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REVIEW 4 major objections 5 minor 32 references

Sparse Identification of Nonlinear Dynamics-based Model Predictive Control for Multirotor Collision Avoidance

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read SINDy learns a drone's changed payload model, and MPC uses it to dodge obstacles.

desk verdict The SINDy-MPC collision-avoidance idea is reasonable, but Table 3's rotational coefficients don't match the stated plant model, so the identification claim doesn't hold as written. read the letter →

arxiv 2412.06388 v1 pith:VF2CADBJ submitted 2024-12-09 cs.RO math.OC

Jayden Dongwoo Lee , Youngjae Kim , Yoonseong Kim , Hyochoong Bang This is my paper · ORCID
classification cs.ROmath.OC
keywords SparseidentificationofnonlineardynamicsModelpredictivecontrolCollisionavoidanceMultirotorUAVData-drivenTrajectorytrackingAerodynamicuncertaintyPayloadparameter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes pairing sparse identification of nonlinear dynamics (SINDy) with model predictive control (MPC) so a multirotor can keep flying accurately when its payload changes. SINDy learns the vehicle's equations of motion from flight data, including aerodynamic drag and the changed mass, and MPC uses that learned model to track a reference path while treating an obstacle as a hard distance constraint. Simulation shows the combined controller tracks a trajectory with lower root-mean-square error than a nominal MPC that ignores the payload, and it avoids a static obstacle. The value of the claim is that a drone carrying unknown cargo can be re-modeled from data rather than re-deriving its physics.

What carries the argument

The enabling object is the sparse regression step of SINDy, where the time derivatives of the translational and rotational states are fit to a library of candidate functions built from prior physics knowledge plus polynomials. The prior functions encode the known thrust-allocation and gyroscopic structure, so the sparse coefficients recovered by sequential thresholded least squares correspond to physical parameters such as inverse mass, aerodynamic force coefficients, and moment coefficients. These coefficients define the approximate dynamics $\dot{x} = \hat{f}(x,u)$ that feed the MPC prediction, with the obstacle encoded as the inequality $\sqrt{(x_{ob}-x)^2+(y_{ob}-y)^2+(z_{ob}-z)^2} \ge D_{\min}$.

What would settle it

Record a closed-loop run on a trajectory with sustained yaw rotations, such as a figure-eight with heading changes, under the same 20% mass uncertainty; if position error remains small despite the identified yaw damping coefficient being 33% off, the under-excitation is harmless, while a large yaw error would show that the claim depends on not exercising that axis.

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Extended reading notes

Core claim

The central claim is that a full-order nonlinear multirotor model, including payload-induced mass and inertia changes and lumped aerodynamic effects, can be recovered by SINDy from data collected with a simple PID controller on a rectangular trajectory, and that the recovered model is accurate enough to serve as the prediction model in MPC. The identified translational coefficients match the true values to within a few percent, while the yaw-axis aerodynamic damping coefficient is off by roughly thirty-three percent because that axis was not excited in training. In closed-loop simulation under twenty percent mass uncertainty and an unknown aerodynamic model, SINDy-MPC tracks the reference with RMSE of 0.81 m in x, 0.38 m in y, and 0.40 m in z, beating the nominal-MPC baseline of 0.91, 0.45, and 0.63 m, and it satisfies the obstacle-avoidance inequality. The paper states that this is the first SINDy-MPC formulation for multirotor collision avoidance.

Load-bearing premise

The load-bearing premise is that the rectangular PID training trajectory excites every dynamic mode the closed-loop task will use; the paper itself reports that the yaw axis was not excited, leaving the model's yaw accuracy unverified for flight regimes that demand yaw.

