Source-linked AI summary
Cascaded Incremental Nonlinear Dynamic Inversion Control for MAV Disturbance Rejection
Ewoud J. J. Smeur, Guido C. H. E. de Croon, Qiping Chu
TL;DR
MAVs need position control that remains effective under wind gusts, particularly near obstacles, where PID control is limited. The paper generalizes INDI to outer-loop control using acceleration-based control increments and evaluates it in severe wind disturbances. INDI achieved more than seven times lower maximum position deviation than comparable PID control, while the analysis also identifies actuator dynamics as a stability boundary.
Problem
MAV position control must withstand wind gusts near obstacles, but conventional PID control performs poorly because gust rejection is constrained by GPS update frequency and slow integral compensation.
Method
The paper generalizes sensor-based Incremental Nonlinear Dynamic Inversion to outer-loop position control, using measured acceleration to increment the previous control input toward a desired acceleration.
Results
More than 7 times lower maximum position deviation than a comparable PID controller was demonstrated during flights in and out of a 10 m/s windtunnel flow.
Takeaways & Limitations
The controller can support MAV operation near obstacles in gusty environments and can be adapted to new platforms using limited modeling and online actuator-effectiveness adaptation.
Takeaways & Limitations
A complete stability assessment requires actuator dynamics to be included; neglecting them does not answer the full stability question.
Abstract
from arXiv · showhide
Micro Aerial Vehicles (MAVs) are limited in their operation outdoors near obstacles by their ability to withstand wind gusts. Currently widespread position control methods such as Proportional Integral Derivative control do not perform well under the influence of gusts. Incremental Nonlinear Dynamic Inversion (INDI) is a sensor-based control technique that can control nonlinear systems subject to disturbances. It was developed for the attitude control of manned aircraft or MAVs. In this paper we generalize this method to the outer loop control of MAVs under severe gust loads. Significant improvements over a traditional Proportional Integral Derivative (PID) controller are demonstrated in an experiment where the quadrotor flies in and out of a windtunnel exhaust at 10 m/s. The control method does not rely on frequent position updates, as is demonstrated in an outside experiment using a standard GPS module. Finally, we investigate the effect of using a linearization to calculate thrust vector increments, compared to a nonlinear calculation. The method requires little modeling and is computationally efficient.
1 Introduction
Outdoor MAVs must maintain position despite strong, spatially variable wind disturbances, especially near obstacles. The paper generalizes INDI to outer-loop position control and evaluates it against PID in severe gusts.
- 1 Introduction: Wind gusts can create position errors that cause collisions near obstacles, while urban and confined environments can produce disturbances up to 7.6 m/s.Indoor disturbances can also arise from propeller backwash near walls.
- 1 Introduction: PID gust rejection is limited by GPS update frequency and slow integral compensation for persistent wind disturbances.Increasing integral gain can improve offset compensation but introduces tracking overshoot, whereas the paper reports this trade-off is absent for INDI.
- 1 Introduction: The proposed outer-loop INDI uses measured acceleration to increment control input toward the desired acceleration, extending disturbance rejection from attitude to position control.The method addresses noisy acceleration filtering and integration with the previously developed INDI attitude controller.
- 1 Introduction: The paper adds a large open-jet windtunnel evaluation, GPS-based outdoor experiment, propeller thrust modeling, and nonlinear thrust-vector increment calculation.The INDI method is also incorporated into the Paparazzi open-source autopilot for experimentation.
2 Incremental nonlinear dynamic inversion for attitude control
The attitude controller uses incremental nonlinear dynamic inversion to track desired angular accelerations, combining measured vehicle response with actuator-aware control design. Its practical implementation filters noisy acceleration signals, estimates control effectiveness, and matches designed and measured attitude responses closely.
- 2.1 Attitude control: The controller derives angular acceleration and thrust from vehicle dynamics, then linearizes changes around the current operating point while treating omitted airspeed and moment effects as disturbances.This reduces modeling requirements but can introduce small angular-acceleration prediction errors.
- 2.1 Attitude control: Noisy angular-acceleration estimates are filtered with a second-order filter, and all compared terms are filtered consistently to compensate for the resulting delay.Angular acceleration is obtained from finite differences of gyroscope measurements, which are noisy because of propeller-induced airframe vibrations.
