Solar Cruiser Disturbance Torque Estimation and Predictive Momentum Management

This paper proposes a novel disturbance-torque-estimation-augmented model predictive control framework that utilizes a Kalman filter and enhanced dynamics modeling to effectively manage momentum on NASA's Solar Cruiser mission, successfully outperforming state-of-the-art methods during large-angle slew maneuvers.

The Gist

The Big Picture: The Solar Sail and the "Spinning Top" Problem

Imagine Solar Cruiser not as a spaceship, but as a giant, ultra-lightweight kite floating in space. Instead of burning fuel to move, it uses the gentle push of sunlight (solar radiation pressure) to glide.

However, there's a catch. Just like a kite in a strong wind, this solar sail isn't perfectly flat. It ripples, bends, and catches the wind unevenly. These imperfections create tiny, constant pushes and twists (disturbances) that try to spin the spacecraft out of control.

To stop this spinning, the spacecraft uses Reaction Wheels (RWs). Think of these as heavy spinning tops inside the ship. When the ship starts to spin one way, the tops spin the other way to keep the ship steady.

The Problem:
Over time, these internal tops get tired. They spin faster and faster to fight the wind, until they reach their maximum speed. Once they hit that limit (saturation), they can't spin any faster. If they can't spin faster, they can't stop the ship from spinning. The ship loses control.

The Solution:
The ship needs to "unwind" these tops. It needs to dump the built-up spin energy without using fuel. It does this using two special tools:

1. The Active Mass Translator (AMT): A heavy weight that slides back and forth inside the ship. Moving the weight changes the ship's balance, using the sunlight to push the ship back into place.
2. Reflectivity Control Devices (RCDs): Tiny switches on the edges of the sail that can turn from "shiny" to "dark." By changing how much light they reflect, they create a tiny twist to stop the ship from rolling.

The Old Way vs. The New Way

The Old Way (The Reactive Firefighter):
Previously, NASA used a simple "if-then" rule.

• Analogy: Imagine a firefighter who only turns on the hose when the fire is already burning the house.
• How it worked: If the spinning tops got too fast, the system would turn on the sliding weight or the light-switches to slow them down.
• The Flaw: This is reactive. By the time the tops are spinning too fast, it's often too late to stop them from breaking. Also, the system didn't know about the "wind" (disturbances) until it felt them, so it was always playing catch-up.

The New Way (The Predictive Chess Player):
This paper introduces a new brain for the spacecraft called Model Predictive Control (MPC), combined with a Kalman Filter.

• The Kalman Filter (The Detective):
  The spacecraft can't see the invisible "wind" (disturbance torque) directly. The Kalman Filter is like a detective that looks at the evidence (how the ship is actually moving) and guesses what the wind is doing right now. It estimates the invisible forces in real-time.

• The MPC (The Chess Grandmaster):
  Instead of just reacting to the current spin, the MPC looks 1000 seconds into the future.

  • Analogy: Imagine playing chess. A reactive player only thinks about the next move. A Grandmaster (MPC) thinks, "If I move here, my opponent will move there, so I should move there to set up a trap."
  • The MPC uses the detective's guess about the wind to calculate the perfect sequence of moves (sliding the weight, flipping the switches) to keep the spinning tops safe before they ever get in trouble.

Why This Paper is a Big Deal

The authors made four major upgrades to this "Chess Grandmaster" system:

1. It Knows the Wind: By adding the Kalman Filter, the system doesn't need to know the wind perfectly in advance. It learns the wind as it blows and adjusts its strategy instantly. This makes the system much more reliable.
2. It Handles Four Tops: Previous models only worked with three spinning tops. Solar Cruiser has four for safety. The new math handles this complex 4-top setup perfectly.
3. It Handles Big Turns: The old system could only hold the ship steady. The new system can plan for large turns (slews). It knows that if it's going to turn the ship 15 degrees, it needs to start "unwinding" the tops before the turn starts, so the tops don't get overwhelmed during the turn.
4. It's Efficient: The new system is smart enough to know when not to move. It has "thresholds" (like a sensitivity setting). If the wind is just a tiny breeze, the system ignores it to save energy and wear-and-tear on the moving parts. It only acts when the wind is strong enough to matter.

The Results: A Smarter, Safer Sail

The authors ran computer simulations to test this new system against the old NASA method.

• The Test: They simulated a large turn that the old system couldn't handle.
• The Result: The old system failed; the spinning tops got stuck, and the ship lost control. The new MPC system, however, saw the trouble coming, started unwinding the tops early, and successfully completed the turn without ever getting stuck.
• Efficiency: The new system also used less energy and moved the sliding weight less often, meaning the spacecraft could last longer in space.

The Bottom Line

This paper presents a smarter autopilot for NASA's giant solar sail. By combining a "detective" that guesses invisible forces with a "grandmaster" that plans ahead, the spacecraft can perform complex maneuvers and stay in control even when the environment is messy and unpredictable. It moves space travel from "reacting to problems" to "predicting and preventing them."

Technical Summary

1. Problem Statement

NASA's Solar Cruiser mission utilizes a massive solar sail (>1,600 m²) for propulsion. A critical challenge in solar sail operations is momentum management: the accumulation of angular momentum in onboard Reaction Wheels (RWs) caused by persistent disturbance torques (e.g., from imperfect sail shapes, structural flexibility, and solar radiation pressure variations). If RWs saturate, the spacecraft loses attitude control authority.

Current state-of-the-art momentum management for Solar Cruiser relies on a decoupled, threshold-based strategy using:

• Active Mass Translator (AMT): Shifts the center of mass (CM) to generate counter-torques.
• Reflectivity Control Devices (RCDs): Binary (on/off) devices that alter sail reflectivity to generate roll torque.

