This paper introduces a Physics-Informed Koopman Neural Operator (PI-KNO) for augmented dynamics visual servoing of multirotors that integrates Koopman operator theory with neural networks. The proposed method establishes a structured learning framework that effectively captures complex system dynamics while embedding physics-based priors. Unlike fully data-driven approaches, PI-KNO improves generalization and minimizes reliance on extensive real-world training data by employing a hybrid loss function that combines physics-informed constraints with real-time observations. The learned model is incorporated into a monotonically weighted nonlinear model predictive control (NMPC) framework, ensuring precise trajectory tracking while adhering to state and input constraints. Experimental results demonstrate that PI-KNO reduces training time by 16.81% and enhances tracking accuracy by 19.56% compared to conventional Data-Driven Koopman Neural Operators (DD-KNO) and Physics-Informed Neural Networks (PINN). Additionally, under 70.83% uncertainty in camera parameters, PI-KNO achieves 10.6% and 22.2% lower tracking errors than PINN and DD-KNO, respectively. These findings underscore the robustness and efficiency of the proposed approach for real-time multirotor visual servoing applications. Note to Practitioners - This work presents an implementation oriented view of a learning based predictive controller for aerial robots designed to operate within the limits of onboard computation and sensing. The proposed PI-KNO approach combines physical modeling and data driven learning to create an accurate and stable dynamic predictor suitable for real time deployment. The architecture is distributed between an NVIDIA Jetson and a Pixhawk. The Jetson runs the vision front end, state estimator, PI-KNO predictor, and NMPC optimizer. The estimator fuses visual and inertial data to provide position, velocity, and attitude states, while the NMPC computes high level motion commands at about 30Hz using the PI-KNO rollout. The Pixhawk executes inner rate loops at 250Hz through the native autopilot for attitude stabilization and motor mixing. Communication between the Jetson and Pixhawk uses standard MAVLink setpoints, requiring no firmware modification. The training workflow begins with a nominal visual servoing multirotor model and limited flight data, from which the operator is trained offline using a physics-informed regularizer. At runtime, the estimator updates the state, PI-KNO predicts short horizon dynamics, the NMPC optimizes control sequences, and the Pixhawk executes the commands. This setup achieves reliable tracking across trajectories, maintains physical consistency under uncertainty, and fits within the computational limits of embedded hardware.

This article introduces the physics-embedded neural network (PENN), an enhanced physics-informed neural network (PINN) architecture tailored for visual servoing applications of multirotors. Classical PINNs, while interpretable and data-efficient due to their incorporation of physical laws in the training loss function, often suffer from poor convergence and sensitivity to network initialization and activation functions (AFs). To overcome these challenges, this work proposes two improved architectures: the layer-wise PENN (L-PENN) and the neuron-wise PENN (N-PENN). These architectures embed nominal physical dynamics directly into the structure of the network, thereby improving both training efficiency and predictive accuracy. A spectral analysis of the Hessian matrix is conducted to rigorously demonstrate the enhanced convergence behavior of the proposed architectures compared to traditional PINNs. The proposed methods are experimentally validated on a visual servoing task using a multirotor platform, with performance evaluated in terms of tracking performance and training time. The results are also benchmarked against existing literature, confirming that both L-PENN and N-PENN significantly outperform classical PINNs and other learning-based control strategies. The article concludes by outlining selection criteria for choosing between the two architectures based on specific characteristics of the application.

This paper addresses the challenge of real-time control of multirotors subjected to partially known and unmodeled dynamics. A physics-informed Koopman operator framework is proposed, where the known physical dynamics and unknown residual effects are separated using a Strang splitting approach. The continuous-time Koopman operator is trained on physics-derived trajectories, while the discrete-time Koopman operator is learned from real-world trajectory data, enabling a data-efficient and globally linearizable model of the multirotor dynamics. The learned linear model is subsequently used to design a discrete-time Sequential Action Control (SAC) policy for real-time trajectory tracking. Experimental validation on a quadrotor platform tracking a lemniscate trajectory demonstrates that the proposed PI-EDMD-based SAC controller achieves superior tracking accuracy and up to 67% lower control energy consumption compared to baseline nonlinear SAC and LQR controllers. These results highlight the effectiveness of the proposed framework in enhancing both trajectory fidelity and actuation efficiency for multirotors.

Multirotor unmanned aerial vehicles (UAVs) frequently experience degraded control authority due to partial actuator faults, compromising mission reliability and safety. Purely data-driven fault diagnostic methods, although effective, typically demand extensive labelled datasets and lack direct interpretability. Physics-informed neural networks (PINNs), which incorporate physical laws directly into their learning process, offer a promising alternative by enabling data-efficient training and interpretable results. This study proposes a PINN for actuator fault diagnosis in quadrotor UAVs by embedding discrete Newton-Euler residuals within its loss function, ensuring predictions remain consistent with rigid-body dynamics. A quadrotor UAV is modelled in a high-fidelity simulation environment, and flight data from these simulations are collected for analysis. A sensitivity study is subsequently conducted, testing the PINN against varied fault magnitudes, fault intervals, and different training dataset sizes (100%, 50%, and 30%).The proposed PINN outperforms a similarly sized multilayer perceptron (MLP), reducing fault detection delay by approximately 20%, consistently achieving macro F1 scores above 0.90, and improving prediction accuracy (R2) and RMSE, even with limited labelled data.

