current profiles, we employ an electrochemical battery model [8]. The simulation procedure involves initializing the battery state, iterating over the generated current profiles, and computing the corresponding voltage response. The resulting dataset consists of $1,000$ pairs of current and voltage trajectories and is systematically divided into training and test sets using a $70\%-30\%$ split. Each entry in the dataset comprises the input current trajectory $I(t)$, the corresponding voltage response $V(t)$, and the associated time horizon $T$. Figure 5 illustrates representative samples from the generated dataset, with current trajectories shown in blue and their corresponding voltage responses in black.

To ensure robust generalization across various scales of input data and to mitigate numerical instability during training, the input current and output voltage sequences are standardized using the training dataset’s mean and standard deviation. The model operates on normalized time in the range $[0,1]$ for each sequence.

Our Neural ODE model consists of two primary components: a neural network-based ODE function and an ODE solver. The ODE function is implemented as a fully connected feedforward neural network with three hidden layers, each employing ReLU activation functions, and outputs the derivative of the voltage. The network takes as input the initial battery voltage, the input current, and the time horizon, enabling it to learn a continuous-time differential equation that governs the voltage dynamics. This learned function is then integrated over time using a fourth-order Runge-Kutta (RK4) solver to generate the battery voltage trajectory. The model is trained using a composite loss function that combines mean squared error (MSE) and root mean squared error (RMSE) between the predicted and ground truth voltage values. After training, the model is evaluated on test current profiles to assess its accuracy in predicting voltage trajectories. The architectural and training hyperparameter details of the model are provided in Tables 3 and 3, respectively. These parameters were identified through a series of empirical experiments, where different configurations were systematically tested to achieve optimal trade-offs between model complexity, training efficiency, and predictive performance.

As discussed in Section 5.1, our package delivery scenario involves two main flight phases: one before the mid-flight incident and another after the incident. Before the mid-flight incident, the aircraft is executing the original flight plan which is from the warehouse to the assigned destination (referred to as “Long”). However, once the mid-flight incident is identified and the speed change is applied, the aircraft needs to assess the feasibility of the original flight plan with the newly updated speed and if it’s not feasible, identify the nearest emergency landing site from the already pre-defined set of locations and fly towards it while still performing the feasibility assessment at every 5 seconds.

Following the mid-flight incident, four alternative flight plans are considered, each corresponding to a potential landing site: the original destination and the three emergency landing sites. These include: (i) the flight plan to the original destination after the incident, which is expected to be infeasible and is labeled “Infeasible”; (ii) the flight plan to the nearest emergency landing site, labeled “Short”; and (iii) the flight plans to the other two emergency landing sites, labeled “EM1” and “EM3”, respectively.

Figure 7 presents a comparison between the actual aircraft power consumption profiles and the approximated power profiles for three flight plans: “Long”, “Infeasible”, and “Short”. These approximations are obtained using the method described in Section 3.1. Since the mid-flight incident requiring cruise speed reduction occurs at $288$ seconds, the second and third plots show the power profiles only for the remaining flight duration from the moment the speed reduction is applied. Furthermore, the lower three plots in Figure 7 compare the actual current profiles against those derived from the predicted power trajectories using the conversion technique outlined in Section 3.2. This analysis enables a direct evaluation of the prediction pipeline’s ability to infer current demands under altered flight conditions.

Because the reliability of our decision-making and contingency management framework heavily depends on the predictive accuracy of the power consumption model and the power-to-current conversion process, we evaluate the performance of these key components in Table 4. The table presents the results of 30 simulation runs for each of all flight plans. For each case, we report the average root mean squared error (RMSE) and mean absolute error (MAE) between the model-based reference approach and the method proposed in this paper. The results demonstrate that the proposed framework is capable of predicting both power and current profiles with reasonable accuracy.

Once the current profiles for the future flight duration at each timestep are obtained, they are fed into the trained data-driven battery model to predict the corresponding voltage trajectories. Figures 8 and 9 present the predicted voltage trajectories for all flight plans using the Neural-ODE-based approach, alongside the reference battery voltage trajectories generated by simulating the detailed battery model. For each voltage prediction shown in Figures 8 and 9, feasibility assessment is performed at 5-second intervals using the criterion described in Section 1. The minimum voltage threshold for mission feasibility is set at 18 V, meaning the predicted voltage trajectory must remain above this threshold throughout the entire operational time horizon for the mission to be considered safe.

