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1. Hölder-Continuous Finite-Time-Stable Tracking Control of Attitude Dynamics

   https://doi.org/10.2514/1.G009106  

   Wang, Ningshan; Sanyal, Amit K (September 2025, Journal of Guidance, Control, and Dynamics)

   This article presents an attitude tracking control scheme with Hölder continuity and finite-time stability. The first part of this article discusses and compares the features of first-order multivariable Hölder-continuous systems with coupled-scalar sliding-mode systems. The advantages of Hölder-continuous systems over sliding-mode systems are presented from the perspectives of control continuity and noise robustness. Thereafter, a Hölder-continuous second-order differentiator is presented with its stability and robustness properties. This is followed by its use in an attitude tracking control scheme, which is covered in the second part of the article. The proposed tracking control scheme is designed directly on the state-space of rigid-body rotational motion, which is the tangent bundle of the Lie group of 3D rotations. The control scheme design, its stability, and its robustness properties are obtained through Lyapunov stability analyses. The proposed Hölder-continuous design is compared with three comparable sliding-mode designs. Numerical simulations on a simulated CubeSat demonstrate the performance of the proposed control scheme and compare it with the sliding-mode control schemes. The numerical simulations also compare the proposed control scheme with other state-of-the-art sliding-mode control approaches in existing research publications. The comparison results demonstrate that the proposed Hölder-continuous attitude control scheme exhibits lower control efforts and tracking control errors over these sliding-mode control schemes in simulations that incorporate actuator dynamics and measurement uncertainties. 

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2. Geometric extended state observer on TSO(3) in the presence of bias in angular velocity measurements

   https://doi.org/10.23919/ACC63710.2025.11107819  

   Wang, Ningshan; Sanyal, Amit K (July 2025, IEEE)

   This article presents an estimation scheme for a rotating rigid body in the presence of unknown disturbance torque and unknown bias in angular velocity measurements. The attitude, angular velocity and disturbance torque are estimated from on-board control inputs, landmark vector measurements, and angular velocity measurements. The estimated attitude evolves directly on the special orthogonal group SO(3) of rigid body rotations. A Lyapunov analysis is given to prove that the proposed estimation scheme is almost globally Lyapunov stable in the absence of measurement noise and dynamic disturbance. The estimation scheme is discretized as a geometric integrator for practical implementation. The geometry-preserving properties of this numerical integrator preserve the Lie group structure of the configuration space, and give long time numerical stability. Numerical simulations demonstrate the stability and robustness properties of the proposed scheme. 

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3. Geometric Adaptive Controls of a Quadrotor Unmanned Aerial Vehicle With Decoupled Attitude Dynamics

   https://doi.org/10.1115/1.4052714  

   Gamagedara, Kanishke; Lee, Taeyoung (March 2022, Journal of Dynamic Systems, Measurement, and Control)

   Abstract This paper presents a geometric adaptive position tracking control system for a quadrotor unmanned aerial vehicle. In particular, the attitude control system is designed on the product of the two-dimensional unit sphere and the one-dimensional circle such that the direction of the thrust that is critical for position tracking is controlled independently from the yawing direction that is irrelevant to the position dynamics. Compared against the prior work with coupled attitude controls on the special orthogonal group, the proposed controller prevents large yaw errors from causing an undesirable performance degradation in tracking a position command. Further, the control input is augmented with adaptive control terms to mitigate the effects of disturbances, and it is formulated globally on the spheres to avoid singularities and complexities of local coordinates. The efficacy of the proposed control system is illustrated by both numerical examples and indoor/outdoor flight experiments. 

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4. Discrete Finite-time Stable Attitude Tracking Control of Unmanned Vehicles on SO(3)

   https://doi.org/10.23919/ACC45564.2020.9147657  

   Hamrah, Reza; Sanyal, Amit K.; Viswanathan, Sasi Prabhakaran (July 2020, 2020 American Control Conference (ACC))

   This paper presents a finite-time stable (FTS) attitude tracking control scheme in discrete time for an unmanned vehicle. The attitude tracking control scheme guarantees discrete-time stability of the feedback system in finite time. This scheme is developed in discrete time as it is more convenient for onboard computer implementation and guarantees stability irrespective of sampling period. Finite-time stability analysis of the discrete-time tracking control is carried out using discrete Lyapunov analysis. This tracking control scheme ensures stable convergence of attitude tracking errors to the desired trajectory in finite time. The advantages of finite-time stabilization in discrete time over finite-time stabilization of a sampled continuous time tracking control system is addressed in this paper through a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned vehicle model. 

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5. Vision-Based Safety-Critical Landing Control of Quadrotors With External Uncertainties and Collision Avoidance

   Lin, J; Miao, Zhiqiang; Wang, Yaonan; Wang, Hesheng; Wang, Xiangke; Fierro, Rafael (July 2024, IEEE Transactions on Control Systems Technology)

   This article addresses the quadrotors’ safety-critical landing control problem with external uncertainties and collision avoidance. A geometrically robust hierarchical control strategy is proposed for an underactuated quadrotor, which consists of a slow outer loop controlling the position and a fast inner loop regulating the attitude. First, an estimation error quantified (EEQ) observer is developed to identify and compensate for the target’s linear acceleration and the translational disturbances, whose estimation error has a nonnegative upper bound. Furthermore, an outer-loop controller is designed by embedding the EEQ observer and control barrier functions (CBFs), in which the negative effects of external uncertainties, collision avoidance, and input saturation are thoroughly considered and effectively attenuated. For the inner-loop subsystem, a geometric controller with a robust integral of the sign of the error (RISE) control structure is developed to achieve disturbances rejection and asymptotic attitude tracking. Based on Lyapunov techniques and the theory of cascade systems, it is rigorously proven that the closed-loop system is uniformly ultimately bounded. Finally, the effectiveness of the proposed control strategy is demonstrated through numerical simulations and hardware experiments. 

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