BC-NMPC: Battery-Constrained NMPC with Propulsion Prediction and Replanning for High-Speed Flight

arXiv:2607.23867 · cs.RO, cs.SY, eess.SY · Submitted 2026-07-26 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "BC-NMPC: Battery-Constrained NMPC with Propulsion Prediction and Replanning for High-Speed Flight".

Dev: A novel method for integrating battery and propulsion system models into a Nonlinear Model Predictive Controller (NMPC) framework enables real-time prediction of voltage, consumed current, power,

Rosa: First, who's behind it and why it matters.

Paper summary: Rosa: So we're talking about this paper, "BC-NMPC: Battery-Constrained NMPC with Propulsion Prediction and Replanning for High-Speed Flight." The main idea here is tackling the issue where a UAV loses its maximum available thrust as the battery drains during fast maneuvers, which usually leads to trajectory tracking errors and collisions <ref:2607.23867#pg0>. It claims they introduced a novel method to integrate both the battery and propulsion models into an NMPC framework so it can predict voltage, current, power, and maximum thrust in real time <ref:2607.23867#pg0>.

Dev: Yeah, that sounds crucial for stability because traditional controllers don't account for that dynamic thrust variation caused by the battery discharge <ref:2607.23867#pg0>. But I'm wondering how they handle the computational demands of running these complex models in real time, given we need a tight loop rate <ref:2607.23867#pg1>.

Taro: What I find interesting is how this directly addresses the problem of what happens when the world misbehaves, like sudden high-speed maneuvers where you lose thrust rapidly <ref:2607.23867#pg0>. It suggests a system that can anticipate that loss and plan accordingly rather than just reacting to it later.

Rosa: Exactly, Taro; they're planning for the depleting thrust before it actually happens, which is a big difference in how the UAV behaves during high-speed flight <ref:2607.23867#pg0>. This approach helps improve trajectory tracking performance significantly when things get intense.

Dev: From an engineering standpoint, the paper mentions that they developed a novel multivariate polynomial model to characterize the electro-mechanical characteristics of the propulsion system <ref:2607.23867#pg1>. That sounds like a lot of fitting, but if it allows for "effective predictions of electrical and mechanical aspects of flight in real-time," that's what we need to hear <ref:2607.23867#pg1>.

Taro: I mean, the modeling part seems key because they isolate the electrical and mechanical systems so they can do an online recalculation of the collective available thrust, which lets them operate at limits that are constantly changing throughout the battery capacity range <ref:2607.23867#pg1>. That dynamic adjustment capability is what I'm excited about for unpredictable flight conditions.

Rosa: It really is about that adaptability; they aren't stuck with a fixed thrust limit, which makes their NMPC much more robust in scenarios where the battery state keeps fluctuating <ref:2607.23867#pg0>. This integration means the system can plan for thrust depletion effectively, which is essential for high-speed flight planning <ref:2607.23867#pg0>.

Paper summary: Dev: And speaking of real-time, I saw they keep the motor model as a resistive load because transients are much faster than the NMPC time step, which is necessary to maintain that computational feasibility <ref:2607.23867#pg1>. That kind of simplification is a trade-off we have to manage carefully when designing the control loop <ref:2607.23867#pg1>.

Taro: The paper also mentions they extended an offline trajectory planner to dynamically replan the trajectory in flight based on evolving thrust limits, which gives them that proactive capability during actual flight <ref:2607.23867#pg0>. That dynamic replanning sounds like it could be vital for handling unexpected disturbances in real-world environments where thrust drops unexpectedly <ref:2607.23867#pg0>.

Rosa: And the validation results are quite compelling; they showed a collisionfree flight to achieve a six-fold decrease in tracking Root Mean Square Error, plus a forty-six percent increase in flight distance and a one hundred percent increase in flight time <ref:2607.23867#pg0>. Those numbers speak volumes about the performance improvement they achieved with this BC-NMPC framework.

Dev: A six-fold decrease in RMSE is substantial, but I still need to know about the latency; they reported a mean computation time of only five milliseconds, which is well within their ten millisecond threshold <ref:2607.23867#pg0>. That low latency confirms that this method could actually run on-board without introducing unacceptable delays into the control loop <ref:2607.23867#pg1>.

Taro: The real-world experiments where they tested it at three point five g acceleration really give confidence, showing it works outside of a purely simulated environment <ref:2607.23867#pg0>. That ability to handle high-speed, agile trajectories in actual flight conditions is what makes this research relevant for real autonomy applications <ref:2607.23867#pg1>.

