Source-linked AI summary
Performance, Precision, and Payloads: Adaptive Nonlinear MPC for Quadrotors
Drew Hanover, Philipp Foehn, Sihao Sun, Elia Kaufmann, Davide Scaramuzza
TL;DR
NMPC performance depends on accurate models, while aerodynamic effects, payload changes, and other uncertainties can degrade quadrotor tracking. The paper proposes L1-NMPC, which combines NMPC with an L1 adaptive controller for real-time compensation, achieving large tracking improvements across mismatched and aggressive-flight conditions without gain retuning.
Problem
NMPC relies on accurate models, but aerodynamic effects, varying payloads, and external disturbances can degrade quadrotor tracking and reliability.
Method
L1-NMPC cascades a nonlinear model predictive controller with an L1 adaptive controller that compensates for model mismatch and disturbances in real time.
Results
L1-NMPC reduced tracking error by over 90% in mass-mismatch cases and outperformed GP-MPC by over 70% in real-world trajectory tests.
Takeaways & Limitations
The same controller can track highly aggressive racing trajectories and carry unknown payloads without additional gain tuning or online retraining.
Abstract
from arXiv · showhide
Agile quadrotor flight in challenging environments has the potential to revolutionize shipping, transportation, and search and rescue applications. Nonlinear model predictive control (NMPC) has recently shown promising results for agile quadrotor control, but relies on highly accurate models for maximum performance. Hence, model uncertainties in the form of unmodeled complex aerodynamic effects, varying payloads and parameter mismatch will degrade overall system performance. In this paper, we propose L1-NMPC, a novel hybrid adaptive NMPC to learn model uncertainties online and immediately compensate for them, drastically improving performance over the non-adaptive baseline with minimal computational overhead. Our proposed architecture generalizes to many different environments from which we evaluate wind, unknown payloads, and highly agile flight conditions. The proposed method demonstrates immense flexibility and robustness, with more than 90% tracking error reduction over non-adaptive NMPC under large unknown disturbances and without any gain tuning. In addition, the same controller with identical gains can accurately fly highly agile racing trajectories exhibiting top speeds of 70 km/h, offering tracking performance improvements of around 50% relative to the non-adaptive NMPC baseline.
SUPPLEMENTARY MATERIAL
The paper motivates adaptive quadrotor control for industrial, transportation, and rescue applications where agile trajectory tracking must tolerate uncertain dynamics and disturbances. It proposes L1-NMPC to compensate for these uncertainties online while retaining aggressive flight capability.
- Motivation: UAV applications require accurate agile-trajectory tracking despite unknown drag, varying payloads, wind gusts, and other external disturbances.These uncertainties can degrade performance and reliability, potentially causing loss of control.
- Motivation: High-fidelity models can improve control performance but are expensive to obtain and require substantial domain expertise.
- Motivation: Robust control methods may enable safer behavior but can impose significant performance degradation, while wind prediction is often impractical.
- Contribution: L1-NMPC cascades nonlinear model predictive control with an L1 adaptive controller to compensate for model uncertainties and disturbances in real time.The architecture targets windy environments, unknown payloads, and aggressive racing trajectories without retuning control gains.
- Contribution: More than 90% tracking-error reduction was achieved with unknown payloads up to 60% of quadrotor mass on a real quadrotor.The method also tracked racing trajectories with unknown slung payloads.
II. RELATED WORK
Prior work established adaptive and predictive approaches for quadrotor control, but often focused on simpler maneuvers, lacked prediction, or had limited real-hardware validation. This paper combines L1 adaptation with nonlinear MPC to address agile flight across simulation and reality.
- Prior quadrotor control: Most quadrotor trajectory-tracking studies focus on hover or slow maneuvers that permit small-angle linear-control assumptions.This work instead targets a wider flight envelope near the platform’s physical limits.
- Adaptive control: L1 adaptive control is used because its rapid adaptation is decoupled from controller robustness and drives systems toward desired reference-model behavior.
- Adaptive control: Earlier adaptive approaches commonly demonstrated simple or slow trajectories, while cascaded MPC methods addressed persistent mismatch without covering the full agile-control problem.
- Predictive control: L1-MPPI had not been demonstrated on real hardware, and its reported simulation footage showed highly oscillatory control performance.The associated MPPI controller was also limited to 50 Hz on desktop hardware.
- This work: The proposed L1-NMPC combines adaptive control with nonlinear MPC to retain prediction-horizon planning and exploit system nonlinearities.The controller is evaluated against several state-of-the-art methods in simulation and on physical hardware.
III. METHODOLOGY
The methodology defines quadrotor frames, orientation, dynamics, thrust allocation, and numerical discretization for a nonlinear model. The model uses world and body coordinates, rotor-generated thrust and torque, and fourth-order Runge–Kutta integration.
