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1. Singularly Perturbed Averaging with Application to Bio-Inspired 3D Source Seeking

   Abdelgalil, M; Eldesoukey, A; Taha, H (July 2023, IEEE)

   We propose a novel 3D source seeking algorithm for rigid bodies with a non-collocated sensor inspired by the chemotactic navigation strategy of sea urchin sperm known as helical klinotaxis. We work directly with the rotation group SO(3) without parameterization in representing the attitude of a rigid body. As a consequence, the proposed algorithm does not require attitude feedback for implementation as opposed to all previous work on 3D source seeking. The stability of the proposed algorithm is proven using an intricate combination of singular perturbation and second order averaging. 

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2. Coordinated Relative Attitude Control and Synchronization of a Multi-body Network of Vehicles

   https://doi.org/10.23919/ACC63710.2025.11108024  

   Srinivasu, Neon; Hashkavaei, Nazanin S; Sanyal, Amit K; Butcher, Eric A (July 2025, IEEE)

   This work analyzes and develops some fundamental results for attitude consensus control of a network of rigid-body vehicles, considered a multi-agent rigid body system (MARBS). The system is analyzed using a full rigid body dynamics model on TSO(3) for each vehicle (agent) in the network. Therefore, the state space of the system is TSO(3)^N, where N is the number of vehicles. Attitude synchronization control laws for each vehicle to reach a consensus attitude with zero angular velocity for a particular type of network are obtained, using a Morse-Lyapunov function. Some fundamental results on equilibria of the network under these attitude consensus control laws are obtained. We show that unlike cooperative control of multi-agent systems with highly simplified dynamics models for agents, like point particles or unicycles where the state space of the dynamics is modeled as a vector space, there are multiple equilibrium solutions possible for attitude consensus control laws for a MARBS with dynamics on TSO(3)^N. Further, the number of equilibria depends on the network graph topology. This is followed by numerical simulation results for two different network graphs, which show this network control framework to be effective in obtaining attitude consensus. 

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3. Geometric Integral Attitude Control on SO(3)

   https://doi.org/10.3390/electronics11182821  

   Eslamiat, Hossein; Wang, Ningshan; Hamrah, Reza; Sanyal, Amit K. (September 2022, Electronics)

   This article proposes a novel integral geometric control attitude tracking scheme, utilizing a coordinate-free representation of attitude on the Lie group of rigid body rotations, SO(3). This scheme exhibits almost global asymptotic stability in tracking a reference attitude profile. The stability and robustness properties of this integral tracking control scheme are shown using Lyapunov stability analysis. A numerical simulation study, utilizing a Lie Group Variational Integrator (LGVI), verifies the stability of this tracking control scheme, as well as its robustness to a disturbance torque. In addition, a numerical comparison study shows the effectiveness of the proposed geometric integral term, when compared to other state-of-the-art attitude controllers. In addition, software-in-the-loop (SITL) simulations show the advantages of utilizing the proposed attitude controller in PX4 autopilot compared to using PX4’s original attitude controller. 

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4. 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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5. 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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