Rosa: It really shows that the theory translates well into practical performance when you test it against those demanding scenarios <ref:2607.23867#pg0>. This BC-NMPC approach seems to be a solid way to ensure trajectory tracking is maintained even when power resources are running low <ref:2607.23867#pg0>.

Dev: But I also want to ask about the limitations; the paper states that while they refined the estimation of internal resistance using a temperature compensation coefficient Kt, current estimation showed moderate errors, specifically an MAE of eight point seven two A and an RMSE of eleven point five eight A <ref:2607.23867#pg0>. That means their prediction of available energy and thrust limits has some uncertainty due to things like dynamic torque from airflow <ref:2607.23867#pg0>.

Paper summary: Taro: That's a fair point; the paper does acknowledge that those moderate errors are attributed to factors like dynamic torque from airflow and non-linear scaling in current measurement, which means it's not perfect prediction for every single microsecond <ref:2607.23867#pg0>. Still, having that level of accuracy for predicting limits is a strong foundation for autonomy <ref:2607.23867#pg1>.

Rosa: So, to wrap up this BC-NMPC paper, the authors are presenting a framework that allows UAVs to plan for thrust depletion by integrating battery and propulsion models into an NMPC system for real-time prediction of key flight parameters <ref:2607.23867#pg0>. It’s designed specifically to handle those dynamic variations in maximum available thrust during battery discharge <ref:2607.23867#pg0>.

Dev: And from a control systems viewpoint, the core innovation is defining that non-linear constraint based on the time-varying thrust limit Tmax, which directly incorporates how much the battery has discharged at each timestep <ref:2607.23867#pg0>. That makes it much more robust than a standard controller because it understands its physical energy constraints in real time <ref:2607.23867#pg1>.

Taro: The implication for autonomy is that we can design systems that are inherently aware of their energy state and proactively adjust their flight path to avoid failure due to power loss, which is a big step forward for complex autonomous missions <ref:2607.23867#pg1>. This isn't just about flying; it's about surviving the limits of your power supply in dynamic situations <ref:2607.23867#pg0>.

Rosa: Thinking about the broader impact, this work suggests that for high-speed or highly agile aerial vehicles, incorporating battery state directly into the control loop isn't justnice to have; it's necessary for reliable operation <ref:2607.23867#pg0>. The fact that they validated it in real-world flight experiments at three point five g acceleration suggests this is applicable beyond just lab simulations <ref:2607.23867#pg1>.

Dev: I think the future work will likely involve extending these polynomial models to handle even more complex battery chemistries or integrating sensor data more tightly to reduce those current estimation errors we saw, like the eleven point five eight A RMSE <ref:2607.23867#pg0>. That refinement could push it into even tighter operational envelopes <ref:2607.23867#pg1>.

Taro: I agree; pushing the accuracy of those internal resistance estimates would definitely strengthen the entire prediction capability, making the system even better at anticipating when thrust will drop significantly <ref:2607.23867#pg0>. That level of predictive power opens up new possibilities for long-duration autonomous flight where energy management is everything <ref:2607.23867#pg1>.

Paper summary: Rosa: So, in short, the BC-NMPC paper gives us a concrete tool for making aerial systems smarter about their energy constraints during demanding maneuvers <ref:2607.23867#pg0>. It moves the control strategy from being reactive to being predictive about thrust limits <ref:2607.23867#pg0>.

Dev: And for us engineers, it’s a reminder that when designing high-performance systems, you can't treat the power source as an infinite resource; you have to model its limitations precisely within your control architecture <ref:2607.23867#pg1>. The low computation time is the real kicker here for implementation <ref:2607.23867#pg1>.

Taro: It gives us a blueprint for autonomous systems that can anticipate physical limitations imposed by their power source, which is a necessary step toward truly resilient flight autonomy <ref:2607.23867#pg1>. We're looking at systems that can handle the unexpected drop in thrust and keep performing well.

Rosa: It seems like this paper really solidifies the path for integrating these kinds of physical constraints into real-time control design for aerial vehicles <ref:2607.23867#pg0>. It’s a practical application of complex modeling to solve a very real problem in flight performance <ref:2607.23867#pg1>.

Dev: So, the authors have shown that this integration works effectively for high-speed maneuvers, even with battery discharge uncertainties, provided you keep the modeling computationally feasible within strict time limits <ref:2607.23867#pg1>. That computational feasibility is what makes it viable for deployment <ref:2607.23867#pg1>.

Taro: We're seeing systems that can handle those dynamic variations in thrust as a standard feature, not just a special case for racing drones <ref:2607.23867#pg0>. That kind of generalized capability is what really matters for future autonomous applications in unpredictable environments <ref:2607.23867#pg1>.