Editorial extensions

If this is right

  • Under 20% mass uncertainty and an unknown aerodynamic payload model, SINDy-MPC tracks the reference with lower RMSE than nominal MPC on all three axes.
  • The obstacle is avoided without a separate planning layer: the collision constraint is folded into the MPC optimization, and computation stays fast enough for a real-time loop.
  • The data-driven model recovers physical coefficients (thrust, drag, gyroscopic coupling) that match the true values to within about 3%, so the model is interpretable rather than a black box.
  • Training data can be gathered by a standard PID controller following a rectangular path, which is practical for a real drone.
  • The method extends SINDy-MPC from attitude and tracking tasks studied earlier to collision-avoidance flight.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the training data under-excites yaw, the 33% yaw-damping error suggests the general claim depends on the test trajectory not stressing that axis; a testable extension is to quantify a persistence-of-excitation score for the data collection trajectory and verify closed-loop performance on trajectories that excite yaw.
  • The same offline-identified model would likely degrade if the payload changes after learning; an implicit extension is to update the SINDy coefficients online with a sliding window, turning the method into an adaptive MPC.
  • The obstacle constraint is a static spherical safe distance; extending to moving obstacles or multiple obstacles would require evaluating the inequality at every prediction step, which the current formulation can likely accommodate but the paper does not demonstrate.
  • The comparison baseline is a nominal MPC without adaptation; a fairer practical test would compare against another adaptive or learning controller under the same uncertainty.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a data-driven model predictive control framework for multirotor trajectory tracking and static-obstacle avoidance. The authors collect flight data from a PID-controlled rectangular trajectory, use sparse identification of nonlinear dynamics (SINDy) with a physics-informed candidate library to identify a full-order translational and rotational model, and then embed the identified model in an MPC formulated with ACADO, adding an obstacle-avoidance inequality constraint. Simulation results are presented for a scenario with 20% mass uncertainty and an unknown aerodynamic model, where SINDy-MPC is reported to track a reference trajectory with lower RMSE than a nominal MPC baseline.

Significance. If the results are valid, the paper offers a useful integration of SINDy and MPC for multirotor collision avoidance under model uncertainty, and it provides a clear demonstration that a sparse, interpretable model can be used inside a constrained optimal-control loop. The use of a physics-informed library and the full-order rotational/translational formulation are reasonable choices, and the reported computation time being below the loop time is a positive indicator for real-time applicability. However, the significance is limited by the fact that the candidate library already contains the true functional forms, so the 'discovery' is largely a coefficient-estimation exercise, and by the lack of independent validation data. Most importantly, the internal consistency problem in the rotational identification table undermines the accuracy claim as written.

major comments (4)
  1. The true rotational coefficients in Table 3 are not consistent with the plant model defined in Eq. (4) and the parameter values in Table 1. Using Ixx=0.0281, Iyy=0.0286, Izz=0.0551 and KM=0.001, Eq. (4) gives for the p-dot row: L coefficient 1/Ixx=35.59, qr coefficient (Iyy-Izz)/Ixx=-0.943, and damping -KM/Ixx=-0.0356. Table 3 instead reports 32.258, +0.8065, and -0.0323, which correspond to a different inertia set of roughly I=[0.0310, 0.0380, 0.0630] kg*m^2. The q and r rows show the same discrepancy. Consequently, the claimed 'within about 3%' identification accuracy is not verifiable as written, and the closed-loop success in Section 5.3 cannot be traced to a validated identified model. This is a load-bearing internal inconsistency, not a matter of presentation.
  2. Table 3 reports identified and true coefficients for the terms p*Omega and q*Omega, but the rotational candidate library in Eq. (21) contains only L, M, N, pq, qr, pr, a constant, and polynomials in p, q, r; there is no Omega term anywhere in the library. As written, the SINDy regression in Eq. (23) cannot produce nonzero p*Omega or q*Omega coefficients. The authors should either add these terms to the library definition or explain why the table includes them. This mismatch makes the method unreproducible.
  3. The data-driven model is validated on the same simulator that generated the training data, and the closed-loop test does not appear to strongly excite the yaw axis, which is the axis for which the authors report a 33% identification error in the damping coefficient. To support the general claim that SINDy discovers the governing equation including aerodynamic effects, the paper should test the identified model on trajectories that differ from the rectangular training trajectory and that include meaningful yaw maneuvers, or should explicitly restrict the claim to the axes and motion regime that were actually excited during data collection.
  4. The MPC formulation and the simulation comparison are incompletely specified. The horizon N, the prediction sampling time, the weight matrices Q and R, the obstacle position and Dmin, and the control-input limits are not reported, so Table 4 cannot be reproduced. In addition, the collision-avoidance claim is supported only by a qualitative trajectory plot; the paper should report the minimum distance to the obstacle or another quantitative metric showing that the inequality constraint is satisfied.
minor comments (5)
  1. There is a typo in the Introduction: 'SIDNy' should be 'SINDy'.
  2. The word 'multitorotor' appears in the text describing the rotational model; it should be 'multirotor'.
  3. The z-translation row reports a constant term of +9.807, but Eq. (3) with the NED gravity vector g=[0,0,g]^T gives a -g term; the sign convention for the z-axis and thrust direction should be clarified.
  4. The allocation matrix in Eq. (7) uses signs and the coefficient c_T without defining the sign convention for the thrust forces T_i or the direction of positive moments; this should be stated to make the model unambiguous.
  5. Reference [20] lists the authors as 'S. L. Brunton E. Kaiser, J. N. Kutz'; the author order and punctuation appear incorrect and should be fixed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the SINDy model is fitted on a rectangular training trajectory and then evaluated on a different reference/obstacle scenario, so the closed-loop result is not forced by construction.