As illustrated in Figure 8, the predicted voltage trajectory for the original flight plan remains above the 18 V threshold at all times and is therefore considered feasible – until the mid-flight incident occurs. However, as shown in the middle plot of Figure 8, once the incident triggers a reduction in cruise speed to 3 m/s, the voltage trajectory violates the threshold at approximately 680 seconds. This indicates that the aircraft can no longer safely complete its flight to the assigned destination. Consequently, the mission is rerouted to the emergency landing site, and feasibility is re-evaluated using the current profile for the short flight plan with the Neural-ODE-based battery model. The result, shown in the final plot of Figure 8, demonstrates that the revised mission remains feasible under the updated flight conditions, thereby ensuring the safety of the aircraft.

To provide a more comprehensive understanding of the mid-flight incident and the rationale behind the chosen contingency plan, Figure 9 presents the voltage predictions for the two alternative flight plans directed toward the other emergency landing sites (“EM1” and “EM3”). The results clearly demonstrate that both of these trajectories become infeasible, as the predicted battery voltage drops below the minimum operational threshold. This confirms the validity of the selected rerouting strategy to the nearest emergency landing site (“Short”).

Furthermore, Figure 10 offers a spatial visualization of the voltage predictions overlaid on the mission map. In this figure, each flight plan is illustrated using a heatmap that encodes predicted battery voltage along the flight trajectory. As shown, the battery begins fully charged at the warehouse, but following the mid-flight incident, the voltage predictions for all flight plans – except for the one directed to Emergency Landing 2 – fall below the critical threshold of $18\text{V}$ at some point along the trajectory. This spatial voltage analysis further reinforces the feasibility of the re-routing decision and highlights the framework’s efficacy in supporting real-time contingency management.

To evaluate the performance of the Neural-ODE-based battery model used for online feasibility assessment, we examine both its prediction accuracy and computational efficiency. For benchmarking purposes, we developed a physics-informed neural network (PINN) [19] based battery model, which is considered a state-of-the-art approach for learning battery dynamics. The PINN model implemented in this study combines a long short-term memory (LSTM) network with an equivalent circuit-based battery model adopted from [14]. This approach enhances the predictive capabilities of the data-driven LSTM by embedding physical laws – specifically, the voltage-current relationships described by the equivalent circuit – directly into the training process. Rather than relying solely on data, the PINN minimizes a composite loss function that penalizes both data mismatch and violations of the governing physical equations. This integration of domain knowledge improves model generalization, increases robustness to noise, and enables physically consistent predictions even in extrapolated conditions.

Figure 11 presents a comparison between the Neural-ODE and PINN-based approaches for the three flight plans. As shown in the left plot, the Neural-ODE-based model consistently outperforms the PINN model in terms of prediction accuracy across all predictions. These differences in prediction accuracy have important implications for the safety and efficiency of aircraft operations. Specifically, for the long flight plan, the PINN-based feasibility assessment would incorrectly classify the mission as infeasible due to its prediction inaccuracies. Conversely, in the case of the infeasible flight plan, the PINN model would fail to detect the voltage threshold violation, potentially resulting in an unsafe decision to proceed with the mission.

In addition to accuracy, computational efficiency is a critical factor, as the framework is intended for real-time use during flight, where computational resources are limited. To assess this, the right plot in Figure 12 shows the average computational time required to perform feasibility assessments for the three flight plans (Long, Infeasible, and Short), comparing the model-based approach with the proposed Neural-ODE approach. All experiments were conducted on a 3.20 GHz Intel Xeon(R) CPU with 125.4 GB of RAM. The results show that the proposed approach is approximately $36$ times faster than the model-based method in the long flight plan case, with a maximum computation time of 3.76 seconds. This demonstrates that the proposed framework is well-suited for in-flight operation, where feasibility assessments must be performed every 5 seconds.