Rosa: It’s exciting to think about what this means for aerial robotics generally; having this level of foresight regarding energy depletion could dramatically improve mission success rates in complex scenarios <ref:2607.23867#pg0>.

Dev: I’m just hoping that as the technology matures, we can push those prediction models even further to reduce those measurement uncertainties we discussed earlier, making the predictions almost perfect for operational use <ref:2607.23867#pg0>. That refinement is the next logical step for this work <ref:2607.23867#pg1>.

Taro: Yeah, improving that prediction accuracy builds a much stronger foundation for autonomous decision-making under real-world stress, which is what we need <ref:2607.23867#pg1>. That's the kind of deep control insight that drives autonomy forward <ref:2607.23867#pg1>.

Rosa: So, it looks like the BC-NMPC framework presents a very practical and well-validated method for managing power limitations in high-speed flight planning <ref:2607.23867#pg0>. It’s a tangible step toward making autonomous aerial vehicles more capable in demanding conditions <ref:2607.23867#pg1>.

Conclusion: Rosa: So we're wrapping up this discussion on 'BC-NMPC: Battery-Constrained NMPC with Propulsion Prediction and Replanning for High-Speed Flight,' which basically shows how to make a UAV smarter about its battery limits during fast flight. Dev, what are your thoughts on the core concept behind that title?

Dev: I think the title really captures the essence because it highlights two major additions: battery constraint handling and dynamic replanning. It suggests they're not just looking at static power limits, but actively predicting and adjusting based on how much energy is left.

Taro: I agree with Dev; 'replanning' is a big word here. It implies the system can react intelligently when things go wrong, like when the battery suddenly runs low mid-maneuver, which is crucial for autonomy.

Rosa: Exactly, and looking at the authors of this work, it seems they focused heavily on making sure this wasn't just theory; I want to know if this stuff actually works outside of a clean simulation environment or if there are practical flight hours they've logged.

Dev: The paper does detail rigorous testing in both simulation and real-world flight experiments, so we have some data on how it performs under actual flight conditions. They even validated the thrust prediction against measured quantities like internal resistance.

Taro: That real-world validation is what really gives me confidence; if it performs reliably at high acceleration in the field, then the autonomy implications are much more tangible than just theoretical math.

Rosa: It seems like this approach moves us closer to building aerial vehicles that can operate safely and effectively in very dynamic environments where power management is constantly challenging.

Dev: The implication here is that we can design control architectures that inherently understand and respect the physical limitations of the energy source, which is a fundamental step for robust flight control systems.

Taro: It means future autonomous missions won't just be about executing pre-planned paths; they'll be about dynamically adapting those paths as their power reserves change.

Rosa: That dynamic adaptation, coupled with real-time thrust prediction, feels like a necessary evolution for complex aerial robotics operating in demanding scenarios.

Dev: And we need to keep an eye on the computational overhead; while it's feasible now, pushing these models to even higher fidelity in the future will require careful management of that processing time.

Taro: Absolutely, because the better we can predict those limits and replan faster than anything else, the more resilient our autonomous systems become when things get unpredictable out there.

Czech Technical University in Prague

cs.RO, cs.SY, eess.SY

Submitted: 2026-07-26

Updated: 2026-10-05

Comments: [Submitted to Elsevier RAS]

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

Importance score: 79/100

The gist: A novel method for integrating battery and propulsion system models into a Nonlinear Model Predictive Controller (NMPC) framework enables real-time prediction of voltage, consumed current, power, and

Key concepts

Multivariate Polynomial Model
This is a mathematical tool used to describe how the electrical and mechanical parts of the propulsion system behave. It uses polynomial equations fitted to real data (like thrust testing) to create a model that can accurately predict outputs like thrust, current consumption, and voltage based on inputs such as battery SOC and throttle settings.
Nonlinear Model Predictive Control (NMPC)
NMPC is an advanced control strategy that uses a mathematical model of the system to predict future behavior over a short time horizon. It optimizes the control inputs to minimize costs while respecting constraints, making it ideal for complex systems like UAVs where dynamics change rapidly.
Time-Varying Thrust Limit (Tmax)
This is a dynamic constraint calculated at every step of the control process. Because battery discharge changes the system's power capacity, Tmax constantly updates based on the current State of Charge (SOC). This ensures the controller always plans within the actual, changing physical limits of available thrust.
Trajectory Replanning
Since battery depletion causes dynamic changes in flight capability, this method allows the system to adjust its planned path while it is already in flight. It dynamically re-plans a time-optimal trajectory based on the currently available collective thrust, ensuring safe and efficient navigation.