- Notation: The quadrotor model uses world and body frames, with the body frame located at the vehicle center of mass and rotors placed in its xy-plane.The frame convention and propeller numbering are illustrated in Figure 2.
- Notation: Unit quaternions represent body orientation, while quaternion-vector products rotate body-frame vectors into the world frame.
- Quadrotor vehicle dynamics: The system dynamics include gravity, collective rotor thrust, mass, diagonal inertia, and body torque.
- Quadrotor vehicle dynamics: A thrust allocation matrix maps individual rotor effects to collective thrust and body torques using rotor positions and drag-torque coefficients.
- Discretization: The continuous dynamics are discretized with an explicit fourth-order Runge–Kutta method.
C. MPC Formulation
The controller combines a discretized NMPC formulation with an L1 adaptive augmentation that estimates matched and unmatched uncertainties and filters the resulting compensation before updating the observer.
- C. MPC Formulation: The NMPC solves a discretized nonlinear optimal control problem using multi-shooting.The formulation is implemented as a quadratic optimization problem and solved with sequential quadratic programming in a real-time iteration scheme.
- D. L1-Adaptive Augmentation: The L1 controller uses a nonlinear reference model and a piecewise-constant adaptation law to estimate matched and unmatched uncertainties.The adaptive input can operate alone or be added to the NMPC signal.
- D. L1-Adaptive Augmentation: The system dynamics are rewritten to represent both matched and unmatched uncertainties.The formulation distinguishes uncertainties that can be compensated directly from those appearing in directions unavailable to the underactuated quadrotor.
- D. L1-Adaptive Augmentation: Unmatched uncertainties appear in the X and Y linear accelerations and cannot be compensated for directly because they lie in the null space of the controllability matrix.The remaining matched uncertainties can be compensated directly.
- D. L1-Adaptive Augmentation: The rotor thrusts used in the angular input are obtained from the NMPC solution at the current time.This connects the adaptive augmentation to the baseline NMPC command.
- D. L1-Adaptive Augmentation: The observer compares an estimated state with the state predicted by the L1 observer to construct the adaptation error.The adaptation matrix is represented by a Hurwitz matrix and the associated discrete-time transition term.
- D. L1-Adaptive Augmentation: A strictly proper first-order filter shapes the adaptive control signal before discrete-time implementation.The filter cutoff frequency is denoted by ωco.
- D. L1-Adaptive Augmentation: The discrete-time observer propagates its predicted state using nominal dynamics, adaptive matched and unmatched estimates, and the adaptation-error term.The propagation uses the sampling interval Ts.
IV. EXPERIMENTS AND RESULTS
The experiments evaluate L1-NMPC against alternative controllers through simulation and real-world tests designed around disturbance rejection, transferability, and agile tracking.
- IV. EXPERIMENTS AND RESULTS: The experiments test comparison with data-driven MPC, response to parametric and non-parametric disturbances, and generalization without gain tuning.The evaluation spans simulation and real-world tests involving large external disturbances and agile maneuvers.
- IV. EXPERIMENTS AND RESULTS: Controller update times are reported in Table I for implementations running on a specified Intel Core i7-8750H laptop with CUDA 11.2.The listed hardware includes 16 Gb of RAM and an Nvidia GeForce GTX 1060.
A. Simulation
The simulation compares L1-NMPC with several state-of-the-art controllers, including data-driven, sampling-based, and adaptive alternatives, under different aerodynamic-model configurations.
- A. Simulation: The simulation compares SRT-NMPC, GP-MPC, MPPI with Baseline Control, INDI-NMPC, and L1-NMPC.L1-NMPC is tested both with and without an aerodynamic model in the underlying NMPC.
1) Without Disturbance:
Without disturbance, the experiments assess controller performance under perfectly known simulated dynamics and then compare tracking performance and computational behavior across methods.
- 1) Without Disturbance:: The no-disturbance experiments use perfectly known mass, inertia, drag, and rotor-arm parameters in both the simulator and NMPC model.These trials estimate the maximum performance achievable under perfect model identification.
- 1) Without Disturbance:: L1-NMPC without an aerodynamic model outperforms INDI-NMPC and GP-MPC except on the fastest circle trajectories.This result indicates partial compensation for unmodeled aerodynamics by the adaptation law.
- 1) Without Disturbance:: Less than 1 cm RMSE improvement is observed for L1-NMPC over a 60 s trajectory when the drag model is enabled.With perfectly matched model parameters, the expected performance benefit is small; SRT-NMPC becomes the remaining simulation baseline because it has 80% less computational overhead than GP-MPC.
