Consistent and Centrally Synergistic Quaternion-Based Attitude Stabilization with Minimal Potential Functions

Core Concepts

This paper proposes a novel synergistic hybrid feedback for robust global attitude stabilization of a rigid-body system using quaternions. The key features are: (1) it utilizes a minimal number of potential functions while demonstrating central synergism, (2) it ensures consistency with respect to the unit quaternion representation, and (3) it incorporates a shared action term that steers the system toward the desired attitude.

Abstract

The paper investigates the problem of robust global attitude stabilization for a rigid-body system using quaternion-based feedback. The authors propose a novel synergistic hybrid feedback with the following key features:

Central Synergism: The feedback utilizes a minimal number of potential functions (PFs) while demonstrating central synergism. This simplifies the switching mechanism compared to previous approaches.

Consistency: The proposed feedback ensures consistency with respect to the unit quaternion representation of rigid-body attitude, eliminating the need for a quaternion conversion mechanism.

Shared Action Term: The state-feedback laws incorporate a shared action term that steers the system toward the desired attitude, leading to a moderate switch of the state-feedback laws and reducing chattering.

The authors first introduce a candidate set of synergistic potential functions (SPFs) that consists of two PFs. They then determine the parameters to ensure both central synergism and consistency properties. Finally, the hybrid feedback is derived from the SPFs and is shown to effectively solve the problem of stabilizing rigid-body attitude while guaranteeing robust uniform global asymptotic stability.

Stats

The paper does not contain any explicit numerical data or statistics. It focuses on the theoretical development of the quaternion-based synergistic hybrid feedback.

Quotes

"The key ingredient of this approach is synergistic potential functions (SPFs), i.e., a family of PFs possessing the synergism property: at every critical point (except the desired attitude) of each PF in the family, there exists another PF with a lower value."
"The gradients of the SPFs constitute a family of state-feedback laws and the synergism property enables a hysteresis-based switching mechanism for state-feedback law selection, ensuring robust GAS results."

Key Insights Distilled From

Quaternion-Based Attitude Stabilization Using Synergistic Hybrid Feedback With Minimal Potential Functions

by Xin Tong,Qin... at arxiv.org 04-15-2024

https://arxiv.org/pdf/2404.08326.pdf

Deeper Inquiries

How can the proposed approach be extended to handle more complex rigid-body systems, such as those with external disturbances or parameter uncertainties

The proposed approach can be extended to handle more complex rigid-body systems by incorporating strategies to address external disturbances or parameter uncertainties. One way to handle disturbances is to design robust controllers that can adapt to varying external conditions. This can be achieved by incorporating robust control techniques such as H-infinity control or sliding mode control into the hybrid feedback framework. These techniques can help the system maintain stability in the presence of disturbances by actively adjusting the control inputs based on the system's response to the disturbances.
For parameter uncertainties, adaptive control methods can be employed to continuously update the controller parameters based on the system's behavior. Adaptive control algorithms, such as model reference adaptive control or adaptive sliding mode control, can help the system adapt to changes in parameters and ensure robust performance even in the presence of uncertainties.
Furthermore, the use of state estimation techniques, such as Kalman filters or observers, can enhance the system's ability to handle uncertainties by providing accurate estimates of the system states. By integrating these estimation techniques with the control algorithm, the system can effectively compensate for uncertainties and disturbances, ensuring stable and reliable performance in complex environments.

What are the potential limitations or drawbacks of the centrally synergistic hybrid feedback approach compared to other quaternion-based attitude stabilization methods

While the centrally synergistic hybrid feedback approach offers several advantages in terms of stability and consistency, there are potential limitations and drawbacks compared to other quaternion-based attitude stabilization methods.
One limitation is the computational complexity of the approach, especially when dealing with high-dimensional systems or a large number of potential functions. The need to evaluate multiple potential functions and perform switching between state-feedback laws can increase the computational burden, leading to higher processing times and resource requirements.
Another drawback is the sensitivity of the approach to the selection of parameters, such as the hysteresis width and the choice of vectors uq. Improper selection of these parameters can affect the stability and performance of the system, requiring careful tuning and analysis to ensure robustness.
Additionally, the requirement for central synergism may limit the flexibility of the control design, as it mandates that each state-feedback law independently stabilizes the system. This constraint may restrict the design space and make it challenging to achieve certain control objectives or handle specific system dynamics effectively.

Can the principles of the angular warping technique and central synergism be applied to other control problems beyond attitude stabilization, such as trajectory tracking or formation control

The principles of the angular warping technique and central synergism can be applied to other control problems beyond attitude stabilization, such as trajectory tracking or formation control. By adapting these concepts to different control scenarios, it is possible to enhance the stability, robustness, and performance of various systems.
In trajectory tracking, the angular warping technique can be used to adjust the reference trajectories based on the system's state, allowing for smoother and more accurate tracking. Central synergism can ensure that the control laws work synergistically to track the desired trajectory while maintaining stability and consistency.
For formation control, the angular warping technique can be utilized to coordinate the movements of multiple agents in a formation. By warping the reference signals based on the relative positions of the agents, the formation can be maintained while avoiding collisions and ensuring a cohesive group behavior. Central synergism can help in ensuring that the agents work together harmoniously to achieve the desired formation.
Overall, the principles of angular warping and central synergism provide a versatile framework for designing advanced control strategies in various applications beyond attitude stabilization, offering improved performance and robustness in complex control scenarios.