Terminology

Summary

A novel method for integrating battery and propulsion system models into a Nonlinear Model Predictive Controller (NMPC) framework enables real-time prediction of voltage, consumed current, power, and maximum available thrust to account for dynamic variations in UAV thrust caused by battery discharge. This approach allows the system to plan for depleting thrust and improve trajectory tracking performance in high-speed flight scenarios.

The gist

This paper presents a novel method for integrating battery and propulsion system models into a Nonlinear Model Predictive Controller (NMPC) framework to enable real-time prediction of the voltage, consumed current, power, and maximum available thrust of the platform.

Modeling Propulsion and Battery Characteristics

The research develops a novel multivariate polynomial model to characterize the electro-mechanical characteristics of the propulsion system. This approach is designed to be computationally-feasible through the use of multivariate polynomials, allowing for effective predictions of electrical and mechanical aspects of flight in real-time. The model isolates the electrical and mechanical systems for modular identification, permitting online recalculation of collective available thrust and enabling flight at constantly-changing platform limits throughout the battery capacity range.

Key modeling components include:

The Electrical Model (Figure 2): This consists of a battery equivalent IR circuit, represented by open circuit voltage (voc) and internal resistance (rb), with four motors represented by variable resistances in parallel. The motor is modeled as a resistive load since transients are much faster than the NMPC time step, and thus they are neglected to maintain real-time computability.

The Motor Model: Each motor-propeller unit is modeled as a resistive load converting electrical power to mechanical power. Polynomial functions (1) through (4) were obtained by fitting data from thrust testing, relating variables such as resistance, force, throttle control signal, terminal voltage, consumed power pin (= vcci), and RPM.

The Battery Model: The equivalent IR circuit model is parameterized based on State of Charge (SOC). Polynomial fitting was used to obtain relationships between SOC and other parameters: soc = a s v cubed oc + b s v squared oc + c s voc + d s, rb = a d s cubed oc + b d s squared oc + c d soc + dd, and voc = a qs cubed oc + b qs squared oc + cq sococdq.

The BC-NMPC Formulation

The system dynamics model defines the UAV state vector as x = [p, v, q, ω, soc], where the input vector u is defined by the scalar thrust forces f1 to f4. The core of the control strategy is an Optimal Control Problem (OCP) formulated using an ACADOS framework. The objective function minimizes a cost term involving state penalties and control input penalties over a prediction horizon N.

The critical innovation lies in defining the non-linear constraint based on the time-varying thrust limit, Tmax, which is calculated using equation (16). This constraint ensures that 0 ≤ Tmax,k − X 4 i=1 fi,k ≤ Tmax,k − X 4 i=1 fmin, where Tmax is dependent only on the SOC at each timestep. This constraint directly incorporates the dynamic variations in maximum available thrust caused by battery discharge.

Trajectory Replanning and Performance Validation

To address trajectory tracking errors during thrust depletion, the paper extends an offline trajectory planner to dynamically re-plan a trajectory in flight. The replanner is chosen for its real-time computability and the ability to generate thrust limited time-optimal trajectories given a specific available collective thrust.

The validation involved rigorous testing in both simulation and real-world flight experiments, including flying an agile high-speed trajectory at 3.5 g acceleration. Comparisons demonstrated significant improvements:

  1. In obstacle-ridden environments, the approach achieved a collisionfree flight to achieve a 6-fold decrease in tracking Root Mean Square Error (RMSE), a 46 % increase in flight distance, and a 100 % increase in flight time.

  2. The computational feasibility was confirmed, with the mean computation time being only 5 ms, meeting the 10 ms Threshold.

Real-World Experimental Results

In real-world tests, the model's predictions were validated against measured quantities. The estimation of internal resistance (r̂b) was refined using a temperature compensation coefficient Kt to match indirect measurements, confirming that the model can reliably predict the internal resistance of the battery during flight. Furthermore, current estimation showed moderate errors (MAE: 8.72 A; RMSE: 11.58 A), which were attributed to factors like dynamic torque from airflow and non-linear scaling in current measurement, but were deemed "sufficient and accurate for the purpose of predicting the available energy and thrust limits for the NMPC.

Improvements for AI systems

This paper presents a sophisticated, integrated control and planning framework for Uncrewed Aerial Vehicles (UAVs) that directly addresses the critical limitation of battery-constrained high-speed flight.

As an AI researcher, I see several high-leverage areas where this methodology can be applied to significantly improve existing AI systems in robotics, autonomy, and control theory.

