Hybrid Dynamical System Approach to Spacecraft Rendezvous Control

Core Concepts

The author presents a hybrid dynamical system approach for impulsive control in spacecraft rendezvous, focusing on separating out-of-plane and in-plane dynamics with tailored feedback control laws.

Abstract

This paper introduces a novel approach to impulsive control in spacecraft rendezvous operations. By isolating different dynamics and using Lyapunov functions, the authors demonstrate effective control strategies through simulations. The work addresses the increasing complexity of space missions and the need for precise maneuvers near target spacecraft. The study highlights the importance of autonomous guidance and control in various space activities like asteroid mining, collision avoidance, and debris removal. The research builds upon previous works that have focused on feedback laws for rendezvous problems using Model Predictive Control (MPC) strategies. However, this study diverges by utilizing a simpler simulation model while incorporating saturations into the analysis without requiring an optimization process in control law computation. The paper delves into the terminal rendezvous stage with a focus on designing efficient impulsive maneuvers using a hybrid systems framework. By separating out-of-plane and in-plane dynamics, specific feedback control laws are proposed based on Lyapunov functions tailored to each dynamic aspect. These functions are found by expressing dynamics in more natural coordinates that capture their physical behavior. Through simulations, the effectiveness of these control laws is demonstrated, showcasing their ability to address thruster saturation and minimum impulse bit requirements effectively.

Stats

Thrust level chosen as uM = 0.2m/s.
Dwell time parameter τ Mz used for simulations: 0.01 and 0.25.
Initial condition for simulation depicted as [−60 0 1000 0]⊤.
Dwell time parameters τ Mα = 0.01 and τ Mβ = 0.02 used for simulations.

Quotes

"The demand for autonomous guidance and control in these tasks is more pressing than ever."
"Our approach diverges from instances using MPC by incorporating saturations into our analysis."
"Future work will include addressing minimum impulse bit requirements."

Key Insights Distilled From

A hybrid dynamical system approach to the impulsive control of spacecraft rendezvous (extended version)

by Alexandre Se... at arxiv.org 03-07-2024

https://arxiv.org/pdf/2403.03633.pdf

Deeper Inquiries

How does this hybrid dynamical system approach compare to traditional methods like MPC

The hybrid dynamical system approach presented in the context offers a different perspective compared to traditional methods like Model Predictive Control (MPC). While MPC is known for its optimality and constraint handling capabilities, it comes with a significant computational cost that may not be feasible for onboard low-cost satellites such as Cubesats. Additionally, providing guarantees on stability and feasibility with MPC can be challenging, especially when dealing with minimum impulse bit requirements. On the other hand, the hybrid dynamical system approach leverages simpler simulation models but incorporates saturations into the analysis without requiring an optimization process in control law computation. This methodology ensures stability, simplifies calculations, and improves efficiency by addressing impulsive control in spacecraft rendezvous operations under the Hill-Clohessy-Wiltshire model.

What are the implications of addressing minimum impulse bit requirements in spacecraft rendezvous operations

Addressing minimum impulse bit requirements in spacecraft rendezvous operations has significant implications for mission success and resource management. By incorporating constraints related to minimum impulse bits into the control design framework, researchers can ensure that spacecraft maneuvers are executed efficiently while meeting specific operational criteria. These requirements play a crucial role in optimizing fuel consumption, minimizing thruster usage, and achieving precise trajectory adjustments during proximity operations. Moreover, considering minimum impulse bit constraints helps enhance overall mission planning strategies by balancing performance objectives with resource limitations effectively.

How can this research be applied to more complex scenarios like formation-flying or eccentric orbits

The research conducted on impulsive control of spacecraft rendezvous using a hybrid dynamical system approach has broad applications beyond basic scenarios like proximity operations under ideal conditions. The findings can be extended to more complex scenarios such as formation-flying missions or eccentric orbits where nonlinear dynamics come into play. For instance:

Formation-Flying: In formation-flying missions involving multiple spacecraft coordinating their movements relative to each other while maintaining specific configurations or patterns requires sophisticated control strategies. The hybrid dynamical system approach's ability to handle impulsive maneuvers within this context can contribute to ensuring stable formations and coordinated actions among spacecraft.
Eccentric Orbits: Dealing with eccentric orbits introduces additional challenges due to varying gravitational forces and orbital characteristics over time. Applying the principles of impulsive control within a hybrid framework allows for adaptive responses to changing dynamics encountered in eccentric orbits while still meeting operational objectives effectively.
By adapting the developed methodologies from this research to these advanced scenarios, space agencies and organizations can enhance their capabilities in managing complex space missions involving intricate orbital dynamics and coordination requirements efficiently.