Efficient Convex MPC and Thrust Allocation for Spacecraft Rendezvous with Thruster Deadband

Core Concepts

This paper presents an efficient Model Predictive Control (MPC) strategy for spacecraft rendezvous that addresses the computational challenges arising from mixed-integer constraints introduced by spacecraft thruster deadband.

Abstract

The paper focuses on developing an MPC controller for a chaser spacecraft attempting to rendezvous with a target spacecraft in a circular orbit around the Earth. The key highlights are:

The spacecraft dynamics are described using the Clohessy-Wiltshire (CW) equations, which provide a simplified linear state-space model. This model accounts for the minimum activation time (deadband) of the spacecraft thrusters, leading to mixed-integer constraints in the optimization problem.

To address the computational complexity of solving the resulting mixed-integer linear program (MILP), the paper proposes two solver algorithms: Projected and Relaxed. These algorithms efficiently approximate the optimal solution, significantly reducing computation time compared to standard MILP solvers.

Simulation results demonstrate that the proposed algorithms produce trajectories and performance metrics (fuel consumption, mission time) that closely match the optimal solution obtained using a standard MILP solver, while being much more computationally efficient.

The paper also investigates the impact of the minimum activation time and the prediction horizon length on the controller's performance and computational requirements.

Overall, the paper presents an effective MPC strategy for spacecraft rendezvous that can be implemented in real-time applications, addressing the key challenge of mixed-integer constraints in the optimization problem.

Stats

The chaser's initial position is [0 0 100 km 0 0 0]⊤.
The target's orbital radius is 7171 km.
The chaser's mass is 2000 kg.
There are 6 thrusters, each with a thrust force of 1000 N.
The minimum activation time (deadband) is 5 s.
The sampling period is 10 s.
The simulation time is 3600 s.

Quotes

"The operational principle of spacecraft thrusters, requiring a minimum activation time that leads to the existence of a control deadband, introduces mixed-integer constraints into the optimization, posing a considerable computational challenge due to the exponential complexity on the number of integer constraints."
"We address this complexity by presenting two solver algorithms that efficiently approximate the optimal solution in significantly less time than standard solvers, making them well-suited for real-time applications."

Key Insights Distilled From

Convex MPC and Thrust Allocation with Deadband for Spacecraft Rendezvous

by Pedr... at arxiv.org 04-08-2024

https://arxiv.org/pdf/2404.04197.pdf

Deeper Inquiries

How could the proposed MPC strategy be extended to handle more complex spacecraft dynamics, such as attitude control or elliptical orbits

To extend the proposed MPC strategy to handle more complex spacecraft dynamics, such as attitude control or elliptical orbits, several modifications and enhancements can be implemented.
For attitude control, the MPC controller can be augmented to include additional state variables representing the spacecraft's orientation. This would involve incorporating the dynamics of the spacecraft's rotational motion into the model, along with constraints on the spacecraft's attitude angles and angular rates. By formulating the control problem to simultaneously optimize both translational and rotational maneuvers, the MPC controller can effectively guide the spacecraft in three-dimensional space.
In the case of elliptical orbits, the dynamics model would need to be adjusted to account for the non-circular nature of the orbits. This would involve modifying the equations of motion to accurately capture the varying distances and velocities of the spacecraft as it traverses the elliptical path. The optimization problem would then need to consider the changing orbital parameters and constraints specific to elliptical orbits, such as varying gravitational forces and orbital eccentricity.
By incorporating these enhancements into the MPC framework, the controller can effectively handle the complexities of attitude control and elliptical orbits, enabling precise and efficient spacecraft maneuvers in challenging space environments.

What are the potential challenges and considerations in implementing the Projected and Relaxed algorithms on actual spacecraft hardware with limited computational resources

Implementing the Projected and Relaxed algorithms on actual spacecraft hardware with limited computational resources poses several challenges and considerations.

Computational Efficiency: The algorithms need to be optimized for efficient execution on the spacecraft's onboard computer, which typically has limited processing power and memory. This may require algorithmic modifications to reduce computational complexity and memory usage while maintaining solution quality.

Real-Time Performance: Ensuring that the algorithms can provide timely solutions within the constraints of the spacecraft's control cycle is crucial. The algorithms must be designed to deliver solutions quickly enough to be actionable for guiding the spacecraft in dynamic environments.

Numerical Stability: Given the constraints of numerical precision on embedded systems, the algorithms must be robust to numerical errors and limitations. Careful consideration of numerical stability and precision is essential to prevent computational issues during runtime.

Hardware Constraints: The algorithms need to be tailored to the specific hardware architecture of the spacecraft's onboard computer, considering factors such as processor type, memory constraints, and communication bandwidth.

By addressing these challenges and considerations, the Projected and Relaxed algorithms can be effectively implemented on spacecraft hardware with limited computational resources, enabling real-time control and optimization of spacecraft maneuvers.

How could the MPC controller be further enhanced to address safety-critical aspects, such as collision avoidance with debris or other spacecraft, while maintaining real-time performance

Enhancing the MPC controller to address safety-critical aspects, such as collision avoidance with debris or other spacecraft, while maintaining real-time performance involves several key considerations and potential enhancements.

Collision Avoidance Constraints: Integrate collision avoidance constraints into the MPC optimization problem to ensure that the spacecraft maintains a safe distance from debris or other objects. This would involve incorporating obstacle detection and avoidance algorithms into the MPC framework.

Safety Margins: Implement safety margins in the control objectives to provide a buffer zone around obstacles or other spacecraft, allowing for proactive collision avoidance maneuvers. These safety margins can be dynamically adjusted based on the proximity of potential hazards.

Sensor Fusion: Utilize sensor fusion techniques to enhance situational awareness and enable the MPC controller to make informed decisions based on real-time sensor data. By integrating data from multiple sensors, such as cameras, lidar, and radar, the controller can accurately detect and respond to potential collision risks.

Adaptive Control Strategies: Implement adaptive control strategies that can dynamically adjust the spacecraft's trajectory in response to changing environmental conditions or unexpected obstacles. This adaptive behavior allows the MPC controller to react swiftly to emerging safety threats while maintaining overall mission objectives.

By incorporating these enhancements, the MPC controller can effectively address safety-critical aspects such as collision avoidance while ensuring real-time performance and optimal spacecraft maneuvering in complex and dynamic space environments.