full rationale

The paper's derivation chain is not circular. SINDy is used offline to fit coefficients from a PID-driven rectangular trajectory; the fitted model is then embedded in an MPC and tested on a different trajectory with a static obstacle. The identified coefficients are compared with analytic 'true' values, and a 33% error on the yaw damping coefficient is openly reported, demonstrating that the identification is not forced to match the truth. The physics-informed library terms encode known functional structure but not the coefficient values, so no self-definitional reduction is present. Self-citations ([15], [21], [29]) appear only as related-work context and do not carry the argument. The open-source ACADO solver and the SINDy baseline literature are independent external support. The main caveat is an internal-consistency issue, not a circularity: the 'true' rotational coefficients in Table 3 do not match the values implied by Eq. (4) and Table 1 (e.g., the p-dot L coefficient should be 1/Ixx = 35.59 rather than 32.258), and Table 3 includes pOmega/qOmega terms absent from the stated model. That is a correctness/reproducibility concern about how the simulated plant or the 'true' parameters were generated; it does not amount to a prediction reducing to its inputs by construction. No load-bearing self-citation chain or fitted-parameter-renamed-as-prediction step was found.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced; the identified model is a fitted representation. The free parameters are tuning choices with no reported values or sensitivity analysis, and the axioms are standard modelling and solver assumptions, one of which (persistent excitation) is explicitly violated for the yaw axis in the paper's own results.

free parameters (6)
  • SINDy L1 regularization parameters (lambda_tr, lambda_ro)
    Chosen to promote sparsity; values not reported and no sensitivity study given.
  • STLS sparsity threshold
    Threshold for coefficient pruning in sequential thresholded least squares; not reported.
  • Polynomial library degrees (d, w)
    Maximum polynomial order for translational and rotational libraries; not reported.
  • MPC horizon N
    Number of prediction steps in the MPC; directly affects performance and is not reported.
  • MPC weight matrices Q and R
    Tuning weights in the quadratic cost; not reported and directly affect tracking and control effort.
  • Obstacle safety distance D_min
    Minimum allowed distance to obstacle in the inequality constraint; not reported.
assumptions (5)
  • domain assumption The multirotor dynamics in Eqs. (1)-(6) with lumped aerodynamic model (9) exactly describe the true plant.
    The simulator and the SINDy training data are generated from these equations; the claim is only validated against this assumed model.
  • ad hoc to paper The candidate function library Psi in Eqs. (17)-(21) contains the true functional terms (thrust terms, gyroscopic couplings, and damping terms), so the true dynamics lie in its span.
    The authors deliberately include physical prior knowledge in the library, which makes the identification a regression over known basis functions rather than open-ended discovery.
  • standard math The STLS algorithm converges to the global sparse solution of the L1 regression problem (22)-(23).
    STLS is a standard heuristic; no proof of global optimality is provided, but the paper reports low coefficient errors.
  • domain assumption The ACADO solver returns a feasible locally optimal solution at each MPC step, including with the nonconvex obstacle inequality constraint.
    No feasibility or stability guarantee is given; the paper only shows one computation-time trace.
  • domain assumption The PID-collected training data are persistently exciting for all states relevant to the closed-loop task.
    The paper acknowledges that yaw excitation was insufficient (33% yaw damping error), so this assumption is only partially satisfied.

