Uncertainties resulting from intricate internal model uncertainties and external environmental disturbances significantly degrade robot planning and control performance. However, recognizing such persistently varying uncertainties in an explainable and lightweight manner is exceptionally challenging. We present two converged uncertainty prediction frameworks through the Fusion of Online Reactive Estimation and Sustained Experience Exploitation for Robots (FORESEER), enabling accurate prediction of two general kinds of uncertainties. Both frameworks feature properties of precision, lightweight, universality, and stability, in comparison with existing solutions. At first, a prediction algorithm for nonlinearly parametric uncertainties is developed by merging analytical basis learning with online symbolic adaptive estimation. Furthermore, an online prediction algorithm for more challenging composite uncertainties is proposed by seamlessly integrating learning-based feedforward and model-based/symbolic feedback observer. Benchmark comparisons on flying drones showcase the accuracy of the FORESEER on various real uncertainties including mass, aerodynamic drag, rain, and rope tension, leading to subsequent high-precision control. Moreover, an energy-saving and time-saving planning strategy is presented by utilizing the favorable wind. The developed algorithms hold the promising potential for direct combination with existing planning/control algorithms, promoting the environmental adaptability of robots.
AlamirM (2022) Learning against uncertainty in control engineering. Annual Reviews in Control53: 19–29.
2.
AnnaswamyAMFradkovAL (2021) A historical perspective of adaptive control and learning. Annual Reviews in Control52: 18–41.
3.
AokiSKLillacciGGuptaA, et al. (2019) A universal biomolecular integral feedback controller for robust perfect adaptation. Nature570(7762): 533–537.
4.
BarabanGSheckellsMKimS, et al. (2020) Adaptive parameter estimation for aerial manipulation. In: 2020 American Control Conference, Denver, CO, USA, 01–03 July 2020, pp. 614–619.
5.
BertinettoLHenriquesJFTorrP, et al. (2019) Meta-learning with differentiable closed-form solvers. In: International Conference on Learning Representations, New Orleans, LA, USA, 06–09 May 2019.
6.
BruderDFuXGillespieRB, et al. (2020) Data-driven control of soft robots using Koopman operator theory. IEEE Transactions on Robotics37(3): 948–961.
7.
BruntonSLProctorJLKutzJN (2016) Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences of the United States of America113(15): 3932–3937.
8.
CastilloASanzRGarciaP, et al. (2019) Disturbance observer-based quadrotor attitude tracking control for aggressive maneuvers. Control Engineering Practice82: 14–23.
9.
ChaffreTWheareJLammasA, et al. (2024) Sim-to-real transfer of adaptive control parameters for AUV stabilisation under current disturbance. The International Journal of Robotics Research44: 407.
10.
ChenKAstolfiA (2020) Adaptive control for systems with time-varying parameters. IEEE Transactions on Automatic Control66(5): 1986–2001.
11.
ChenRTRubanovaYBettencourtJ, et al. (2018) Neural ordinary differential equations. In: Advances in Neural Information Processing Systems, Montréal, QC, Canada, 02–08 December 2018, Vol. 31.
12.
ChenYCWoolseyCA (2024) A structure-inspired disturbance observer for finite-dimensional mechanical systems. IEEE Transactions on Control Systems Technology32(2): 440–455.
13.
ChenWBallanceDGawthropP, et al. (2000) A nonlinear disturbance observer for robotic manipulators. IEEE Transactions on Industrial Electronics47(4): 932–938.
14.
ChenWYangJGuoL, et al. (2016) Disturbance-observer-based control and related methods—an overview. IEEE Transactions on Industrial Electronics63(2): 1083–1095.
15.
ChenCChenXMaC, et al. (2022) Gradient-based bi-level optimization for deep learning: a survey. arXiv preprint arXiv:2207.11719.
16.
ChowdharyGJohnsonE (2010) Concurrent learning for convergence in adaptive control without persistency of excitation. In: 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, 15–17 December 2010, pp. 3674–3679.
17.
ClaveraINagabandiALiuS, et al. (2019) Learning to adapt in dynamic, real-world environments through meta-reinforcement learning. In: International Conference on Learning Representations, New Orleans, LA, USA, 06–09 May 2019.
18.
CranmerMGreydanusSHoyerS, et al. (2020) Lagrangian neural networks. arXiv preprint arXiv:2003.04630.
19.
DoyleJ (1996) Robust and optimal control. IEEE Conference on Decision and Control2: 1595–1598.
20.
DuanYAchermannFLimJ, et al. (2024) Energy-optimized planning in non-uniform wind fields with fixed-wing aerial vehicles. arXiv preprint arXiv:2404.02077.
