PaperlayerView exact revision on arXiv

Source-linked AI summary

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

Krishna Bhavithavya Kidambi

arXiv:2609.12188v1cs.ROcs.SYeess.SY

TL;DR

Battery-powered multirotors must plan around the coupled effects of disturbance exposure, closed-loop control demand, battery evolution, and actuator capability. This paper evaluates candidate trajectories by propagating vehicle, motor, and battery dynamics, and reports lower energy use and position-tracking error than a disturbance-aware fixed-reference baseline.

  • Problem

    Trajectory planning generally does not propagate the complete coupling among trajectory-dependent disturbance exposure, control and rotor demand, battery terminal voltage, and resulting actuator authority during candidate evaluation.

    Source: §I · p. 2

  • Method

    The planner evaluates candidate trajectories through coupled closed-loop vehicle, motor, and battery propagation, including voltage-dependent rotor capability.

    Source: §I · p. 2

  • Results

    Energy consumption fell by 7.46% and position-tracking RMSE by 72.0% relative to the disturbance-aware baseline.

    Source: D. Planning Ablation · p. 10

  • Takeaways & Limitations

    Under depleted-battery conditions, battery-dependent terms alter the selected trajectory, but trajectory modification alone cannot guarantee feasibility when actuator capability is insufficient.

    Source: D. Planning Ablation · p. 12

    Experimental flight validation remains future work to assess coupled vehicle–battery predictions under measured disturbances and hardware limitations.

    Source: §VI · p. 13

Abstract

from arXiv · show

This paper presents a battery-aware predictive trajectory-planning and control framework for multirotors operating under spatially localized disturbances. Candidate trajectories are evaluated through closed-loop vehicle--motor--battery propagation, allowing disturbance-induced control demand, electrical energy, battery evolution, and terminal-voltage-dependent actuator capability to enter the planning process. % A reduced-order battery model is numerically benchmarked against an independently implemented Simscape equivalent-circuit reference, with a power NRMSE of $0.64\%$ and a cumulative-energy discrepancy below $0.7\%$. % In a $150$-s, $640$-m mission containing three disturbance regions, the selected trajectory reduces electrical energy consumption by $7.46\%$ and position-tracking RMSE by approximately $72\%$ relative to the disturbance-aware fixed-reference baseline. % Planner ablations show that battery-dependent terms are nonbinding at nominal SOC but alter the selected trajectory under a depleted-battery stress condition. % Execution with multiple feedback controllers further demonstrates that controller selection changes the tradeoff among tracking accuracy, energy consumption, and actuator utilization. % The results demonstrate the benefit of accounting for predicted closed-loop energetic and battery--actuator consequences during trajectory selection.

I. INTRODUCTION

Battery-powered multirotor planning must account for how disturbance exposure and trajectory shape affect control demand, energy use, and battery-limited actuator authority. The paper motivates coupled closed-loop trajectory evaluation and retains the vehicle’s translational–rotational dynamics in its model.

I. INTRODUCTION

  • Existing planners generally do not propagate the complete trajectory–disturbance–control–battery–actuator coupling during candidate evaluation.The coupled effects include disturbance-dependent control and rotor demand, electrical load, terminal voltage, and available actuator authority.Source: §I · pp. 1–2
  • The framework evaluates candidate trajectories by propagating vehicle and propulsion dynamics with battery state, electrical demand, terminal voltage, and voltage-dependent rotor authority.Its planner uses this prediction to modify disturbance exposure while accounting for tracking, energy, battery requirements, and actuator constraints.Source: §I · p. 2

A. Multirotor Dynamics

  • The rigid-body model retains translational–rotational coupling, so lateral acceleration depends on vehicle attitude and the trajectory’s required thrust history.That attitude and thrust history determines rotor demand and associated battery load.Source: A. Multirotor Dynamics · p. 3

B. Motor and Propulsion Dynamics

The propulsion model distinguishes rotor-speed requests from battery-limited commands and physical rotor response. Terminal voltage sets the instantaneous rotor-speed capability available to realize a controller request.

B. Motor and Propulsion Dynamics

  • The commanded rotor speed is capped by the instantaneous battery-terminal-voltage-dependent rotor-speed capability.Battery discharge can reduce available rotor-speed capability relative to the nominal hardware limit.Source: B. Motor and Propulsion Dynamics · p. 3
  • The model distinguishes controller-requested rotor speed, battery-limited motor command, and resulting physical rotor speed.This distinction allows the analysis to assess whether a requested action remains realizable as terminal voltage evolves.Source: B. Motor and Propulsion Dynamics · p. 3
  • A first-order motor model governs the transition from commanded rotor speed to actual rotor speed.The motor time constant, τm, characterizes the response.Source: B. Motor and Propulsion Dynamics · p. 3

C. Disturbance Model

The study models spatially localized wind disturbances and evaluates candidate trajectories through their closed-loop consequences. Its formulation assumes the disturbance field is known over the mission and modifies only the vertical trajectory along a prescribed horizontal path.