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Cite this review

Pith. "Pith review of Sparse Identification of Nonlinear Dynamics-based Model Predictive Control for Multirotor Collision Avoidance." pith.science (2026). https://pith.science/paper/VF2CADBJ

@misc{pith2026241206388,
  author       = {Pith},
  title        = {Pith review of: Sparse Identification of Nonlinear Dynamics-based Model Predictive Control for Multirotor Collision Avoidance},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VF2CADBJ}},
  note         = {Machine review of arXiv:2412.06388}
}
read the original abstract

This paper proposes a data-driven model predictive control for multirotor collision avoidance considering uncertainty and an unknown model from a payload. To address this challenge, sparse identification of nonlinear dynamics (SINDy) is used to obtain the governing equation of the multirotor system. The SINDy can discover the equations of target systems with low data, assuming that few functions have the dominant characteristic of the system. Model predictive control (MPC) is utilized to obtain accurate trajectory tracking performance by considering state and control input constraints. To avoid a collision during operation, MPC optimization problem is again formulated using inequality constraints about an obstacle. In simulation, SINDy can discover a governing equation of multirotor system including mass parameter uncertainty and aerodynamic effects. In addition, the simulation results show that the proposed method has the capability to avoid an obstacle and track the desired trajectory accurately.

Figures

Figures reproduced from arXiv: 2412.06388 by the authors.

Figure 1
Figure 1. Configuration of multirotor with payload. The position and Euler angles measured in the {I} frame are represented by vectors η = [x, y, z] ⊤ ∈ R 3 and Ω = [ϕ, θ, ψ] ⊤ ∈ R 3 . The velocity in {I} frame is represented by vectors ν = [ ˙x, y,˙ z˙] ⊤ ∈ R 3 . The angular rates measured in the {B} frame is represented by vectors ω = [p, q, r] ⊤ ∈ R 3 . The multirotor dynamics can be summarized as (1) - (6), where the foll… view at source ↗
Figure 2
Figure 2. Concept of SINDy. In practice, X˙ can be computed directly from the data in X. The numerical differential method such as simple forward Euler finite-difference can be utilized to obtain these values. For noisy data, the total variation regularized derivative typically yields numerically robust results [20]. Alternatively, it can be computed using SINDy methods for discrete-time systems xk+1 = F(xk), as in the DMD al… view at source ↗
Figure 3
Figure 3. Schematic of SINDy-MPC. 4.1 Data Collection for SINDy To obtain an accurate model, we should obtain rich data to discover a target system. The basic strategy to collect data is to use random control input to avoid an imbalance. For example, if our target system is an automobile, we can give arbitrary wheel angle and lateral acceleration as control input while not considering the stability of system. However, aerial … view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Schematic of control mode to collect data. 4.2 Modeling of Multirotor using SINDy When we formulate a nominal model for MPC, we should need a dynamics of multirotor system because a kinematics is known in advance. Therefore, we should find a translational and rotationa…
Figure 5
Figure 5. Figure 5: Concept of model predictive control. min u1,···uN X N k=1 ((ri − yi))⊤Q(ri − yi) + u ⊤ i Rui), s.t. x˙ = ˆf(x,u), umin ≤ u ≤ umax, x1 = xinit, p (xob − x) 2 + (yob − y) 2 + (zob − z) 2 ≥ Dmin, (25) where r is the reference trajectory, ˆf is the data-driven multirotor m…
Figure 6
Figure 6. Figure 6: Data collection using PID controller [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: shows the performance of translational and rotational acceleration pre￾diction using the SINDy method. The data-driven model shows an accurate prediction performance compared to the one-step prediction. In translational motion, the obtained parameters consist of a thru…
Figure 8
Figure 8. Figure 8: Trajectory tracking performance of SINDy-MPC and MPC [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: Trajectory tracking error [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Thrust result (left) and computation time (right). 6 Conclusion In this study, a novel data-driven model predictive control is proposed for a multirotor with payload. The suggested approach integrates sparse identification of nonlinear dynamics and model predictive co…