21.
EschmannJAlbaniDLoiannoG (2024) Learning to fly in seconds. IEEE Robotics and Automation Letters9(7): 6336–6343.
22.
EstevezJGarateGLopez-GuedeJM, et al. (2024) Review of aerial transportation of suspended-cable payloads with quadrotors. Drones8(2): 35.
23.
FaesslerMFranchiAScaramuzzaD (2017) Differential flatness of quadrotor dynamics subject to rotor drag for accurate tracking of high-speed trajectories. IEEE Robotics and Automation Letters3(2): 620–626.
24.
FinnCAbbeelPLevineS (2017) Model-agnostic meta-learning for fast adaptation of deep networks. In: International Conference on Machine Learning, Sydney, NSW, Australia, 06–11 August 2017, pp. 1126–1135.
25.
FoehnPBrescianiniDKaufmannE, et al. (2020) AlphaPilot: autonomous drone racing. In: Robotics: Science and Systems, Corvallis, OR, USA, 12–16 July 2020.
26.
FuTSuSLuY, et al. (2024) iSLAM: imperative SLAM. IEEE Robotics and Automation Letters9: 4607.
27.
GreiffMVinodANabiS, et al. (2023) Quadrotor motion planning in stochastic wind fields. In: American Control Conference, San Diego, CA, USA, 31–02 June 2023, pp. 4619–4625.
28.
GreydanusSDzambaMYosinskiJ (2019) Hamiltonian neural networks. In: Advances in Neural Information Processing Systems, Vancouver, BC, Canada, 08–14 December 2019.
29.
GuerreroJAEscarenoJABestaouiY (2013) Quad-rotor MAV trajectory planning in wind fields. In: 2013 IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, 06–10 May 2013, pp. 778–783.
30.
GuoKPanY (2023) Composite adaptation and learning for robot control: a survey. Annual Reviews in Control55: 279–290.
31.
GuoKJiaJYuX, et al. (2019) Dual-disturbance observers-based control of UAV subject to internal and external disturbances. In: Chinese Automation Congress, Hangzhou, Zhejiang, China, 22–24 November 2019, pp. 2683–2688.
32.
GuoKJiaJYuX, et al. (2020) Multiple observers based anti-disturbance control for a quadrotor UAV against payload and wind disturbances. Control Engineering Practice102: 104560.
33.
GuoLLiWZhuY, et al. (2023) Composite disturbance filtering: a novel state estimation scheme for systems with multisource, heterogeneous, and isomeric disturbances. IEEE Open Journal of the Industrial Electronics Society4: 387–400.
34.
GuoYRenZWangC (2024) iMTSP: solving min-max multiple traveling salesman problem with imperative learning. In: 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems, Abu Dhabi, United Arab Emirates, 14–18 October 2024.
35.
HaggertyDABanksMJKamenarE, et al. (2023) Control of soft robots with inertial dynamics. Science Robotics8(81): eadd6864.
36.
HamdadouNBouadiHHebabliaN, et al. (2024) Stochastic estimator based adaptive sliding mode control for a quadrotor in rainy flight conditions. Unmanned Systems12(01): 133–148.
37.
HanJ (2009) From PID to active disturbance rejection control. IEEE Transactions on Industrial Electronics56(3): 900–906.
38.
HanoverDFoehnPSunS, et al. (2021) Performance, precision, and payloads: adaptive nonlinear MPC for quadrotors. IEEE Robotics and Automation Letters7(2): 690–697.
39.
HanoverDLoquercioABauersfeldL, et al. (2024) Autonomous drone racing: a survey. IEEE Transactions on Robotics40: 3044–3067.
40.
HaseliMCortésJ (2019) Approximating the Koopman operator using noisy data: noise-resilient extended dynamic mode decomposition. In: American Control Conference, Philadelphia, PA, USA, 10–12 July 2019, pp. 5499–5504.
41.
HentzenDStastnyTSiegwartR, et al. (2019) Disturbance estimation and rejection for high-precision multirotor position control. In: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, Macau, China, 03–08 November 2019, pp. 2797–2804.
42.
HospedalesTAntoniouAMicaelliP, et al. (2022) Meta-learning in neural networks: a survey. IEEE Transactions on Pattern Analysis and Machine Intelligence44(9): 5149–5169.
43.
HuangKRanaRSpitzerA, et al. (2023) DATT: deep adaptive trajectory tracking for quadrotor control. In: Conference on Robot Learning, Atlanta, GA, USA, 06–09 November 2023.
44.
JiaJGuoKYuX, et al. (2022) Accurate high-maneuvering trajectory tracking for quadrotors: a drag utilization method. IEEE Robotics and Automation Letters7(3): 6966–6973.