C. Disturbance Model

  • The disturbance field is assumed known a priori over the mission; uncertainty in its locations and prescribed wind characteristics is not considered.The horizontal reference path is fixed, so the planner modifies only the vertical trajectory and disturbance-region encounter intervals remain fixed.Source: C. Disturbance Model · p. 3
  • The selected trajectory sets the altitude of each disturbance encounter and thereby affects the aerodynamic loading the closed-loop controller must reject.The disturbance modifies relative airflow, which determines aerodynamic load.Source: C. Disturbance Model · p. 4

D. Problem Formulation

  • Each candidate trajectory is evaluated by propagating coupled closed-loop vehicle, motor, and battery dynamics across the mission horizon.Battery power affects terminal voltage, which sets rotor-speed capability and feeds back into commanded rotor speed.Source: D. Problem Formulation · p. 4
  • Battery and actuator requirements enter trajectory optimization as penalties, while planning-variable bounds are hard constraints and mission feasibility is checked after optimization.Here, “predictive” means full-mission forward propagation before execution, not receding-horizon optimization.Source: D. Problem Formulation · p. 4

III. BATTERY AND ACTUATOR MODEL

The battery and actuator model couples propulsion demand to evolving battery state, terminal voltage, and rotor authority during candidate evaluation. An SOC-dependent two-RC equivalent circuit captures charge depletion and transient voltage response, with stated model-form and operating-scope limitations.

III. BATTERY AND ACTUATOR MODEL

  • An SOC-dependent two-RC Thevenin model couples battery state and propulsion demand to terminal voltage and voltage-dependent rotor-speed limits.Its SOC-dependent open-circuit voltage, ohmic resistance, and two polarization branches evolve alongside vehicle and motor dynamics.Source: §III · p. 4, A. SOC-Dependent Equivalent-Circuit… · p. 4

A. SOC-Dependent Equivalent-Circuit Battery Model

  • The battery state tracks SOC, discharge current, and two polarization voltages, with resistance and polarization parameters obtained from SOC-dependent lookup quantities.The lookup quantities are interpolated over the prescribed operating SOC range.Source: A. SOC-Dependent Equivalent-Circuit… · pp. 4–5
  • The model captures cumulative charge depletion and transient load-induced voltage depression while allowing instantaneous power capability to vary with battery state.The instantaneous power-delivery condition is used to classify a candidate trajectory as electrically infeasible when violated.Source: A. SOC-Dependent Equivalent-Circuit… · p. 5
  • The model assumes discharge-only operation, omits thermal and ageing effects, and uses lookup parameters that are not identified from cell-specific experimental characterization.It also neglects cell-to-cell imbalance, hysteresis, self-discharge, and regenerative charging.Source: A. SOC-Dependent Equivalent-Circuit… · p. 5

B. Propulsion Power and Battery Load

The propulsion-load model estimates electrical demand from rotor states, including both aerodynamic power and rotor acceleration. This demand and auxiliary loads determine battery power and cumulative energy, while disturbances and tracking alter the rotor histories that drive battery and propulsion capability.

B. Propulsion Power and Battery Load

  • Rotor electrical load combines cubic rotor-speed power with a transient correction for increasing rotor speed, using a reduced-order approximation rather than a detailed electromechanical motor model.The correction applies only when commanded rotor speed exceeds actual speed; the model is not a detailed BLDC motor model.Source: B. Propulsion Power and Battery Load · p. 5
  • Total requested battery power includes auxiliary electrical load, and integrating that power gives cumulative electrical energy consumed over time.The auxiliary load represents onboard electronics and other non-propulsive systems.Source: B. Propulsion Power and Battery Load · p. 5
  • Trajectory tracking and disturbances alter feedback-control demand and rotor-speed histories, which subsequently alter electrical load, battery state, and available propulsion capability.Source: B. Propulsion Power and Battery Load · p. 6

C. Battery-Dependent Actuator Authority

The planner evaluates modified trajectories through coupled closed-loop vehicle, motor, battery, and actuator dynamics. Its candidate evaluations account for voltage-dependent rotor limits and the anticipated tracking, energy, battery, and actuator consequences of disturbances.