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Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages

  1. [1]

    J. Kim, Y. Choi, S. Jeon, J. Kang, and H. Cha. Optrone: Maximizing performance and energy resources of drone batteries. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 39(11):3931–3943, 2020

    work page 2020

  2. [2]

    K. Yang, G. Y. Yang, and S. I. H. Fu. Research of control system for plant protection uav based on pixhawk. Procedia Computer Science, 166:371–375, 2020

    work page 2020

  3. [3]

    Kwak and Y

    J. Kwak and Y. Sung. Autonomous uav flight control for gps-based navigation. IEEE Access, 6:37947–37955, 2018

    work page 2018

  4. [4]

    Chowdhury, A

    S. Chowdhury, A. Emelogu, M. Marufuzzaman, S. G. Nurre, and L. Bian. Drones for disaster response and relief operations: A continuous approximation model. International Journal of Production Economics, 188:167–184, 2017

    work page 2017

  5. [5]

    A. Khan, S. Gupta, and S. K. Gupta. Emerging uav technology for disaster detec- tion, mitigation, response, and preparedness. Journal of Field Robotics, 39(6):905– 955, 2022

    work page 2022

  6. [6]

    Aggarwal and N

    S. Aggarwal and N. Kumar. Path planning techniques for unmanned aerial vehicles: A review, solutions, and challenges. Computer communications, 149:270–299, 2020

    work page 2020

  7. [7]

    Rub ´ ı, R

    B. Rub ´ ı, R. P´ erez, and B. Morcego. A survey of path following control strategies for uavs focused on quadrotors. Journal of Intelligent & Robotic Systems, 98(2):241– 265, 2020

    work page 2020

  8. [8]

    S. H. Mathisen, K. Gryte, T. Johansen, and T. I. Fossen. Non-linear model pre- dictive control for longitudinal and lateral guidance of a small fixed-wing uav in precision deep stall landing. In Aiaa infotech@ aerospace, page 0512. 2016

    work page 2016

Show all 32 references
  1. [9]

    W. Jung, S. Lim, D. Lee, and H. Bang. Unmanned aircraft vector field path following with arrival angle control. Journal of Intelligent & Robotic Systems, 84:311–325, 2016

    2016

  2. [10]

    Lee and H

    H. Lee and H. J. Kim. Trajectory tracking control of multirotors from modelling to experiments: A survey. International Journal of Control, Automation and Systems, 15(1):281–292, 2017

    2017

  3. [11]

    H. Ahn, J. Park, H. Bang, and Y. Kim. Model predictive control-based multirotor three-dimensional motion planning with point cloud obstacle. Journal of Aerospace Information Systems, 19(3):179–193, 2022

    2022

  4. [12]

    J. L. Proctor, S. L. Brunton, and J. N. Kutz. Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems, 15(1):142–161, 2016

    2016

  5. [13]

    M. O. Williams, I. G. Kevrekidis, and C. W. Rowley. A data–driven approximation of the koopman operator: Extending dynamic mode decomposition. Journal of Nonlinear Science, 25:1307–1345, 2015

    2015

  6. [14]

    Sansica, J

    A. Sansica, J. C. Loiseau, M. Kanamori, A. Hashimoto, and J. C. Robinet. System identification of two-dimensional transonic buffet. AIAA Journal, 60(5):3090–3106, 2022

    2022

  7. [15]

    J. D. Lee, D. Seo, J. Shin, and H. Bang. Fast state-of-health estimation method for lithium-ion battery using sparse identification of nonlinear dynamics. arXiv, 2024

    2024

  8. [16]

    He and D

    X. He and D. R. Williams. Pressure feedback control of aerodynamic loads on a delta wing in transverse gusts. AIAA Journal, 61(4):1659–1674, 2023

    2023

  9. [17]

    R. Cao, K. Lu, and Y. Liu. An interpretable data-driven learning approach for nonlinear aircraft systems with noisy interference.IEEE Transactions on Aerospace and Electronic Systems, pages 1–12, 2024