45.
JiaJZhangWGuoK, et al. (2024) EVOLVER: online learning and prediction of disturbances for robot control. IEEE Transactions on Robotics40: 382–402.
46.
JiaJYangZWangM, et al. (2025) Feedback favors the generalization of neural ODEs. In: International Conference on Learning Representations, Singapore, 24–28 April 2025.
47.
JohnsonC (1970) Further study of the linear regulator with disturbances–the case of vector disturbances satisfying a linear differential equation. IEEE Transactions on Automatic Control15(2): 222–228.
48.
JordanM (2023) Challenge of uncertainty quantification for emerging AI systems. In: INCLUSION Conference on the Bund, Shanghai, China, 07–09 September 2023.
49.
KaiJMAllibertGHuaMD, et al. (2017) Nonlinear feedback control of quadrotors exploiting first-order drag effects. IFAC-PapersOnLine50(1): 8189–8195.
KimDLeeSHongTH, et al. (2023) Exploration-based model learning with self-attention for risk-sensitive robot control. Npj Robotics1(1): 7.
52.
KumarADaumeHIII (2012) Learning task grouping and overlap in multi-task learning. In: International Conference on Machine Learning, Edinburgh, Scotland, UK, 26–01 July 2012, pp. 1723–1730.
53.
LaleSRennPIAzizzadenesheliK, et al. (2024) Falcon: Fourier adaptive learning and control for disturbance rejection under extreme turbulence. Npj Robotics2(1): 6.
54.
LeeHKimHJ (2017) Constraint-based cooperative control of multiple aerial manipulators for handling an unknown payload. IEEE Transactions on Industrial Informatics13(6): 2780–2790.
55.
LeeHBattleARainaR, et al. (2006) Efficient sparse coding algorithms. In: Advances in Neural Information Processing Systems, Vancouver, BC, Canada, 04–07 December 2006.
56.
LeeTLeokMMcclamrochNH (2010) Control of complex maneuvers for a quadrotor UAV using geometric methods on SE(3). Mathematics15(2): 391–408.
57.
LiGCaoY (2021) Numerical simulation of helicopter rotor performance degradation in natural rain encounter. International Journal of Aerospace Engineering2021(1): 1–15.
58.
LiZZengJThirugnanamA, et al. (2022) Bridging model-based safety and model-free reinforcement learning through system identification of low dimensional linear models. In: Robotics: Science and Systems, New York City, NY, USA, 27 June –July 1, 2022.
59.
LiHZhongHGaoJ, et al. (2023) A nonlinear trajectory tracking control strategy for quadrotor with suspended payload based on force sensor. IEEE Transactions on Intelligent Vehicles9: 704.
60.
LuoL (2021) Architectures of neuronal circuits. Science373(6559): eabg7285.
61.
LutterMPetersJ (2023) Combining physics and deep learning to learn continuous-time dynamics models. The International Journal of Robotics Research42(3): 83–107.
62.
LyuXZhouJGuH, et al. (2018) Disturbance observer based hovering control of quadrotor tail-sitter VTOL UAVs using H∞ synthesis. IEEE Robotics and Automation Letters3(4): 2910–2917.
63.
LyuSZhangYWangJ, et al. (2025) Toward air operation aerial manipulator control with a refined anti-disturbance architecture. IEEE Transactions on Automation Science and Engineering22: 4076–4091.
64.
MairalJBachFPonceJ, et al. (2009) Online dictionary learning for sparse coding. In: International Conference on Machine Learning, Montreal, Canada, 2009, 689–696.
65.
MarkovDAPetruccoLKistAM, et al. (2021) A cerebellar internal model calibrates a feedback controller involved in sensorimotor control. Nature Communications12(1): 1–21.
66.
MarkovskyIRastelloMLPremoliA, et al. (2006) The element-wise weighted total least-squares problem. Computational Statistics & Data Analysis50(1): 181–209.
67.
Martínez-RozasSAlejoDCaballeroF, et al. (2023) Path and trajectory planning of a tethered uav-ugv marsupial robotic system. IEEE Robotics and Automation Letters8(10): 6475–6482.
68.
NakahiraYLiuQSejnowskiTJ, et al. (2021) Diversity-enabled sweet spots in layered architectures and speed–accuracy trade-offs in sensorimotor control. Proceedings of the National Academy of Sciences of the United States of America118(22): e1916367118.
69.
NguyenHTCheahCCTohKA (2022) An analytic layer-wise deep learning framework with applications to robotics. Automatica135: 110007.
70.
