⚡ electrical engineering

Battery-Aware Predictive Trajectory Planning and Control for Multirotors Under Disturbances

This paper introduces a battery-aware predictive trajectory planning and control framework for multirotors that integrates closed-loop vehicle, motor, and battery dynamics to optimize flight paths under spatially localized disturbances, significantly reducing energy consumption and tracking error while adapting to varying battery states and controller choices.

Original authors: Krishna Bhavithavya Kidambi

Published 2026-09-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Krishna Bhavithavya Kidambi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Unmanned aerial vehicles, the small flying robots often called drones, are increasingly expected to perform long, autonomous tasks in the real world. These machines rely entirely on batteries for power, and their ability to complete a mission depends on a delicate balance between the energy stored in their cells and the effort required to keep them in the air. When a drone flies through calm air, its energy consumption is predictable. However, the real world is rarely calm. Wind gusts and turbulent pockets of air act as invisible obstacles, forcing the drone's computer to work harder to stay on course. This extra effort drains the battery faster and lowers the voltage available to the motors. As the battery weakens, the motors lose their ability to spin as fast as they did when fully charged, creating a chain reaction where a rough flight path can leave the drone with too little power to finish its job. The challenge for engineers is to plan a flight path that not only avoids obstacles but also anticipates how the wind will drain the battery and limit the motors' future strength.

A researcher at the University of Dayton has developed a new way to plan these flights that treats the battery, the motors, and the wind as a single, connected system rather than separate parts. Instead of simply drawing a line from point A to point B, their software simulates the entire journey before the drone ever leaves the ground. It calculates how a specific path would interact with known wind disturbances, how much extra energy the motors would need to fight that wind, and how that energy drain would lower the battery voltage. Crucially, the system then asks a second question: if the battery voltage drops to a certain level, will the motors still be strong enough to follow that same path? By running this complex simulation for many possible routes, the software selects the one that keeps the drone safe, accurate, and powered for the longest time.

In a detailed computer simulation, the researcher tested this approach on a mission lasting 150 seconds, covering a distance of 640 meters. The route included three distinct zones where strong, localized wind disturbances were expected to hit the drone. The researcher compared their new battery-aware planning method against a standard approach that knew about the wind but did not account for how the battery would change during the flight. The results were significant. The new method chose a flight path that dipped lower in altitude when approaching the wind zones, effectively steering the drone through calmer air layers. This simple adjustment reduced the total electrical energy consumed by 7.46 percent. More importantly, it dramatically improved the drone's ability to stay on its intended line. The standard method struggled to hold its position against the wind, resulting in large errors, while the battery-aware plan reduced the tracking error by approximately 72 percent.

The researcher also discovered that the benefit of this new method depends heavily on the state of the battery. When the battery started the mission with a high charge, the software made the same smart adjustments whether it was told to worry about the battery or not. In these conditions, the battery was strong enough that the motors never reached their limits, so the extra battery calculations did not change the final route. However, the researcher ran a second test where the drone started with a depleted battery, simulating a stressful, low-power scenario. In this case, the battery-aware planner chose a distinctly different path, altering the flight altitude more aggressively than the other methods. This showed that when power is scarce, knowing exactly how the battery voltage will drop allows the planner to make different, safer choices. The study confirmed that ignoring the battery's changing strength can lead to poor decisions when the drone is already running low on power.

To ensure the results were robust, the researcher tested the chosen flight path using four different types of control software that the drone could use to steer itself. Even though the flight path remained exactly the same, the different controllers produced different results in terms of energy use and accuracy. One controller managed to track the path very precisely but used more energy, while another was slightly less accurate but more efficient. This highlighted a key finding: the planning software and the steering software play different roles. The planner sets the route based on what it predicts will happen to the battery and motors, but the final outcome still depends on how the drone's steering system reacts to the wind. The study did not claim to have solved every problem of drone flight, but it provided a clear demonstration that planning a route while simultaneously predicting how the battery and motors will behave leads to safer and more efficient missions.

The researcher verified their mathematical models by comparing them against a highly detailed, industry-standard simulation tool, finding that their simplified model was accurate enough for repeated use in planning. They also noted that while their method worked well in the simulation, it currently relies on knowing exactly where the wind will be before the flight starts. Future work will aim to update these plans in real-time as the drone flies, allowing it to react to wind that was not predicted beforehand. For now, the study proves that treating a drone's flight plan, its battery health, and its motor limits as a single, interconnected puzzle is a powerful way to extend the range and reliability of autonomous flight.

Technical Summary: Battery-Aware Predictive Trajectory Planning and Control for Multirotors Under Disturbances

Problem Statement
Multirotor unmanned aerial vehicles (UAVs) operating in disturbance-prone environments face a complex coupling between trajectory selection, closed-loop control demand, and battery dynamics. Environmental disturbances (e.g., wind) increase feedback control effort and rotor demand, accelerating battery discharge and reducing terminal voltage. As the mission progresses, the available actuator authority becomes constrained by the evolving battery state. Existing trajectory planning methods often treat trajectory generation, feedback control, and battery dynamics independently or fail to propagate the complete closed-loop interaction where trajectory-dependent disturbance exposure alters control demand, which in turn affects battery terminal voltage and subsequently limits actuator capability. This paper addresses the need for a planning framework that explicitly accounts for these coupled energetic and actuator consequences during trajectory selection.