- 2.1 Attitude control: INDI inverts measured angular-acceleration error into incremental motor commands, with the thrust increment supplied by the outer loop.The control diagram combines angular-acceleration error and thrust increments with filtered motor feedback and actuator dynamics.
- 2.1 Attitude control: Attitude feedback uses quaternion error on the real platform, while a small-angle simplification supports linear time-invariant gain design based on modeled first-order actuator dynamics.The gains are selected from desired closed-loop poles and zeros rather than from a fully nonlinear analysis.
- 2.1 Attitude control: The designed attitude response differs from the measured quadrotor response by at most 6.4% of the step magnitude at 0.14 s across 25 repetitions.Figure 5 reports the measured mean and standard deviation alongside the theoretically designed response.
- 2.1 Attitude control: Actuator dynamics are essential to stability and performance analysis: neglecting them can make the same gains unstable for different actuator dynamics such as α = 0.02.Lyapunov stability results that neglect actuator dynamics do not answer the complete stability question.
3 Incremental nonlinear dynamic inversion applied to linear accelerations
The outer-loop INDI controller derives linear-acceleration commands from measured acceleration and incremental thrust-vector changes, while avoiding an aerodynamic drag model. Filtering is applied consistently so the inverted control law can use noisy accelerometer measurements.
- Acceleration model: Measured acceleration is rotated into the NED frame and combined with gravity to obtain the acceleration used by the controller.The thrust vector depends on attitude and total rotor thrust in the NED frame.
- Disturbance handling: The derivation omits aerodynamic-force derivatives because wind and drag are difficult to estimate, treating their effects as disturbances observed through measured acceleration.The approach therefore does not require an aerodynamic drag model.
- Filtering: All terms associated with the previous timestep are filtered consistently to account for accelerometer noise and filter delay.The same filtering convention is applied before obtaining the inverted INDI control law.
- Incremental acceleration control: The controller inverts the linearized acceleration relation to compute an incremental command from desired and measured acceleration.The command increment is defined as u_c − u_f, making the law explicitly incremental.
4 Implementation
The implementation combines an acceleration-based outer INDI loop with PD position control, thrust modeling, adaptive actuator-effectiveness estimation, and an optional nonlinear inversion. Incremental feedback allows small modeling errors to be corrected over successive input updates.
- Position control: The outer INDI structure converts acceleration error into roll, pitch, and thrust increments, with the thrust increment passed directly to the inner loop.Acceleration is estimated from the accelerometer by rotation and gravity addition.
- Position control: Position control uses a manually tuned PD controller to generate the acceleration reference for the outer INDI loop.The gains are selected for a fast response with little overshoot and depend mainly on position-update rate and inner-loop speed.
- Adaptive control effectiveness: The adaptive method adds a thrust row to the control-effectiveness matrix, and experiments show each rotor’s effectiveness converged close to its offline value after 30 seconds.Ten manually piloted flights supplied excitation for the adaptation experiment.
- Thrust estimation: A thrust model fits a quadratic thrust-versus-rotational-rate curve from static measurements, while assuming static rotor effectiveness for computational speed.The model uses measured propeller RPM and avoids recalculating the inverse effectiveness matrix at every timestep.
- Linearization: The nonlinear inversion retains the incremental structure while computing new thrust, roll, and pitch commands without linearizing the input function.This addresses the nonlinear dependence of force on roll and pitch, especially for large input increments.
5 Windtunnel experiment
A controlled windtunnel experiment evaluates outer-loop INDI against a tuned PID controller during repeated entry into and exit from a strong wind flow. INDI restores acceleration tracking after disturbances and substantially limits position deviation relative to PID.
- Experimental setup: The experiment uses a 2.85 m by 2.85 m open-jet facility capable of 30 m/s, with flying in and out of the flow representing a strong gust.The professional windtunnel provides a more quantitative disturbance than the earlier fan experiment.
- Controller comparison: PID tuning trades faster offset compensation from higher integral gain against greater overshoot, whereas the stated trade-off does not occur for INDI.Both outer-loop controllers use the inner-loop INDI attitude controller.
- Results: About half a second after entering the wind stream, INDI’s acceleration coincided with the reference again despite a large disturbance spike.The controller increments its inputs from the measured acceleration error.