NygaardTFMartinCPTorresenJ, et al. (2021) Real-world embodied ai through a morphologically adaptive quadruped robot. Nature Machine Intelligence3(5): 410–419.
71.
OlleroATognonMSuarezA, et al. (2021) Past, present, and future of aerial robotic manipulators. IEEE Transactions on Robotics38(1): 626–645.
72.
O’ConnellMShiGShiX, et al. (2022) Neural-fly enables rapid learning for agile flight in strong winds. Science Robotics7(66): eabm6597.
73.
PanJLiDWangJ, et al. (2024) Autogeneration of mission-oriented robot controllers using bayesian-based koopman operator. IEEE Transactions on Robotics40: 903–918.
74.
ParksP (1966) Liapunov redesign of model reference adaptive control systems. IEEE Transactions on Automatic Control11(3): 362–367.
75.
PetersenKBPedersenMS (2008) The matrix cookbook. Technical University of Denmark7(15): 510.
76.
PlooijMWolfslagWWisseM (2015) Robust feedforward control of robotic arms with friction model uncertainty. Robotics and Autonomous Systems70: 83–91.
77.
PravitraJAckermanKACaoC, et al. (2020) L1-adaptive MPPI architecture for robust and agile control of multirotors. In: 202 IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, NV, USA, 24 October 2020–24 January 2021, IEEE, 7661–7666.
78.
QinTLiPShenS (2018) VINS-mono: a robust and versatile monocular visual-inertial state estimator. IEEE Transactions on Robotics34(4): 1004–1020.
79.
RenYLiuJChenH, et al. (2021) Vision-encoder-based payload state estimation for autonomous mav with a suspended payload. In: 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems, Prague, Czech Republic, 27 September–01 October 2021, IEEE, 9632–9638.
80.
RichardsSMAzizanNSlotineJJ, et al. (2023) Control-oriented meta-learning. The International Journal of Robotics Research42(10): 777–797.
81.
RomeroASongYScaramuzzaD (2024) Actor-critic model predictive control. In: 2024 IEEE International Conference on Robotics and Automation, Yokohama, Japan, 13–17 May 2024, pp. 14777–14784.
82.
RudinLIOsherSFatemiE (1992) Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena60(1-4): 259–268.
83.
RuggieroFLippielloVOlleroA (2018) Aerial manipulation: a literature review. IEEE Robotics and Automation Letters3(3): 1957–1964.
84.
RuvoloPEatonE (2013) Ella: an efficient lifelong learning algorithm. Proceedings of the 30th International Conference on Machine Learning28: 507–515.
85.
SariyildizEOboeROhnishiK (2020) Disturbance observer-based robust control and its applications: 35th anniversary overview. IEEE Transactions on Industrial Electronics67(3): 2042–2053.
86.
SarmaAALiJSLStenbergJ, et al. (2022) Internal feedback in biological control: architectures and examples. In: 2022 American Control Conference (ACC), Atlanta, GA, USA, 08–10 June 2022, 456–461.
87.
SauerTYorkeJACasdagliM (1991) Embedology. Journal of Statistical Physics65: 579–616.
88.
SavioloAFreyJRathodA, et al. (2024) Active learning of discrete-time dynamics for uncertainty-aware model predictive control. IEEE Transactions on Robotics40: 1273–1291.
89.
SeeberRHaimovichHHornM, et al. (2021) Robust exact differentiators with predefined convergence time. Automatica134: 109858.
90.
SinhaAMaloPDebK (2018) A review on bilevel optimization: from classical to evolutionary approaches and applications. IEEE Transactions on Evolutionary Computation22(2): 276–295.
91.
Sira-RamirezHOliver-SalazarMA (2013) On the robust control of buck-converter DC-motor combinations. IEEE Transactions on Power Electronics28(8): 3912–3922.
92.
SmeurEJChuQDe CroonGC (2016) Adaptive incremental nonlinear dynamic inversion for attitude control of micro air vehicles. Journal of Guidance, Control, and Dynamics39(3): 450–461.
93.
SongYRomeroAMüllerM, et al. (2023) Reaching the limit in autonomous racing: optimal control versus reinforcement learning. Science Robotics8(82): eadg1462.
94.
SoriaESchianoFFloreanoD (2021) Predictive control of aerial swarms in cluttered environments. Nature Machine Intelligence3(6): 545–554.
95.
SreenathKMichaelNKumarV (2013) Trajectory generation and control of a quadrotor with a cable-suspended load - a differentially-flat hybrid system. In: IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, 06–10 May 2013, pp. 4888–4895.
96.
