Optimal attitude consensus for multi rigid bodies network considered on the lie group SO(3) with connectivity preserving property

Mansourinasab, Sara; Sojoodi, Mahdi; Moghadasi, Seyed Reza

doi:10.1049/cth2.12293

Cited by 6 publications

(2 citation statements)

References 35 publications

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“…By using the actor-critic reinforcement learning framework and a non-singular fast terminal sliding mode, an neural network-based fixed-time control strategy is developed for achieving optimal attitude consensus control [20]. Mansourinasab [21] proposes distributed optimal attitude consensus control for single-integrator multi-rigid bodies with an undirected network, while simultaneously guaranteeing the connectivity preservation property for agents using a descent gradient algorithm. Qi [22] addresses the problem of attitude consensus control for multiple rigid spacecraft where only a subset of followers can obtain the leader's state information.…”

Section: Introductionmentioning

confidence: 99%

Optimal attitude consensus control for rigid spacecraft formation based on control Lyapunov functions

Wang

Zhang

Zhou

et al. 2023

IET Control Theory & Appl

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In this article, the optimal attitude consensus control problem of distributed spacecraft formation through local information exchange is solved in the presence of parameter uncertainty and disturbance. The attitude dynamics model of rigid spacecraft formation is established based on unit quaternion under an undirected graph. Then, the optimal attitude consensus control scheme based on control Lyapunov functions is adopted for rigid spacecraft formation. The approach to construct an appropriate Lyapunov function for multiple spacecraft is developed. Then the lumped disturbance is estimated by an extended state observer (ESO) and using the sliding mode control approach improves the robustness of the controller. The proposed optimal controller can not only ensure the global consensus convergence of the system but also make the preset performance index function achieve the minimum value. In addition, the mathematical proof is given for the stability analysis of the system by the Lyapunov stability theory. Finally, some simulations and comparisons are presented to demonstrate the validity and advantages of the proposed controller.

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Section: Introductionmentioning

confidence: 99%

Optimal attitude consensus control for rigid spacecraft formation based on control Lyapunov functions

Wang

Zhang

Zhou

et al. 2023

IET Control Theory & Appl

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“…Linear matrix inequality (LMI) method is used to solve the optimizations related to the constrained model predictive control (MPC) control of a 3D pendulum on SO(3) in ref. [7]. It is shown that using LMI for solving MPC problem on manifold needs less control efforts than standard MPC.…”

Section: Introductionmentioning

confidence: 99%

Neighboring extremal nonlinear model predictive control of a rigid body on SO(3)

2023

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The issue of implementing nonlinear model predictive control (NMPC) on mechanical systems evolving on special orthogonal group (SO(3)) is taken into consideration in the first place. Necessary conditions of optimality are extracted based on Lie group variational integrators, leading to a two-point boundary value problem (TPBVP) which is solved using sensitivity derivatives and indirect shooting methods. Fast Newton-like methods referred to as fast solvers which are commonly used to solve the TPBVP are established based on the repetition of a nonlinear process. The numerical schemes employed to alleviate the computation burden consist of eliminating some constraint-related but non-essential terms in the trend of sensitivity derivatives calculation and for solving the TPBVP equations. As another claim, assuming that a first attempt to resolve the NMPC problem is accessible, the problem subjected to some changes in its initial conditions (due to some re-planning schemes) can be resolved cost-effectively based on it. Instead of solving the whole optimization process from the scratch, the optimal control inputs and states of the system are updated based on the neighboring extremal (NE) method. For this purpose, two approaches are considered: applying NE method on the first solution that leads to a neighboring optimal solution, or assisting this latter by updating the NMPC-related optimization using exact TPBVP equations at some predefined intermediate steps. It is shown through an example that the first method is not accurate enough due to error accumulations. In contrast, the second method preserves the accuracy while reducing the computation time significantly.

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A lie group PMP approach for optimal stabilization and tracking control of autonomous underwater vehicles

Anil,

Gajbhiye,

Mohan

2024

Intl J Robust & Nonlinear

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In this research, we explore a finite horizon optimal stabilization and tracking control scheme for the dynamical model of a 6‐DOF Autonomous Underwater Vehicle (AUV). Dynamical equations of the AUV are represented in a Lie group () framework, encompassing both translational and rotational motions. Utilizing a left Lie group action on , we define error function for velocities via a right transport map to effectively address optimal trajectory tracking. The optimal control objective is formulated as a trade‐off problem, aiming to minimize both errors and control effort simultaneously. Left action on yields the left trivialized Hamiltonian function from which the concomitant state and costate dynamical equations are derived using Pontryagin's Minimum Principle (PMP). Consequently, the resulting two‐point boundary value problem is solved to obtain optimal trajectories. We demonstrate the optimality of the resulting solution obtained from the derived control law. For ensuring boundedness in the presence of small disturbances, this study incorporates the effects of internal parametric uncertainties associated with added mass and inertia components, along with the influence of external disturbances induced by ocean currents. Through simulation validations, we confirm the alignment of our results with the theoretical developments, demonstrating that the proposed control law effectively mitigates both parametric uncertainties and ocean current disturbances.

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Optimal attitude consensus for multi rigid bodies network considered on the lie group SO(3) with connectivity preserving property

Cited by 6 publications

References 35 publications

Optimal attitude consensus control for rigid spacecraft formation based on control Lyapunov functions

Optimal attitude consensus control for rigid spacecraft formation based on control Lyapunov functions

Neighboring extremal nonlinear model predictive control of a rigid body on SO(3)

A lie group PMP approach for optimal stabilization and tracking control of autonomous underwater vehicles

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