    2024

  10. [18]

    Istiqphara, O

    S. Istiqphara, O. Wahyunggoro, and A. I. Cahyadi. Enhanced equation discovery of 3-dof robotic manipulator dynamics using lasso model selection criteria with variable segregation algorithm. IEEE Access, 12:20574–20590, 2024

    2024

  11. [19]

    A. Liu, Y. Xue, H. Qin, and Z. Zhu. Physics-informed identification of marine vehi- cle dynamics using hydrodynamic dictionary library-inspired adaptive regression. Ocean Engineering, 296:117013, 2024

    2024

  12. [20]

    S. L. Brunton E. Kaiser, J. N. Kutz. Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Proceedings of The Royal Society A, 474(2219), 2018

    2018

  13. [21]

    M. Kang, J. D. Lee, S. Yun, and H. Bang. Data-driven model discovery and control of high-performance trainer aircraft via sparse identification of nonlinear dynamics. 34th Congress of the International Council of the Aeronautical Sciences, 2024

    2024

  14. [22]

    Bhadriraju, J

    B. Bhadriraju, J. S. I. Kwon, and F. Khan. A data-driven framework integrating lyapunov-based mpc and oasis-based observer for control beyond training domains. Journal of Process Control, 138:103224, 2024

    2024

  15. [23]

    Manzoor, H

    T. Manzoor, H. Pei, Y. Xia, Z. Sun, and Y. Ali. Compound learning-based model predictive control approach for ducted-fan aerial vehicles. IEEE Transactions on Neural Networks and Learning Systems, pages 1–13, 2024

    2024

  16. [24]

    Manzoor, T.and Pei, Z

    H. Manzoor, T.and Pei, Z. Sun, and Z. Cheng. Model predictive control technique for ducted fan aerial vehicles using physics-informed machine learnwing. Drones, 7(1), 2023

    2023

  17. [25]

    Bhattacharya, R

    D. Bhattacharya, R. Hashem, L. K. Cheng, and W. Xu. Nonlinear model predictive control of a robotic soft esophagus. IEEE Transactions on Industrial Electronics, 69(10):10363–10373, 2022

    2022

  18. [26]

    Kelm and S

    B. Kelm and S. Myschik. Model-based control reconfiguration of a multirotor uav using online system identification by sparse regression (sindyc). AIAA A VIATION 2023 Forum

    2023

  19. [27]

    Z. M. Manaa, M. R. Elbalshy, and A. M. Abdallah. Data-driven discovery of the quadrotor equations of motion via sparse identification of nonlinear dynamics. AIAA SCITECH 2024 Forum

    2024

  20. [28]

    R. D. Vel´ azquez-S´ anchez, J. O. Escobedo-Alva, R. Pe˜ na-Garc ´ ıa, R. Tapia-Herrera, and J. A. Meda-Campa˜ na. Identification of high-order nonlinear coupled systems using a data-driven approach. Applied Sciences, 14(9), 2024

    2024

  21. [29]

    J. D. Lee, S. Im, and H. Bang. Data-driven fault detection and isolation for quadro- tor using sparse identification of nonlinear dynamics and Thau observer. 2024 International Conference on Unmanned Aircraft Systems, pages 382–389, 2024

    2024

  22. [30]

    H. Lee, J. Kim, and Y. Kim. Sliding surface-based integral reinforcement learn- ing for optimal tracking control of quadcopters considering uncertainties. IEEE Transactions on Aerospace and Electronic Systems, pages 1–15, 2024

    2024

  23. [31]

    Houska, H

    B. Houska, H. J. Ferreau, and M. Diehl. Acado toolkit–an open source framework for automatic control and dynamic optimization. Optimal Control Applications and Methods, 32:298 – 312, 05 2011

    2011

  24. [32]

    Pid control of quadrotor uavs: A survey

    Ivan Lopez-Sanchez and Javier Moreno-Valenzuela. Pid control of quadrotor uavs: A survey. Annual Reviews in Control, 56:100900, 2023

    2023

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Reviewed August 11, 2026 · model on record in the stance chip above.