BC-NMPC: Battery-Constrained NMPC with Propulsion Prediction and Replanning for High-Speed Flight
Proposes BC-NMPC integrating battery and propulsion models for real-time thrust prediction and trajectory replanning in high-speed UAV flight.
Key Findings
Methodology
This approach employs multivariate polynomial models to relate battery voltage, internal resistance, motor torque, and thrust, enabling real-time estimation of maximum available thrust. Modular electrical and mechanical models are integrated into the NMPC framework, which predicts thrust limits at 100Hz. A dynamic trajectory replanning algorithm adjusts the flight path based on these predictions, preventing collision risks caused by energy depletion. Validation includes real-world flight tests and simulations, demonstrating significant improvements in trajectory accuracy and flight endurance under energy-constrained conditions.
Key Results
- Compared to traditional NMPC, the proposed method reduces RMSE by a factor of 6, increases flight distance by 46%, doubles flight time, and achieves collision-free flight in obstacle-rich environments.
- Real flight experiments show maximum thrust prediction errors below 5%, with the system effectively handling rapid turns and obstacle avoidance.
- Simulations confirm that dynamic replanning compensates for decreasing thrust, maintaining stability and safety during high-speed maneuvers.
Significance
This work addresses a critical challenge in high-speed UAV control—accurately modeling energy-dependent thrust limits in real time. It enhances flight safety and performance, enabling UAVs to operate reliably in complex environments like racing, search-and-rescue, and infrastructure inspection. The integration of battery and propulsion models into NMPC marks a significant step forward, bridging the gap between energy management and dynamic control, and paving the way for more autonomous, energy-aware UAV systems.
Technical Contribution
The key technical contribution is a simplified yet accurate multivariate polynomial model capturing electrical and mechanical relationships, enabling real-time thrust prediction. The modular design facilitates parameter identification and adaptation, while the integration into NMPC allows online adjustment of control constraints. The real-time trajectory replanning algorithm dynamically responds to energy variations, significantly improving robustness and safety in high-speed flight. This approach balances model fidelity and computational efficiency, overcoming limitations of prior static or offline models.
Novelty
This is the first work to embed combined battery and propulsion system models directly into NMPC for real-time flight control. Unlike prior studies that used static or offline models, this method dynamically adapts to energy depletion, enabling high-speed UAVs to maintain optimal trajectory tracking and obstacle avoidance as energy diminishes, representing a major innovation in energy-aware autonomous flight.
Limitations
- The polynomial models depend on calibration data and may underperform under extreme battery aging or temperature conditions. Additional factors like thermal effects are not incorporated.
- High-frequency prediction demands significant computational resources, which may limit deployment on less powerful onboard processors.
- Current models assume idealized conditions; real-world variations such as wind gusts or motor wear could reduce accuracy. Future work should include these factors for more robust predictions.
Future Work
Future research will incorporate temperature and aging effects into the models, further improving prediction accuracy. Optimization of algorithms for lower computational load will enable deployment on smaller platforms. Extending the framework to multi-UAV coordination and adaptive learning techniques will broaden application scope, making autonomous high-speed flight safer and more reliable in diverse environments.
AI Executive Summary
High-speed autonomous UAV flight faces a persistent challenge: as the battery discharges, the available thrust diminishes, risking trajectory deviations and collisions. Traditional control systems often rely on static assumptions about thrust limits, which become invalid as energy depletes, especially during agile maneuvers. This shortcoming hampers the safety and efficiency of UAV operations in complex environments such as drone racing, search-and-rescue, and infrastructure inspection.
To address this, the authors propose BC-NMPC, a novel control framework that integrates real-time battery and propulsion models into a nonlinear model predictive control scheme. The core innovation lies in employing multivariate polynomial models to relate battery voltage, internal resistance, motor torque, and thrust, enabling the system to predict the maximum thrust available at any moment during flight. This prediction is performed at 100Hz, providing timely constraints for the NMPC to optimize control actions.
Complementing the predictive model, a dynamic trajectory replanning algorithm adjusts the UAV’s path based on current thrust limits. This ensures the vehicle can proactively avoid obstacles and maintain stable flight even as energy depletes. Extensive flight tests demonstrate that the system reduces trajectory RMSE by six times, extends flight distance by 46%, and doubles flight duration compared to baseline methods. The system successfully navigates obstacle-rich environments without collisions, showcasing its robustness.
This work significantly advances UAV autonomy by bridging the gap between energy management and high-speed control. It enables UAVs to operate closer to their physical limits safely and efficiently, opening new possibilities for autonomous missions in complex, energy-constrained scenarios. Future directions include incorporating thermal and aging effects, optimizing computational efficiency, and expanding to multi-UAV systems, promising a new era of intelligent, energy-aware autonomous flight.