Here are specific improvements and the resulting capabilities:

)1. Improvement Area: Dynamic Constraint Modeling for Reinforcement Learning (RL) Agents

The paper introduces a mechanism to incorporate time-varying physical constraints (maximum available thrust, which depends on State of Charge (SOC)) directly into a Nonlinear Model Predictive Controller (NMPC). This moves beyond static safety margins.

  • Improvement: Integrate the derived polynomial/model relationships for battery dynamics and propulsion limits into the state-space definition or as hard/soft constraints within an RL environment.

  • Improved AI System Capability: An RL agent trained in this environment will develop an innate, physics-aware understanding of energy depletion. Instead of learning a trajectory that simply works until it fails (as in standard RL), the agent will learn to prioritize energy management—for instance, by learning to conserve thrust or perform optimal maneuvers earlier to ensure a successful mission completion, leading to more robust policies in resource-scarce scenarios.

)2. Improvement Area: Real-Time Trajectory Replanning for Safety and Optimality

The paper implements a trajectory replanning algorithm based on the predicted thrust limits (using PMM planner [21]) to generate time-optimal, feasible trajectories in real-time.

  • Improvement: Replace standard pathfinding or planning modules within autonomous navigation stacks with this Thrust-Aware Replanning module.

  • Improved AI System Capability: Autonomous vehicles in complex, dynamic environments (like drone racing or search and rescue) can execute high-speed maneuvers without risking collision due to thrust saturation. The system can dynamically calculate the fastest path that respects the current energy budget, maximizing flight distance/time under realistic constraints rather than just minimizing path length irrespective of feasibility.

)3. Improvement Area: High-Fidelity Sensor Fusion for State Estimation

The paper validates its model using a comprehensive state vector including position, velocity, attitude (quaternion), body rates, and SOC estimation via Coulomb counting fused with noisy measurements (IMU/GNSS).

  • Improvement: Develop a sensor fusion architecture that explicitly utilizes the polynomial fitting derived in Section IV to estimate unmeasurable internal states like battery resistance and SOC from noisy current/voltage measurements.

  • Improved AI System Capability: Autonomous systems can operate reliably in environments where primary sensors might be temporarily compromised (e.g., GNSS denial, high electromagnetic interference). The system gains resilience by using the internal dynamic model of the propulsion system to fill in the blanks for battery health and power status, significantly extending operational endurance beyond what is possible with simple Coulomb counting alone.

)4. Improvement Area: Computational Efficiency via Polynomial Modeling

The paper achieves real-time feasibility (mean computation time of 5 ms) by using multivariate polynomials instead of computationally expensive electrochemical or full electro-mechanical models for the NMPC optimization.

  • Improvement: Create a library of Fast, Approximate State Predictors based on polynomial fitting for various system components (motor resistance, thrust vs. voltage).

  • Improved AI System Capability: This allows complex control algorithms (like NMPC) to be deployed on embedded hardware with limited computational power that were previously restricted to simpler linear models. It enables the deployment of high-performance, battery-aware control in resource-constrained edge devices (e.g., small drones or low-cost UAVs).

)5. Improvement Area: Comprehensive Performance Benchmarking for Model Validation

The paper rigorously compares its BC-NMPC against a baseline model (Moseler model) and validates it against real-world flight data, specifically quantifying RMSE improvements in obstacle-ridden environments (e.g., 6x RMSE decrease, 100% time increase).

  • Improvement: Establish standardized metrics for evaluating control systems based on Constraint Adherence and Resource Efficiency rather than just tracking error.

  • Improved AI System Capability: AI control systems can be benchmarked not just on accuracy (how close the predicted state is to the true state), but on their ability to maintain operational feasibility (stay within thrust limits) and efficiency (maximizing distance per unit of energy). This shifts the focus from pure tracking accuracy to mission success metrics.

Abstract

Trajectory tracking performance of Uncrewed Aerial Vehicles (UAVs) degrades during an agile high-speed flight due to the depletion of the battery and subsequent loss of maximum available thrust. In applications such as drone racing, this leads to a failure to complete the race due to possible collisions with obstacles. In this paper, we present a novel method for integrating battery and propulsion system models into a Nonlinear Model Predictive Controller (NMPC) framework to enable real-time prediction of the voltage, current, power, and maximum available thrust of the platform. Our proposed approach achieves lower trajectory tracking error as a result of its real-time thrust awareness, and with the help of trajectory replanning, it allows the UAV to fly in time-optimal regime throughout the mission. The accuracy of this proposed model was verified in real-world flight experiments, while the effectiveness of the replanning algorithm was evaluated in simulation. By the end of the battery capacity, compared to an unaware controller, our novel controller achieved a 25% reduction in mean position error without replanning, and an 88 % reduction with replanning.

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