This paper presents a prescribed performance finite-time observer-based super-twisting controller (PPFTOST) for cooperative aerial suspended transport systems. The proposed controller integrates a prescribed performance framework, an appointed-time disturbance observer (ATDO) for disturbance estimation, and a fast terminal sliding mode super-twisting controller (FTSMSTC) for rapid convergence with reduced chattering. Through this combination, the closed-loop system achieves finite-time convergence of both the disturbance estimation error and the sliding variables, while ensuring that the tracking errors remain within prescribed performance bounds. In simulations against an ATDO-only baseline, the PPFTOST reduced payload-tracking root mean square error by 8.2%, 6.7%, and 9.3% on the x, y, and z axes, respectively, with all actuator commands remaining within limits. These results demonstrate that the proposed method enables accurate, robust, and smooth multi-UAV load transport under realistic disturbance conditions.

This study introduces a dynamics-driven visual servoing methodology tailored for an over-actuated quadrotor equipped with tilting rotors. The mathematical framework encompasses both translational and rotational dynamics, incorporating the tilting rotor angles to facilitate autonomous control over attitude and position. The stereo camera model is derived utilizing stacked Jacobians. The proposed dynamics-driven methodology establishes a direct correspondence between the dynamics of image pixel accelerations captured by the stereo cameras and the thrust and torque commands of the over-actuated tilting quadrotor. This obviates the necessity for computationally intensive inverse Jacobian computations typically required in traditional visual servoing methods. By employing an over-actuated tilting rotor configuration instead of a conventional quadrotor setup, the dynamics-driven approach surmounts limitations in independently controlling the pose and attitude. It enables the tracking of not only the 3D position but also the orientation of points of interest using the onboard stereo cameras. Simulation outcomes affirm the efficacy of the approach in achieving precise visual tracking.

This paper presents a robust decentralised control approach for modular aerial parcel delivery using persistently excited physics-informed neural networks (PE-PINNs). The proposed method enables each propeller module to independently generate control efforts based solely on its local state information and that of its 1-hop neighbors, without requiring global system knowledge. The PE-PINN is trained to approximate the optimal centralized control policy by incorporating the nominal system dynamics and accounting for modeling uncertainties. Key innovations include estimating the Lipschitz constant to ensure persistent excitation during training, and a decentralised control formulation that minimizes the difference between the learned and optimal control efforts. Experimental results on a modular aerial testbed demonstrate the PE-PINN's ability to achieve high-accuracy fixed-point hover and trajectory tracking performance, outperforming a prior decentralised control approach by 8.57% and 24.17% respectively. The proposed framework enables scalable and robust control of modular aerial systems for parcel delivery applications.

This article presents a visual servoing strategy that integrates the capabilities of a physics-informed neural network (PINN) to estimate system uncertainties and inaccuracies with a dynamics-centered visual servoing technique for multirotors. The proposed method effectively combines these approaches, eliminating the need for inverse Jacobian calculations to determine multirotor motion by directly relating pixel variations to the multirotor's torque and thrust inputs, while also strengthening the method's robustness through the utilization of the PINN to model and address uncertainties in camera and multirotor parameters, as well as the modeling inaccuracies inherent in the dynamics-centered visual servoing technique. In contrast to existing state-of-the-art data-driven approaches, the proposed PINN approach requires, on average, 65% less labeled data to characterize uncertainties and inaccuracies. To ensure real-time implementation of the visual servoing model, the PINN-learned model is combined with an adaptive horizon monotonically weighted nonlinear model predictive controller (NMPC), capable of processing control efforts at rates 10 times faster than existing Tube MPC and Adaptive MPC strategies. These findings are validated through real-time trajectory tracking experiments, which not only highlight the effectiveness of the proposed approach in approximating modeling inaccuracies but also its capability in handling uncertainties upto 70% in camera parameters.

This article focuses on developing an adaptive fast terminal sliding-mode controller (AFTSMC) with power rate proportional reaching law for the position and altitude tracking of a quadrotor in the presence of parametric uncertainties and bounded external disturbance. A nonlinear fast terminal sliding surface is proposed for the fast and finite-time convergence of the tracking error despite having the system states far away from the equilibrium point. Also, a power rate proportional reaching law has been proposed that ensures fast and finite-time convergence of the sliding manifold while attenuating the chattering phenomena in the sliding phase. To avoid the problem associated with over-estimation of the unknown disturbance bound, which eventually leads to chattering, an adaptive tuning law for gain adaptation is developed based on the Lyapunov’s stability theory that completely eradicates the necessity of knowing the upper bound of the disturbancea priori. The finite-time stability of a closed-loop system is investigated using the Lyapunov theory. The effectiveness of the proposed scheme is compared with an adaptive sliding-mode controller (ASMC) using extensive simulation and validated on the DJI Matrice 100 quadrotor as a proof of concept on the hardware platform.

