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1. 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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2. Asymptotically stable optimal multi-rate rigid body attitude estimation based on lagrange-d'alembert principle

   https://doi.org/10.3934/jgm.2023004  

   Bhatt, Maulik; Sanyal, Amit K.; Sukumar, Srikant (January 2023, Journal of Geometric Mechanics)

   The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states. 

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3. A Finite-Time Stable Observer for Relative Attitude Estimation

   https://doi.org/10.1109/CDC40024.2019.9029806  

   Wang, Ningshan; Hamrah, Reza; Sanyal, Amit K. (December 2019, 2019 IEEE 58th Conference on Decision and Control (CDC))

   Relative motion estimation of one rigid body with respect to another is a problem that has immediate applications to formations and maneuvers involving multiple unmanned vehicles or collision avoidance between vehicles. A finite-time stable observer for relative attitude estimation of a rigid object using onboard sensors on an unmanned vehicle, is developed and presented here. This observer assumes sensor inputs from onboard vision and inertial sensors, with the vision sensors measuring at least three points on the object whose relative locations with respect to a body-fixed frame on the object are also assumed to be known. In the absence of any measurement noise, the estimated relative attitude is shown to converge to the actual relative pose in a finite-time stable manner. Numerical simulations indicate that this relative attitude observer is robust to persistent measurement errors and converges to a bounded neighborhood of the true attitude. 

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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. An Anti-Windup Compensator for a Rigid-Body NDI-Based Manual Attitude Control System

   https://doi.org/10.1109/CONTROL60310.2024.10531835  

   Soltani, Ali; Turner, Matthew C; Richards, Christopher M (April 2024, IEEE)

   In this paper, an anti-windup compensation scheme is proposed for the manual mode of a rigid body attitude control system to make the angular velocity dynamics globally asymptotically stable despite actuator saturation. The addressed anti-windup design problem is challenging since the nominal control law includes a nonlinear dynamic inversion element to cancel the nonlinearity in the angular velocity dynamics. The stability of the compensated closed-loop system is proved via the Lyapunov stability criterion appropriately. Moreover, the superiority of the compensated system versus the uncompensated one is demonstrated by simulation. 

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