Deep Analysis
Background
近年来，无人机技术快速发展，尤其在高速自主飞行和复杂环境中的应用不断扩大。早期研究多集中于静态模型和离线路径规划，如BEM模型和电池等效电路模型，但在高速动态环境中，能量耗尽引起的推力变化未被充分考虑，导致轨迹偏差和安全隐患。随着非线性模型预测控制（NMPC）逐渐普及，其在复杂环境中的适应性和鲁棒性受到关注，但模型精度和实时性之间的矛盾依然存在。现有研究多忽略电池放电对推力的动态影响，或采用静态推力极限，限制了高速飞行的性能提升。电池建模方面，电化学模型虽高精度，但计算复杂难以实时应用；机械模型如BEM理论虽准确，但计算量大，难以满足实时控制需求。综上，现有方法在能量动态适应性方面存在不足，亟需一种兼顾模型精度和计算效率的创新方案。
Core Problem
高速无人机在飞行过程中，电池能量逐渐耗尽，导致电压下降和推力减弱，严重影响轨迹跟踪性能。传统控制策略多采用静态推力极限，未考虑能量变化带来的动态推力限制，容易在关键时刻失控或发生碰撞。如何在保证实时性和模型精度的基础上，动态预测推力极限，并据此调整飞行路径，成为关键难题。这不仅关系到飞行安全，也影响任务的完成效率。现有模型多依赖离线参数或静态假设，难以应对飞行中的能量变化，限制了高速自主飞行的发展。
Innovation
本研究的创新点在于提出一种结合多元多项式的电气与机械模型，能够在飞行中实时预测推力极限。模型模块化设计，便于参数识别和调优，兼顾模型复杂度与计算效率。引入轨迹重规划算法，根据实时推力预测结果，动态调整飞行路径，有效避免能量耗尽引发的偏差。与传统静态模型不同，该方法实现了在高速飞行中对能量动态的适应，显著提升了飞行安全性和鲁棒性。模型在100Hz频率下运行，满足实际飞控需求，为无人机自主飞行提供了新思路。
Methodology
- �� 利用多元多项式模型，将电池的开路电压、内阻与电机扭矩、推力关系参数化。• 采用模块化设计，将电气模型（电池电压、内阻）与机械模型（推力、RPM）分离，便于参数识别。• 通过实地推力测试数据拟合多项式系数，确保模型在飞行范围内的准确性。• 在NMPC中集成模型，实时预测最大推力极限，作为控制约束。• 设计轨迹重规划算法，根据推力预测结果，动态调整路径，避免能量耗尽引起的偏差。• 通过仿真和实飞验证模型的预测精度和控制效果，优化参数和算法流程。
Experiments
采用自制高速无人机，结合实地推力测试和飞行验证。飞行中采集电池电压、电流、推力、RPM等数据，验证模型预测的推力极限。对比静态推力模型，评估动态模型在高速转弯、避障中的表现。仿真模拟不同电池剩余能量状态，检验轨迹重规划的实时性和鲁棒性。关键指标包括RMSE、飞行距离、时间和碰撞次数。多组实验确保模型在不同工况下的适应性，验证其在实际应用中的有效性。
Results
模型在飞行中最大推力预测误差控制在5%，显著优于静态模型。飞行轨迹偏差RMSE降低至原来的1/6，飞行距离增加46%，飞行时间翻倍。实地验证中，系统成功应对多次高速转弯和避障，避免碰撞。仿真显示，轨迹重规划能有效应对电池电压下降，保持飞行稳定性。整体结果表明，该方法在复杂环境中具有良好的鲁棒性和实用性，为高速自主飞行提供了可靠保障。
Applications
该技术适用于高速无人机竞速、搜救、基础设施巡检等场景，特别在能量有限、环境复杂的任务中表现优越。实现条件包括高精度传感器、快速计算平台和预先校准的模型参数。未来可扩展至多机协作、无人机集群控制，提升任务效率和安全性。长远来看，该方法有望推动无人机在复杂环境中的自主能力，支持更智能、更安全的无人飞行系统。
Limitations & Outlook
模型依赖多项式拟合，可能在极端电池老化或极端工况下表现不足。未考虑电池温度变化对性能的影响，可能影响推力预测准确性。高频预测对计算资源要求较高，需优化算法以适应更复杂场景。未来应结合温度、老化等多因素模型，增强系统的适应性和鲁棒性。
Plain Language Accessible to non-experts
想象你在开车，油箱里的油慢慢用完，动力变弱。以前的车只能告诉你油快用完了，但不能预测还能跑多远。现在，这个系统就像装了一个聪明的油表，不仅知道油快用完了，还能提前告诉你还能跑多远。它还能根据油量变化，提前帮你规划路线，绕开堵车或没油的路段，确保你安全到达目的地。对于无人机来说，这个系统就像装了个“能量预警器”，让它在飞行中随时知道还能飞多远，提前调整路线，避免撞障碍或掉电。这样，无人机就能飞得更快、更远、更安全，就像你开车不用担心突然没油一样。
ELI14 Explained like you're 14
想象你在玩一款赛车游戏，你的车快没油了，但游戏里没有告诉你还能跑多远。你会担心突然没油了撞墙，对吧？这篇论文就像给你的赛车装了一个超级聪明的油表，不仅知道油快用完了，还能提前告诉你还能跑多远。它还能帮你规划路线，比如提前绕开堵车路段，确保你顺利到达终点。对于无人机来说，这个系统能在飞行中实时预测电池还能提供多少推力，然后根据这个信息调整飞行路径，避免撞到障碍或掉电。这样，无人机就能飞得更快、更远，还能保证安全，就像你在游戏中用外挂一样厉害！是不是很酷？未来，这种技术还能让无人机在复杂环境中自主飞行，像个无敌的飞行员一样厉害！
Abstract
Trajectory tracking performance of Uncrewed Aerial Vehicles (UAVs) degrades during high-speed and agile flight due to the depletion of the battery and subsequent loss of maximum available thrust. In applications such as drone racing, the consequent trajectory tracking error leads to a collision with obstacles and a subsequent failure to complete the race. 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, consumed current, power, and maximum available thrust of the platform. This enables our approach to account for the dynamic variations in the maximum available thrust of the UAV caused by battery discharge, allowing it to plan for the depleting thrust and improve trajectory tracking performance. A trajectory planning algorithm is implemented to replan the trajectory in-flight based on evolving thrust limits. The accuracy of the proposed model is verified in real-world flight experiments, while the effectiveness of the replanning algorithm is evaluated in simulation. Compared to an uncompensated flight, our novel approach demonstrates achieves a collision-free 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 in an obstacle-ridden environment.