SunSRomeroAFoehnP, et al. (2022) A comparative study of nonlinear MPC and differential-flatness-based control for quadrotor agile flight. IEEE Transactions on Robotics38(6): 3357–3373.
97.
TakensF (1981) Detecting strange attractors in turbulence. In: Dynamical Systems and Turbulence. Springer, pp. 366–381.
98.
TalEKaramanS (2020) Accurate tracking of aggressive quadrotor trajectories using incremental nonlinear dynamic inversion and differential flatness. IEEE Transactions on Control Systems Technology29(3): 1203–1218.
99.
TangSWüestVKumarV (2018) Aggressive flight with suspended payloads using vision-based control. IEEE Robotics and Automation Letters3(2): 1152–1159.
ThrunSPrattL (1998) Learning to learn: introduction and overview. In: Learning to Learn. Springer, pp. 3–17.
102.
TibshiraniR (1996) Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society - Series B: Statistical Methodology58(1): 267–288.
103.
TobinJFongRRayA, et al. (2017) Domain randomization for transferring deep neural networks from simulation to the real world. In: IEEE/RSJ International Conference on Intelligent Robots and Systems. Vancouver, BC, Canada, 24–28 September 2017, pp. 23–30.
104.
TognonMFranchiA (2017) Dynamics, control, and estimation for aerial robots tethered by cables or bars. IEEE Transactions on Robotics33(4): 834–845.
105.
WanT (2013) Aerodynamic analysis of helicopter rotor blades in heavy rain condition. In: 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Grapevine, TX, 07–10 January 2013, p. 653.
106.
WangBMaZLaiS, et al. (2024a) Neural moving horizon estimation for robust flight control. IEEE Transactions on Robotics40: 639–659.
107.
WangCJiKGengJ, et al. (2024b) Imperative learning: a self-supervised neural-symbolic learning framework for robot autonomy. arXiv preprint arXiv:2406.16087.
108.
WangHLiHZhouB, et al. (2024c) Impact-aware planning and control for aerial robots with suspended payloads. IEEE Transactions on Robotics40: 2478–2497.
109.
WangHZuoZXueW, et al. (2024d) Switching longitudinal and lateral semi-decoupled active disturbance rejection control for unmanned ground vehicles. IEEE Transactions on Industrial Electronics71(3): 3034–3043.
110.
WattersonMKumarV (2020) Control of quadrotors using the hopf fibration on SO(3). In: Robotics Research, the 18th International Symposium ISRR. Springer, pp. 199–215.
111.
WonDOMüllerKRLeeSW (2020) An adaptive deep reinforcement learning framework enables curling robots with human-like performance in real-world conditions. Science Robotics5(46): eabb9764.
112.
WoolfreyJLuWLiuD (2021) Predictive end-effector control of manipulators on moving platforms under disturbance. IEEE Transactions on Robotics37(6): 2210–2217.
113.
WuYDingZXuC, et al. (2021) External forces resilient safe motion planning for quadrotor. IEEE Robotics and Automation Letters6(4): 8506–8513.
114.
XieFShiGO’ConnellM, et al. (2024) Hierarchical meta-learning-based adaptive controller. In: IEEE International Conference on Robotics and Automation, Yokohama, Japan, 13–17 May 2024.
115.
XuLLuHWangJ, et al. (2025) Oscillation suppression-enhanced cooperative control via refined cooperative disturbance estimation for aerial co-transportation system. IEEE Transactions on Automation Science and Engineering22: 8371–8385.
116.
YangJMKimJH (1999) Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots. IEEE Transactions on Robotics and Automation15(3): 578–587.
117.
YangFWangCCadenaC, et al. (2023) iPlanner: imperative path planning. In: Robotics: Science and Systems, Daegu, Republic of Korea, 10–14 July, 2023.
118.
ZadorAEscolaSRichardsB, et al. (2023) Toward next-generation artificial intelligence: catalyzing the neuroai revolution. Nature Communications14(1): 1597.
119.
ZhaiZMoradiMKongL, et al. (2023) Model-free tracking control of complex dynamical trajectories with machine learning. Nature Communications14(1): 5698.
120.
ZhangDLoquercioAWuX, et al. (2023) Learning a single near-hover position controller for vastly different quadcopters. In: 2023 IEEE International Conference on Robotics and Automation, London, UK, 29 May–02 June 2023, pp. 1263–1269.
121.
ZhouXWangZYeH, et al. (2021) EGO-planner: an ESDF-free gradient-based local planner for quadrotors. IEEE Robotics and Automation Letters6(2): 478–485.
122.
ZhouXWenXWangZ, et al. (2022) Swarm of micro flying robots in the wild. Science Robotics7(66): eabm5954.
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