- Results: 0.21 m entering and 0.20 m leaving the windtunnel were INDI’s position errors, versus 1.51 m maximum error for PID.The measurements average seven repetitions; INDI counteracted its position error within three seconds.
- Results: Accelerometer feedback gives INDI greater variance than PID in steady wind-free portions, while stronger filtering could reduce noise at the cost of slower disturbance rejection.The comparison uses average trajectories and one standard deviation across seven repetitions.
6 Outdoor takeoff with wind
The outdoor takeoff experiment compares outer-loop INDI and PID control during wind disturbance using GPS-based position estimates. INDI achieves lower average maximum position error, although some runs show anomalously large errors associated with possible GPS problems.
- 6 Outdoor takeoff with wind: The experiment uses a standard external GPS receiver to evaluate disturbance rejection in an outdoor takeoff scenario.The external receiver was added because the quadrotor’s built-in GPS produced substantial position-estimate variation.
- 6.1 Results: One INDI flight was rejected because the state-estimation filter had not converged before takeoff, biasing the measured acceleration and position.The resulting acceleration bias produced a position offset.
- 6.1 Results: 0.24 m versus 0.85 m average maximum position error: INDI outperforms PID during windy outdoor takeoff.The comparison used twelve PID flights and thirteen INDI flights, with the position reference reset before each flight.
- 6.1 Results: Some INDI runs show relatively large errors despite similar average error after some time for both controllers.The anomalous runs may reflect GPS errors, potentially during satellite changes, rather than the main takeoff disturbance.
7 Nonlinear increment
The nonlinear thrust-vector increment is evaluated against a linearized calculation during aggressive acceleration reversals. The nonlinear implementation better averages the unintended vertical acceleration toward zero, but residual effects remain and larger changes require further study.
- 7 Nonlinear increment: Linearization errors become more significant for larger virtual-control changes, while filter cutoff frequency determines how quickly subsequent increments can correct them.The experiment uses the largest acceleration changes possible without actuator saturation, and further experiments are needed for larger changes.
- 7.1 Results: The linearized calculation causes a pronounced downward acceleration after the commanded reversal because thrust is initially reduced during the bank change.The linearized case also shows a slight upward acceleration during the initial lateral command.
- 7.1 Results: The nonlinear calculation instead produces initial upward acceleration and an upward-then-downward response after the reversal as thrust is adjusted through changing bank angles.The nonlinear increment accounts for the tilted thrust vector while actuator dynamics respond faster than rotational dynamics.
- 7.1 Results: The nonlinear implementation produces vertical acceleration that averages closer to the intended 0 m/s2 than the linearized implementation.The maneuver commands +4 m/s2 and −4 m/s2 lateral accelerations for successive half-second intervals, and is repeated 25 times.
- 7.1 Results: Residual unintended vertical acceleration remains because nonlinear input increments are realized imperfectly and the inner loop omits the nonlinear thrust curve.Thus, the nonlinear calculation improves tracking but does not eliminate vertical-acceleration error.
8 Conclusions
The paper demonstrates cascaded INDI for MAV attitude and position control, emphasizing disturbance rejection in gusts and reduced modeling requirements. It reports substantially lower windtunnel position deviation than PID and identifies actuator saturation and modeling assumptions as important boundaries.
- 8 Conclusions: More than 7 times lower maximum position deviation than a comparable PID controller is achieved when flying through a 10 m/s windtunnel flow.The conclusion attributes this result to cascaded INDI for both inner-loop attitude and outer-loop position control.
- 8 Conclusions: The controller can support operation close to obstacles in gusty environments while requiring only limited platform-specific modeling.Except for position and velocity gains, parameters can be determined from a test flight and actuator-dynamics identification.
- 8 Conclusions: Online adaptation of control effectiveness can accommodate airframe changes and support implementation on new platforms.The paper also reports outdoor applicability of the control method.
- 8 Conclusions: Nonlinear thrust-vector increments reduce maximum vertical-acceleration tracking error during an aggressive maneuver, but their broader benefit remains unresolved.The conclusion states that further research is needed to establish whether the improvement is significant.
- 8 Conclusions: Actuator saturation can still lead to instability because direct inversion and saturation may realize the control objective suboptimally across axes.The paper notes that axis-priority-aware control allocation may address this issue, based on preliminary research.