This paper investigates the motion prediction problem for human–robot-interactive (HRI) system subject to large communication delays. A data-driven inverse optimal control (IOC) approach is applied to identify the human input through learning from the trajectory demonstrations of the robot end-effector. Based on the identification results, a motion predictor with cascade structure is proposed to estimate the real-time states of HRI system using the delayed discrete measurements, which consists of a continuous-discrete time observer and several sub-predictors in a chain. The proposed predictor can handle with arbitrary large delays through utilizing sufficient numbers of sub-predictors. The convergence of prediction errors is demonstrated via Lyapunov–Krasovskii method. Simulations of a multi-multi-degree-of-freedom HRI system verifies the ability of proposed predictor to perform an accurate estimation under large delays and noises.
Ab AzarNShahmansoorianADavoudiM (2020) From inverse optimal control to inverse reinforcement learning: A historical review. Annual Reviews in Control50: 119–138.
2.
Ahmed-AliTCherrierELamnabhi-LagarrigueF (2011) Cascade high gain predictors for a class of nonlinear systems. IEEE Transactions on Automatic Control57(1): 221–226.
3.
AroraSDoshiP (2021) A survey of inverse reinforcement learning: Challenges, methods and progress. Artificial Intelligence297: 103500.
4.
BogertKDoshiP (2018) Multi-robot inverse reinforcement learning under occlusion with estimation of state transitions. Artificial Intelligence263: 46–73.
5.
BouraouiIFarzaMMénardT, et al. (2015) Observer design for a class of uncertain nonlinear systems with sampled outputs—Application to the estimation of kinetic rates in bioreactors. Automatica55: 78–87.
6.
ByeonSSunDHwangI (2022) An inverse optimal control approach for learning and reproducing under uncertainties. IEEE Control Systems Letters7: 787–792.
7.
ChangTTianGZhangS, et al. (2024) Model predictive control parameter optimization method for autonomous vehicles. Transactions of the Institute of Measurement and Control. Epub ahead of print 6 December. DOI: 10.1177/01423312241291095.
8.
ChenHLiuZ (2021) Time-delay prediction–based smith predictive control for space teleoperation. Journal of Guidance, Control, and Dynamics44(4): 872–879.
9.
ColombelJDaneyDCharpilletF (2022) On the reliability of inverse optimal control. In: 2022 international conference on robotics and automation (ICRA), Philadelphia, PA, 23–27 May, pp. 8504–8510. New York: IEEE.
10.
CuiLPangBKrstićM, et al. (2025) Learning-based adaptive optimal control of linear time-delay systems: A value iteration approach. Automatica171: 111944.
11.
FanZXAdhikaryACLiS, et al. (2022) Disturbance observer based inverse optimal control for a class of nonlinear systems. Neurocomputing500: 821–831.
12.
FarzaMHernández-GonzálezOMénardT, et al. (2018) Cascade observer design for a class of uncertain nonlinear systems with delayed outputs. Automatica89: 125–134.
13.
FinnCLevineSAbbeelP (2016) Guided cost learning: Deep inverse optimal control via policy optimization. Proceedings of Machine Learning Research48: 49–58.
14.
FranceschiPPedrocchiNBeschiM (2022) Inverse optimal control for the identification of human objective: A preparatory study for physical human-robot interaction. In: 2022 IEEE 27th international conference on emerging technologies and factory automation (ETFA), Stuttgart, 6–9 September, pp. 1–6. New York: IEEE.
15.
FranceschiPPedrocchiNBeschiM (2023) Identification of human control law during physical human–robot interaction. Mechatronics92: 102986.
16.
Hernández-GonzálezOFarzaMMenardT, et al. (2016) A cascade observer for a class of mimo non uniformly observable systems with delayed sampled outputs. Systems & Control Letters98: 86–96.
17.
Hernandez-MejiaGAlanisAYHernandez-VargasEA (2018) Neural inverse optimal control for discrete-time impulsive systems. Neurocomputing314: 101–108.
18.
IngaJCreutzAHohmannS (2021) Online inverse linear-quadratic differential games applied to human behavior identification in shared control. In: 2021 European control conference (ECC), Delft, 29 June–2 July, pp. 353–360. New York: IEEE.
KamalapurkarRFischerNObuzS, et al. (2016) Time-varying input and state delay compensation for uncertain nonlinear systems. IEEE Transactions on Automatic Control61(3): 834–839.
21.
KiumarsiBLewisFLModaresH, et al. (2014) Reinforcement q-learning for optimal tracking control of linear discrete-time systems with unknown dynamics. Automatica50(4): 1167–1175.
22.
KumarSAjmeriM (2023) Smith predictor–based sliding mode control with hyperbolic tangent function for unstable processes. Transactions of the Institute of Measurement and Control45(10): 1923–1932.
23.
LiYYangLHuangD, et al. (2022) A proactive controller for human-driven robots based on force/motion observer mechanisms. IEEE Transactions on Systems, Man, and Cybernetics: Systems52(10): 6211–6221.