Methodology
The author proposes a battery-aware predictive trajectory planning and control framework that evaluates candidate trajectories through a forward propagation of a coupled vehicle–motor–battery model over the mission horizon.

System Modeling:
- Vehicle Dynamics: A rigid-body multirotor model (6-DOF) incorporating aerodynamic drag and external wind disturbances.
- Propulsion & Control: A motor model distinguishing between controller-requested rotor speeds, battery-limited commands, and actual rotor speeds. The control allocation accounts for motor saturation and battery-dependent limits.
- Battery Model: A reduced-order, State-of-Charge (SOC)-dependent equivalent-circuit model (two-RC Thevenin). It captures cumulative charge depletion and transient voltage depression. The model calculates terminal voltage ( $V_b$ ) based on instantaneous power demand ( $P_b$ ) and SOC.
- Actuator Coupling: A critical feature is the voltage-dependent rotor-speed limit, $\omega_{max}(V_b)$ . As $V_b$ drops due to discharge, the maximum achievable rotor speed decreases, potentially rendering a controller's requested command infeasible.
Planning Framework:
- Parameterization: The planner modifies a nominal mission trajectory by adding localized vertical deviations ( $\delta$ ) in the vicinity of known disturbance regions. Horizontal paths remain fixed.
- Closed-Loop Propagation: For each candidate trajectory, the system simulates the full mission. The reference trajectory determines disturbance exposure, which drives the feedback controller. The resulting control demand dictates rotor speeds, electrical power, and battery evolution. The battery state then updates the actuator limit, which feeds back into the rotor command.
- Optimization: A nonlinear optimization (SQP) minimizes a composite objective function. This function balances electrical energy consumption, trajectory modification magnitude, and tracking error, while penalizing violations of SOC, terminal voltage, and actuator utilization constraints.
Numerical Verification:
- The reduced-order battery model was benchmarked against an independently implemented Simscape equivalent-circuit reference. The reduced-order model achieved a power Normalized Root Mean Square Error (NRMSE) of 0.64% and a cumulative energy discrepancy below 0.7%.

Key Results
The framework was evaluated on a 150-second, 640-meter mission containing three spatially localized wind disturbance regions.

Nominal SOC (92%) Performance:
- Compared to a disturbance-aware fixed-reference baseline, the battery-aware planner reduced electrical energy consumption by 7.46% and position-tracking Root Mean Square Error (RMSE) by approximately 72%.
- Ablation Study: At nominal SOC, the "energy-aware, battery-unaware" planner and the "battery-aware" planner selected identical trajectories. This indicates that at healthy battery states, the improvements stem primarily from reducing disturbance exposure and associated control demand, rather than avoiding active battery-dependent actuator constraints (which were non-binding).
Depleted SOC Stress Test (55%):
- When the initial SOC was reduced to 55%, the battery-aware planner selected a different trajectory with larger altitude deviations compared to the energy-only planner.
- This demonstrates that battery-dependent terms become consequential to the planning decision as electrical and actuator limits become restrictive. However, even with trajectory modification, the mission remained infeasible under this severe stress condition (voltage dropped below limits), highlighting that trajectory planning alone cannot guarantee feasibility if the battery state is too depleted.
Controller Sensitivity:
- Executing the same battery-aware trajectory with different feedback controllers (PD, Adaptive, Sliding-Mode, RISE) revealed significant tradeoffs.
- The Adaptive controller achieved the lowest tracking error (3.69 m) with a minimal energy penalty (+0.62% vs. PD).
- The RISE controller offered good tracking but incurred higher energy costs (+6.37% vs. PD).
- This confirms that controller selection significantly alters the tradeoff among tracking accuracy, energy consumption, and actuator utilization, even when the trajectory is fixed.

Significance and Claims
The paper claims that the primary contribution is a coupled closed-loop prediction framework that integrates vehicle dynamics, motor response, battery evolution, and voltage-dependent actuator authority directly into the trajectory selection process.

The author asserts that:

Interdependence: Trajectory planning, closed-loop control, and battery dynamics must not be treated independently. The selected trajectory dictates disturbance exposure and control demand, which governs battery evolution, which in turn constrains future propulsion authority.
Predictive Value: By propagating these interactions forward, the planner can proactively select trajectories that minimize the cumulative energetic and actuator consequences of disturbance exposure.
Context-Dependent Benefits: The benefit of battery-aware planning is twofold:
- At nominal SOC, it improves performance by shaping the trajectory to reduce disturbance-induced control effort.
- Under depleted-battery conditions, it alters the trajectory selection to account for shrinking actuator authority, although it cannot fully compensate for insufficient energy reserves.
Controller Interaction: The framework highlights that the "best" trajectory depends on the specific feedback controller used, as different controllers impose different energetic and actuator loads for the same reference.

The paper concludes that accounting for predicted closed-loop energetic and battery–actuator consequences provides a systematic basis for selecting disturbance-aware multirotor trajectories. Future work is identified as extending this to receding-horizon planning with online disturbance estimation and developing feasibility-aware replanning strategies for when actuator capability becomes insufficient.

Technical Summary: Battery-Aware Predictive Trajectory Planning and Control for Multirotors Under Disturbances

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