This paper proposes a novel 3 DoF vision augmented Quadrotor model for visual servoing. The proposed model eliminates the necessity of deploying a separate visual-servoing controller and a robot controller, thereby reducing the on-board computational load drastically. The proposed model, as opposed to the conventional PBVS and IBVS approaches, helps in the use of torque control strategies. To utilize this feature of the model, a non-singular fast-terminal sliding mode modified super-twisting controller (NSFTSM-MSTC) is proposed. The non-singular fast-terminal sliding manifold ensures the fast and finite time convergence of the error between the desired and actual points of interest, while ensuring smoother transitions in the quadrotor states. The modified super-twisting reaching law ensures that the control input is continuous thereby ensuring chattering attenuation. The overall system stability is presented using Lyapunov’s stability criteria and an expression for convergence time is also derived. The proposed theory is validated using numerical simulations and is compared with the existing conventional sliding mode based visual servoing approach (CSMVS).

This paper presents an approach for position and attitude control of a quadrotor using adaptive backstepping technique along with an uncertainty observer via Recurrent Neural Network (RNN). The quadrotor dynamics are expressed as two subsystems, namely translational and rotational, on which the backstepping control law has been developed. In comparison with feedforward neural networks, RNN has better dynamic characteristics and approximation capabilities. Therefore, an RNN based uncertainty observer has been employed to accommodate the system uncertainties as well as the unknown external disturbances. The proposed controller consists of two parts - an adaptive backstepping based controller that contains an RNN observer and a robust controller to deal with the approximation error induced by the RNN. The RNN parameters have been updated via an update law based on Lyapunov stability theory in an online manner where the overall system stability is also guaranteed. The proposed approach has been implemented in simulations for trajectory tracking of the quadrotor in the presence of parametric uncertainties and external disturbances. Also, the hardware results are presented to show the effectiveness of the proposed approach on DJI Matrice 100.

This paper proposes a fast terminal sliding mode super twisting controller (FTSMSTC) design for quadrotor position and altitude tracking in the presence of bounded disturbances. A nonlinear fast terminal sliding manifold has been proposed for fast convergence of the tracking error to zero in finite time unlike the conventional sliding mode control (CSMC) that guarantee only asymptotic convergence of the tracking error. The super twisting reaching law has been proposed to deal with the chattering phenomena, which is inherent in the CSMC. The finite time stability of the complete closed loop system is investigated using Lyapunov stability theory and an analytical expression for the convergence time has also been derived. The effectiveness of the designed controller is checked against the CSMC using MATLAB simulation. The controller has been experimentally validated using the DJI Matrice M100 as a proof of utility in real time applications.

This paper proposes a vision-based sliding mode control technique for autonomous landing of a quadrotor over the static platform. The proposed vision algorithm estimates the quadrotor's position relative to an ArUco marker placed on a static platform using an on-board monocular camera. The relative position is provided as an input to a Fast-terminal Sliding Mode Super Twisting Controller (FTSMSTC) which ensures finite time convergence of the relative position between the landing pad marker and the quadrotor. In addition, the proposed controller attenuates chattering phenomena and guarantees robustness towards bounded external disturbances and modelling uncertainties. The proposed vision-based control scheme is implemented using numerical simulations and validated in real-time on the DJI Matrice 100.

This paper proposes a vision-based sliding mode control technique for autonomous tracking of a moving vehicle by a quadrotor. The proposed vision algorithm estimates the quadrotor's position relative to moving vehicle using an on-board monocular camera. The relative position is provided as an input to a Fractional Order Sliding mode Controller (FOSMC) which ensures the convergence of the relative position between the moving vehicle and the quadrotor thereby enabling it to track the vehicle effectively. In addition, the proposed controller guarantees robustness towards bounded external disturbances and modelling uncertainties. The proposed vision-based control scheme is implemented using numerical simulations and validated in real-time on the DJI Matrice 100. Theses validations help in gaining into the maximum allowable speed of the moving target for the quadrotor to successfully track the object. This plays a vital role in surveillance operations and intruder chase.

This paper demonstrates an hybrid methodology of quadrotor navigation and control in an environment with obstacles by combining a Q-learning strategy for navigation with a non-linear sliding mode control scheme for position and altitude control of the quadrotor. In an unknown environment, an optimal safe path is estimated using the Q-learning scheme by considering the environment as a 3D grid world. Furthermore, a non-singular terminal sliding mode control (NTSMC) is employed to navigate the quadrotor through the planned trajectories. The NTSMC that is employed for trajectory tracking ensures robustness towards bounded disturbances as well as parametric uncertainties. In addition, it ensures finite time convergence of the tracking error and avoids issues that arise due to singularities in the dynamics. The effectiveness of the proposed navigation and control scheme are validated using numerical simulations wherein a quadrotor is required to pass through a window.