24.
LiZWangMMaG (2023) Adaptive optimal trajectory tracking control of AUVs based on reinforcement learning. ISA transactions137: 122–132.
25.
LinJWangMWuHN (2023) Composite adaptive online inverse optimal control approach to human behavior learning. Information Sciences638: 118977.
26.
LofbergJ (2004) Yalmip: A toolbox for modeling and optimization in MATLAB. In: 2004 IEEE international conference on robotics and automation (IEEE Cat. No. 04CH37508), Taipei, Taiwan, 2–4 September, pp. 284–289. New York: IEEE.
27.
LuZHuangPLiuZ (2017) Predictive approach for sensorless bimanual teleoperation under random time delays with adaptive fuzzy control. IEEE Transactions on Industrial Electronics65(3): 2439–2448.
28.
LuoJHuangDLiY, et al. (2021) Trajectory online adaption based on human motion prediction for teleoperation. IEEE Transactions on Automation Science and Engineering19(4): 3184–3191.
29.
MinXLiYTongS (2020) Adaptive fuzzy output feedback inverse optimal control for vehicle active suspension systems. Neurocomputing403: 257–267.
30.
MolloyTLFordJJPerezT (2020) Online inverse optimal control for control-constrained discrete-time systems on finite and infinite horizons. Automatica120: 109109.
31.
PriessMCConwayRChoiJ, et al. (2014) Solutions to the inverse LQR problem with application to biological systems analysis. IEEE Transactions on control systems technology23(2): 770–777.
32.
Ramírez-RasgadoFFarzaMM’SaadM, et al. (2021) Observer design for a class of disturbed nonlinear systems with multirate sampled outputs involving multiple long time-varying delays. In: 2021 9th international conference on systems and control (ICSC), Caen, 24–26 November, pp. 493–498. New York: IEEE.
33.
SajadiMAtaeiMEkramianM (2018) Cascade high-gain observers for a class of nonlinear systems with large delayed measurements. International Journal of Systems Science49(12): 2558–2570.
34.
SansanayuthTNilkhamhangITungpimolratK (2012) Teleoperation with inverse dynamics control for PHANToM Omni haptic device. In: 2012 proceedings of SICE annual conference (SICE), Akita, Japan, 20–23 August, pp. 2121–2126. New York: IEEE.
35.
ShenSSongALiH, et al. (2022) Cascade predictor for a class of mechanical systems under large uncertain measurement delays. Mechanical Systems and Signal Processing167: 108536.
36.
TarguiBHernández-GonzálezOAstorga-ZaragozaCM, et al. (2018) A chain observer for a class of nonlinear systems with long multiple delays in output measurements. In: 2018 European control conference (ECC), Limassol, Cyprus, 12–15 June, pp. 1590–1595. New York: IEEE.
37.
TréangleCFarzaMM’SaadM (2019) Observer design for a class of disturbed nonlinear systems with time-varying delayed outputs using mixed time-continuous and sampled measurements. Automatica107: 231–240.
38.
WangPZhangX (2022) Inverse optimal missile guidance law under constraints based on prescribed-time explicit reference governor. ISA transactions129: 395–404.
39.
WuHN (2022) Online learning human behavior for a class of human-in-the-loop systems via adaptive inverse optimal control. IEEE Transactions on Human-Machine Systems52(5): 1004–1014.
40.
YanJLiJBaiG, et al. (2025) An attention-BiLSTM network identification method for time-delay feedback nonlinear system. Applied Intelligence55(1): 29.
41.
YangYDingZWangR, et al. (2021) Data-driven human-robot interaction without velocity measurement using off-policy reinforcement learning. IEEE/CAA Journal of Automatica Sinica9(1): 47–63.
42.
YangYGuoFLiJ, et al. (2024) New delay-dependent position/force hybrid controller design for uncertain telerobotics without force sensors. Transactions of the Institute of Measurement and Control46(2): 253–267.
43.
YuCLiYFangH, et al. (2021) System identification approach for inverse optimal control of finite-horizon linear quadratic regulators. Automatica129: 109636.
44.
ZengXYangYDingS, et al. (2024) Global adaptive coordinated control of human–robot mooring system without velocity measurements. Transactions of the Institute of Measurement and Control. Epub ahead of print 7 November. DOI: 10.1177/01423312241273753.
45.
ZhangHRinghA (2024) Inverse optimal control for averaged cost per stage linear quadratic regulators. Systems & Control Letters183: 105658.
46.
ZhangHUmenbergerJHuX (2019) Inverse optimal control for discrete-time finite-horizon linear quadratic regulators. Automatica110: 108593.
47.
ZhangZLiYYuC (2021) Online inverse identification of noncooperative dynamic games. In: 2021 IEEE international conference on unmanned systems (ICUS), Beijing, China, 15–17 October, pp. 408–413. New York: IEEE.