Limitations of existing methods:

• Reactive Nature: Threshold-based controllers react only after momentum accumulates, failing to proactively prevent saturation during large maneuvers.
• Unmodeled Disturbances: Previous Model Predictive Control (MPC) attempts assumed exact knowledge of disturbance torques and constant Solar Radiation Pressure (SRP) forces, which is unrealistic due to sail deformation and attitude-dependent SRP.
• Hardware Mismatch: Prior MPC models often assumed 3-RW configurations or ignored the offset between the CM and Center of Pressure (CP), whereas Solar Cruiser uses a 4-RW assembly with a significant CM-CP offset.
• Limited Maneuverability: Existing methods are primarily designed for attitude holding, not large-angle slew maneuvers.

2. Methodology

The authors propose a Disturbance-Torque-Estimation-Augmented Model Predictive Control (MPC) framework. The system integrates real-time estimation with predictive optimization to handle the coupled, nonlinear dynamics of the solar sail.

A. System Dynamics & Modeling

• Nonlinear Dynamics: The model incorporates the 4-RW assembly, the AMT-induced time-varying inertia matrix, and the offset between the CM and CP.
• Attitude-Dependent SRP: Unlike prior work, the SRP force and disturbance torques are modeled as functions of the spacecraft's attitude and sail shape deformation.
• Linearization: For real-time implementation, the nonlinear dynamics are linearized around the current state and trajectory to create a Linear Time-Varying (LTV) model used for prediction.

B. Disturbance Estimation (Kalman Filter)

A Kalman Filter (KF) is employed to estimate unmodeled disturbance torques and system model errors in real-time.

• State Augmentation: The disturbance torque ($\tau_{dist}$) is treated as an augmented state variable assumed to be constant or slowly varying.
• Dynamic Covariance: The filter's error covariance is scaled dynamically based on the desired angular velocity to adapt to changes during slew maneuvers.
• Role: The estimated disturbance is fed directly into the MPC prediction model, allowing the controller to "see" and compensate for unknown torques before they cause saturation.

C. Model Predictive Control (MPC) Formulation

The MPC solves a constrained Quadratic Program (QP) at every 100-second momentum management step to determine optimal AMT and RCD commands.

• Prediction Horizon: 10 steps (1000 seconds).
• Control Allocation: Uses a pseudo-inverse method to map the desired body-frame torque to the individual 4-RW commands, ensuring RWs stay within saturation limits.
• Constraints:
  • Hard Constraints: Physical limits on AMT position/rate and RW saturation.
  • Soft Constraints: A "safe operating envelope" for RW momentum. Violations are penalized quadratically via a slack variable ($\alpha$) in the objective function, allowing the optimizer to trade off performance for feasibility rather than failing immediately.
• RCD Handling: The binary nature of RCDs is relaxed to a continuous variable during optimization and then quantized using Pulse Width Modulation (PWM) to generate the actual on/off commands.
• Actuation Thresholds: To improve efficiency and reduce noise, small MPC demands below specific thresholds (e.g., 30% of max AMT travel) are filtered out (set to zero).

3. Key Contributions

1. Robust MPC with Disturbance Estimation: This is the first realistically implementable momentum management policy for a solar sail with AMT/RCDs that outperforms current threshold-based methods by using a Kalman Filter to estimate unknown disturbances in real-time.
2. 4-RW Assembly Integration: The first MPC-based momentum management policy to explicitly account for a realistic 4-RW redundant configuration and the associated control allocation, rather than assuming a simplified 3-RW system.
3. High-Fidelity Simulation: The framework incorporates critical physical realities often ignored in prior work, including the CM-CP offset, attitude-dependent SRP forces/torques, and sail shape deformations.
4. Large-Angle Slew Capability: The policy successfully manages momentum during large-angle slew maneuvers, a capability lacking in previous "attitude-hold-only" MPC formulations.

4. Simulation Results

The authors validated the method using high-fidelity simulations of Solar Cruiser, comparing the proposed MPC against NASA's current state-of-the-art threshold-based controller.

• Performance under Large Slews:
  • Threshold Method: Failed to manage momentum during a $15^\circ$ slew maneuver, leading to RW saturation and loss of attitude control.
  • Proposed MPC: Successfully managed the same maneuver, keeping all RWs within safe operating limits by proactively unloading momentum before saturation occurred.
• Impact of Disturbance Estimation:
  • MPC without disturbance estimation (nominal) resulted in RWs stabilizing near saturation limits.
  • MPC with Kalman Filter estimation drove RW momentum significantly lower, preserving control authority and demonstrating that disturbance estimation is critical for robustness.
• Actuator Efficiency:
  • The proposed MPC reduced total AMT travel distance and optimized RCD usage during attitude hold phases compared to the benchmark.
  • While RCD on/off cycles increased slightly due to PWM quantization, the total "on" time was optimized, and the approach avoided the long, potentially overheating activation pulses seen in the benchmark method.
• Computational Feasibility: The QP solver averaged 32.86 ms per step on a standard desktop, confirming the method is viable for real-time onboard flight computers.

5. Significance

This work establishes a new benchmark for solar sail momentum management. By bridging the gap between theoretical MPC and practical implementation through disturbance estimation and high-fidelity modeling, the authors demonstrate that solar sails can perform more aggressive maneuvers with greater reliability.

The framework paves the way for future deep-space solar sail missions by:

• Extending the operational envelope for large-angle maneuvers.
• Reducing reliance on fuel-based desaturation (thrusters).
• Providing a robust architecture that can handle the uncertainties inherent in large, flexible space structures.

This research is a critical step toward the operational success of NASA's Solar Cruiser and future generations of solar sail spacecraft.