C. Battery-Dependent Actuator Authority

  • Available rotor-speed capability depends on terminal voltage, and rotor commands are clipped to that battery-dependent limit.The command, electrical load, current, and terminal voltage are iteratively coupled during prediction.Source: C. Battery-Dependent Actuator Authority · p. 6
  • The planner’s reserve measures distinguish remaining rotor-speed capability from requested utilization; utilization at or above 1 indicates the battery-dependent capability has been reached or exceeded.Overall feasibility also requires the unsaturated request to satisfy the nominal hardware condition.Source: C. Battery-Dependent Actuator Authority · p. 6

IV. BATTERY-AWARE PREDICTIVE TRAJECTORY PLANNING

  • The planner evaluates localized altitude modifications while accounting for their closed-loop tracking, energy, battery, and actuator consequences under disturbances.It preserves the nominal horizontal mission and evaluates candidates by propagating coupled vehicle, motor, battery, and actuator dynamics.Source: §IV · p. 6

A. Predictive Planning Framework

  • The planning vector selects signed altitude modifications, subject to bounds on altitude, vertical velocity, and vertical acceleration.These trajectory constraints are enforced directly during optimization.Source: A. Predictive Planning Framework · pp. 6–7
  • Each candidate is propagated over the complete mission horizon before execution, linking reference-driven disturbance exposure and control demand to rotor speeds, electrical load, battery evolution, and actuator authority.The optimization is performed before the mission, not in a receding-horizon manner.Source: A. Predictive Planning Framework · p. 7

B. Candidate Trajectory Parameterization

Candidate references use localized vertical deviations to adjust the nominal trajectory near disturbance regions. The planner then evaluates each candidate by closed-loop propagation, including coupled battery–actuator dynamics and electrical-feasibility checks.

B. Candidate Trajectory Parameterization

  • Compact C2 basis functions specify signed peak altitude changes around disturbance intervals, with smooth boundaries that avoid abrupt altitude changes.Disturbance exposure is evaluated from vehicle position; the basis functions locate altitude modifications rather than directly prescribing the disturbance experienced.Source: B. Candidate Trajectory Parameterization · p. 7

C. Closed-Loop Battery-Aware Prediction

  • Candidate references are propagated through the vehicle model under a fixed planning controller, with control allocation and battery–actuator coupling determining rotor commands and electrical load.Terminal voltage, rotor capability, power, and current are iteratively updated during prediction.Source: C. Closed-Loop Battery-Aware Prediction · p. 7
  • Candidates violating the battery power-delivery condition are flagged as electrically infeasible, while numerical continuation allows objective evaluation and retains the violation penalty.After coupling is resolved, current and rotor commands propagate battery and motor states across the mission.Source: C. Closed-Loop Battery-Aware Prediction · p. 8

D. Objective Function and Mission Feasibility

The planner balances energy, trajectory modification, and tracking through a weighted objective, with additional penalties for battery, actuator, endpoint, and physical-infeasibility conditions. It then applies explicit mission-feasibility checks to the selected trajectory.

D. Objective Function and Mission Feasibility

  • A normalized weighted objective balances electrical energy, trajectory modification, and closed-loop tracking performance while penalizing battery, actuator, and terminal conditions.Its objective terms are combined using nonnegative weights.Source: D. Objective Function and Mission… · p. 8
  • One-sided quadratic penalties encourage actuator reserve and preferred utilization, while endpoint penalties distinguish continuous terminal-error cost from a threshold-triggered penalty.Preferred actuator thresholds shape the objective but do not define the physical actuator boundary.Source: D. Objective Function and Mission… · p. 8
  • Physical battery-power and battery–actuator coupling violations incur explicit optimization penalties, and the selected trajectory undergoes separate mission-feasibility checks.The mission-feasibility conditions include successful battery–actuator coupling throughout the mission.Source: D. Objective Function and Mission… · p. 8

V. SIMULATION RESULTS AND DISCUSSION

The simulations evaluate how trajectory selection, disturbance exposure, closed-loop tracking, energy use, battery evolution, and actuator capability interact during a long-duration mission. The setup compares disturbance-aware, energy-aware battery-unaware, and battery-aware planning, with results reported for the lowest-cost tested initialization rather than a globally optimal solution.

V. SIMULATION RESULTS AND DISCUSSION

  • The evaluation proceeds from battery-model benchmarking to full-mission trajectory comparison, planner ablations at nominal and reduced initial SOC, and tests with multiple feedback controllers.The simulations examine tracking, energy consumption, battery evolution, and battery-dependent actuator capability.Source: §V · p. 9

A. Simulation Setup and Mission Description

  • The 150-s, 640-m mission includes takeoff, horizontal flight, and landing, with three spatially localized disturbance regions during horizontal flight.The mission starts at 92% SOC unless otherwise stated and flies at a nominal altitude of 5 m.Source: A. Simulation Setup and Mission… · p. 9
  • The evaluation compares a fixed nominal reference, energy-aware trajectory modification without battery-state information, and battery-aware planning using coupled vehicle–motor–battery prediction.All selected trajectories are evaluated using the same coupled plant.Source: A. Simulation Setup and Mission… · p. 9
  • Because the trajectory optimization is nonconvex, the reported trajectory is the lowest-cost result among tested initializations and is not claimed to be globally optimal.The optimization uses three initial altitude-offset vectors.Source: A. Simulation Setup and Mission… · p. 9

B. Battery Model Numerical Verification

The selected trajectory reduces mission energy and tracking error relative to the disturbance-aware baseline. Battery-model benchmarking, nominal-SOC ablations, and a low-SOC stress test qualify how battery-dependent prediction affects planning.

