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Abstract: In recent years, physics-informed neural networks (PINNs) have shown remarkable potential in modeling conservative systems of rigid-body dynamics. However, when applied to practical interaction tasks of manipulators (e.g., part assembly and medical operations), existing PINN frameworks lack effective external force modeling mechanisms, resulting in significantly degraded prediction accuracy in dynamic interaction scenarios. Additionally, because industrial robots (including UR5 and UR10e robots) are generally not equipped with joint torque sensors, obtaining precise dynamics training data remains challenging. To address these issues, this study proposes two enhanced PINNs that integrate motor dynamics and external force modeling. First, two data-driven Jacobian matrix estimation methods are introduced to incorporate external forces: one method learns the mapping between end-effector velocity and joint velocity to approximate the Jacobian matrix, while the other first learns the system’s kinematic behavior and then derives the Jacobian matrix through analytical differentiation of the forward kinematics model. Second, current-to-torque mapping is embedded as physical prior knowledge to establish direct correlations between system motion states and motor currents. Experimental results on two different manipulators demonstrate that both models achieve high-precision torque estimation in complex external force scenarios without requiring joint torque sensors. Compared with state-of-the-art methods, the proposed models improve overall modeling accuracy by 31.12% and 37.07% on average across various complex scenarios, while reducing joint trajectory tracking errors by 40.31% and 51.79%, respectively.

考虑电机与外力耦合的机器人动力学预测

[1]Akbari M, Mehr JK, Ma L, et al., 2023. Uncertainty-aware safe adaptable motion planning of lower-limb exoskeletons using random forest regression. Mechatronics, 95:103060.

[2]Caccavale F, Siciliano B, Villani L, 2003. The Tricept robot: dynamics and impedance control. IEEE/ASME Trans Mechatron, 8(2):263-268.

[3]Chen ZX, Renda F, Le Gall A, et al., 2025. Data-driven methods applied to soft robot modeling and control: a review. IEEE Trans Autom Sci Eng, 22:2241-2256.

[4]Cheng S, Hu BB, Wei HL, et al., 2025. Deep learningbased hybrid dynamic modeling and improved handling stability assessment for autonomous vehicles at driving limits. IEEE Trans Veh Technol, 74(4):5582-5593.

[5]Chrosniak JY, Ning J, Behl M, 2024. Deep dynamics: vehicle dynamics modeling with a physics-constrained neural network for autonomous racing. IEEE Robot Autom Lett, 9(6):5292-5297.

[6]Clochiatti E, Scalera L, Boscariol P, et al., 2024. Electromechanical modeling and identification of the UR5 eseries robot. Robotica, 42(7):2430-2452.

[7]Crane CD III, Duffy J, 1998. Kinematic Analysis of Robot Manipulators. Cambridge University Press, New York, USA.

[8]Djeumou F, Neary C, Goubault E, et al., 2022. Neural networks with physics-informed architectures and constraints for dynamical systems modeling. Proc 4^th Learning for Dynamics and Control Conf.

[9]Duong T, Altawaitan A, Stanley J, et al., 2024. Port-Hamiltonian neural ODE networks on Lie groups for robot dynamics learning and control. IEEE Trans Robot, 40:3695-3715.

[10]Gu WB, Primatesta S, Rizzo A, 2024. Physics-informed neural network for quadrotor dynamical modeling. Rob Auton Syst, 171:104569.

[11]Gupta JK, Menda K, Manchester Z, et al., 2020. Structured mechanical models for robot learning and control. Proc 2^nd Annual Conf on Learning for Dynamics and Control, p.328-337.

[12]Hu HB, Shen ZK, Zhuang CG, 2025. A PINN-based friction-inclusive dynamics modeling method for industrial robots. IEEE Trans Ind Electron, 72(5):5136-5144.

[13]Khatib O, 1987. A unified approach for motion and force control of robot manipulators: the operational space formulation. IEEE J Robot Automat, 3(1):43-53.

[14]Laddach K, ngowski R, Rutkowski TA, et al., 2022. An automatic selection of optimal recurrent neural network architecture for processes dynamics modelling purposes. Appl Soft Comput, 116:108375.

[15]Lahoud M, Marchello G, D’Imperio M, et al., 2024. A deep learning framework for non-symmetrical Coulomb friction identification of robotic manipulators. Proc IEEE Int Conf on Robotics and Automation, p.10510-10516.

[16]Li ZL, Bai JS, Ouyang HJ, et al., 2024. Physics-informed neural networks for friction-involved nonsmooth dynamics problems. Nonl Dyn, 112(9):7159-7183.

[17]Li ZM, Wu SS, Chen WB, et al., 2024. Extrapolation of physics-inspired deep networks in learning robot inverse dynamics. Mathematics, 12(16):2527.

[18]Li ZM, Wu SS, Chen WB, et al., 2025. Physics-informed neural networks for compliant robotic manipulators dynamic modeling. J Comput Sci, 90:102633.

[19]Liu JY, Borja P, Della Santina C, 2024. Physics-informed neural networks to model and control robots: a theoretical and experimental investigation. Adv Intell Syst, 6(5):2300385.

[20]Lutter M, Peters J, 2023. Combining physics and deep learning to learn continuous-time dynamics models. Int J Rob Res, 42(3):83-107.

[21]Lutter M, Ritter C, Peters J, 2019. Deep Lagrangian networks: using physics as model prior for deep learning. Proc 7^th Int Conf on Learning Representations.

[22]Phong LD, Choi J, Lee W, et al., 2015. A novel method for estimating external force: simulation study with a 4-DOF robot manipulator. Int J Precis Eng Manuf, 16(4):755-766.

[23]Pikulińki M, Malczyk P, Aarts R, 2025. Data-driven inverse dynamics modeling using neural-networks and regression-based techniques. Multibody Syst Dyn, 63(3):341-366.

[24]Roehrl MA, Runkler TA, Brandtstetter V, et al., 2020. Modeling system dynamics with physics-informed neural networks based on Lagrangian mechanics. IFAC-PapersOnLine, 53(2):9195-9200.

[25]Shah SV, Saha SK, Dutt JK, 2012. Modular framework for dynamic modeling and analyses of legged robots. Mech Mach Theory, 49:234-255.

[26]Sousa CD, Cortesão R, 2014. Physical feasibility of robot base inertial parameter identification: a linear matrix inequality approach. Int J Robot Res, 33(6):931-944.

[27]Tao Y, Chen S, Liu HT, et al., 2025. Robot hybrid inverse dynamics model compensation method based on the BLL residual prediction algorithm. Robotica, 43(1):350-367.

[28]Trinh M, Geist AR, Monnet J, et al., 2025. Newtonian and Lagrangian neural networks: a comparison towards efficient inverse dynamics identification. https://arxiv.org/abs/2506.17994

[29]Wu SS, Li ZM, Chen WB, et al., 2024. Dynamic modeling of robotic manipulator via an augmented deep Lagrangian network. Tsinghua Sci Technol, 29(5):1604-1614.

[30]Xu PF, Han CB, Cheng HX, et al., 2022. A physics-informed neural network for the prediction of unmanned surface vehicle dynamics. J Marine Sci Eng, 10(2):148.