2) Model Mismatch:
The experiments evaluate NMPC under mass, inertia, and rotor-arm model mismatches. L1-NMPC substantially improves robustness, especially for mass mismatch, while extreme payload cases exceed the simulated vehicle’s thrust limits.
- Model-mismatch cases: The model-mismatch tests vary quadrotor mass, inertia, and rotor-arm geometry across increasing-speed 5 m radius circle trajectories.Mass increases by 660 g, inertia doubles, and rotor-arm geometry is altered to represent a center-of-gravity shift.
- Experimental control: The baseline NMPC comparison includes an additional positional-error integrator because pure-mass disturbances otherwise produce steady-state target Z-height offsets.Controller gains remain unchanged from the nominal tests.
- Mass mismatch: L1-NMPC reduces tracking error by over 90% in all mass-mismatch cases.Only NMPC with integrator action and L1-NMPC compensate for the mass mismatch.
- Inertia and rotor-arm mismatch: For inertia and rotor-arm disturbances, INDI-NMPC and L1-NMPC perform almost identically, with less than 5 mm performance difference across 10 cases.The adaptive architecture remains robust to these uncertainties without gain tuning or model learning.
B. Real World Experiments
Real-world tests cover nominal circles, unknown payloads, aerodynamic disturbances, and agile racing trajectories. Across these settings, L1-NMPC improves tracking and compensates for disturbances without updating model parameters or controller gains.
- Experimental settings: The real-world evaluation uses five settings spanning increasing-speed circles, unknown payloads, aerodynamic forces, and mildly to highly aggressive flight.The tested trajectories reach 19.4 m s−1, with payload and disturbance conditions included.
- Nominal flight: Without an aerodynamic model, L1-NMPC outperforms GP-MPC by over 70% and slightly outperforms INDI-NMPC in nominal increasing-speed circles.SRT-NMPC with a linear aerodynamic model matches GP-MPC and is used as the baseline moving forward.
- Unknown payload: With a 450 g payload, L1-NMPC achieves less than 1 cm steady-state Z-position error, compared with over 35 cm for non-adaptive MPC.The payload represents a mass increase of over 60%, and the adaptive controller applies higher rotor thrust immediately after takeoff.
- Aerodynamic disturbance: Under fan-generated aerodynamic disturbance, L1-NMPC compensates in real time and maintains acceptable, albeit reduced, tracking performance.The baseline NMPC shows sizeable tracking degradation in the same setting.
- Agile flight with payload: With a 100 g slung payload, L1-NMPC reduces tracking error by 44% relative to non-adaptive NMPC and outperforms INDI-NMPC by 34%.The trajectory reaches 11.9 m s−1 and exceeds 2 g of peak linear acceleration.
- Highly aggressive flight: On the most aggressive trajectory, L1-NMPC improves performance by 49% relative to baseline SRT-NMPC and trails INDI-NMPC by less than 5 cm RMSE.The trajectory reaches around 20 m s−1 and exceeds 4 g of linear acceleration.
- Robustness and deployment: All experiments use unchanged high-level MPC and adaptive-controller settings, demonstrating accurate tracking across varied trajectories and unknown disturbances with minimal computational overhead.The onboard implementation solves the optimal control problem at 100 Hz.
V. DISCUSSION
The L1 adaptive controller improves baseline NMPC tracking by immediately compensating for model mismatch and external disturbances, with benefits across the tested cases. The discussion also contrasts adaptive approaches and identifies controller choices under specific maneuver and model-accuracy conditions.
- Immediate compensation for model mismatch and external disturbances enhances baseline NMPC tracking across all tested cases.
- At least 50% greater performance benefit than GP-MPC is achieved without its large computational overhead.
- L1-MPPI exhibits high-frequency body-rate oscillations, while its sampling approach may suffer from the curse of dimensionality in 4D.
- For aggressive maneuvers with over 4g linear accelerations and high model confidence, INDI-NMPC offers the best performance among the considered controllers.
VI. CONCLUSION
The paper augments multi-shooting NMPC with an L1 adaptive inner loop that compensates for model mismatch using rotor-level adaptation and real-time corrective control. The resulting L1-NMPC improves performance over non-adaptive and data-driven baselines, supports aggressive racing and payloads without gain retuning, but may violate actuator constraints.
- The proposed architecture augments multi-shooting NMPC with an L1 adaptive inner-loop controller to compensate for model mismatch.
- 10 microseconds is sufficient for the adaptive controller to compute corrective control signals with minimal computational overhead.
- The method outperforms state-of-the-art data-driven MPC methods in simulation and extensive real-world quadrotor tracking tests.
- L1-NMPC flies highly aggressive racing trajectories and carries payloads without additional gain tuning.
- A potential drawback is actuator-constraint violation caused by the inner-loop cascade.