B. Battery Model Numerical Verification

  • The reduced-order battery model has 0.6379% power NRMSE and a 0.6852% cumulative-energy discrepancy against the Simscape reference, but this is a model-to-model benchmark, not experimental validation.The benchmark also reports 0.0239-percentage-point SOC RMSE and 0.1095 V terminal-voltage RMSE; the voltage comparison has a larger systematic discrepancy while preserving load-dependent voltage depressions.Source: B. Battery Model Numerical Verification · pp. 9–10, Figure 1 · p. 10

C. Closed-Loop Mission Response

  • Altitude transitions briefly increase control and electrical demand, but reduced feedback effort through disturbance regions lowers cumulative energy consumption.The trajectory redistributes control effort over the mission rather than reducing instantaneous power at every moment.Source: C. Closed-Loop Mission Response · p. 10

D. Planning Ablation

  • Energy falls by 7.46% and position-tracking RMSE by 72.0% relative to the disturbance-aware baseline, as altitude offsets move below nominal during three disturbance encounters.Mission energy decreases from 14.1078 to 13.0552 Wh, while position-tracking RMSE decreases from 15.5226 to 4.3461 m.Source: D. Planning Ablation · p. 10, Figure 2 · p. 11
  • At 92% initial SOC, battery-dependent actuator constraints remain nonbinding, and the battery-aware and energy-aware battery-unaware planners select the same solution.Both trajectories stay below approximately 90% peak actuator utilization; the nominal-SOC improvement is primarily attributed to reduced disturbance exposure and closed-loop demand.Source: D. Planning Ablation · p. 10, C. Closed-Loop Mission Response · p. 10, Table II · p. 11
  • At 55% initial SOC, battery-dependent information changes the selected trajectory, but the battery-aware result remains infeasible, with 12.0814 V minimum terminal voltage and 107.4351% maximum actuator utilization.The stress condition is intentionally severe and is presented as an ablation, not as recovery of mission feasibility.Source: D. Planning Ablation · pp. 11–12, Table III · p. 11

E. Sensitivity to Feedback-Control Architecture

The conclusion reports reduced energy use and tracking error in the nominal-SOC mission, while the feedback-controller comparison shows that tracking, energy, and actuator use trade off even with a fixed planned trajectory.

E. Sensitivity to Feedback-Control Architecture

  • Adaptive control achieved the lowest mission-level position RMSE (3.6881 m), while PD consumed the least energy (13.0552 Wh).The adaptive controller’s RMSE was 4.3407 m for PD; adaptive control used 13.1363 Wh.Source: E. Sensitivity to Feedback-Control… · pp. 12–13, Table IV · p. 12
  • All four controllers met mission-feasibility criteria, but the controller with the lowest tracking error did not also minimize energy, actuator utilization, or terminal error.The fixed battery-aware reference was executed under identical vehicle, battery, disturbance, actuator-limit, and initial-state conditions.Source: E. Sensitivity to Feedback-Control… · pp. 12–13

VI. CONCLUSION

  • At nominal SOC, the selected trajectory reduced electrical energy consumption by 7.46% and position-tracking RMSE by approximately 72%; battery-dependent terms changed trajectory selection under depleted-battery stress.The conclusion attributes the nominal-SOC improvements primarily to reduced disturbance exposure and electrical demand.Source: §VI · p. 13
  • The framework evaluates candidate trajectories through predicted closed-loop interactions among multirotor dynamics, control, motor response, battery evolution, and voltage-dependent actuator capability.The conclusion identifies receding-horizon planning, online disturbance estimation, battery-state updates, and experimental flight validation as future work.Source: §VI · p. 13

APPENDIX

The appendix lists SOC breakpoints for lookup tables and identifies the pack-level, SOC-dependent two-RC parameters used in the numerical study.

APPENDIX

  • Table V lists SOC-dependent two-RC equivalent-circuit parameters used in the numerical study, with all quantities specified at pack level.Source: Table V · p. 14
  • The lookup-table SOC breakpoints are 0.05, 0.15, 0.30, 0.50, 0.70, 0.85, and 1.00.Piecewise-linear interpolation is used between consecutive breakpoints for Voc, R0, R1, R2, τ1, and τ2.Source: APPENDIX · p. 14
Loading 2609.12188v1…