⚡ electrical engineering

Preferential corridor shaping for satellite proximity maneuvers via Multiple Attractors Potential Field

This paper proposes a novel Multiple Attractors Potential Field guidance strategy within the Hill-Clohessy-Wiltshire dynamic model to enable autonomous satellite proximity maneuvers that adhere to specific preferential corridors by introducing fictitious local attractors, particularly in scenarios with known initial configurations such as docking with obstacles or fly-around inspections.

Original authors: Erica Scantamburlo, Marco Luigi Ottavi, Matteo Melchiorre, Stefano Mauro

Published 2026-08-20

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CC BY 4.0

Original authors: Erica Scantamburlo, Marco Luigi Ottavi, Matteo Melchiorre, Stefano Mauro

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the silent expanse of low Earth orbit, satellites are not merely drifting objects; they are active participants in a complex, high-stakes ballet of proximity. As humanity's reliance on space infrastructure grows, the ability for one spacecraft to safely approach, inspect, and even dock with another has become a critical capability. This is the realm of rendezvous and proximity operations, where a "chaser" satellite must navigate the delicate environment around a "target" without colliding. The physics governing this dance are well understood, described by equations that predict how two objects move relative to one another when they are close together in a circular orbit. However, knowing the rules of motion is different from having a reliable guide to navigate the specific, often crowded, paths required for a mission. Traditional navigation tools, which rely on creating an invisible landscape of forces to push a satellite away from danger and pull it toward a goal, often fail when a mission demands a specific route. If a satellite needs to approach a target from a precise angle to avoid a shadow, or to align with a docking port that is shielded from view, standard methods can get the spacecraft stuck in a dead end or push it along a path that violates safety constraints.

Researchers at the Politecnico di Torino in Italy have proposed a new way to solve this navigation puzzle, a method designed to force a satellite to follow a preferred corridor even when the natural forces of the orbit might suggest otherwise. Their work, published in a recent study, introduces a technique called the Multiple Attractors Potential Field. To understand how this works, one must first visualize the traditional approach. Imagine a satellite trying to reach a target while avoiding obstacles. Engineers often use a system of artificial forces: a gentle pull toward the destination and a strong repulsion from any nearby hazards. This creates a smooth valley in a landscape of energy where the satellite naturally rolls toward the goal. The problem arises when the terrain has hidden bumps or when the satellite needs to take a detour that the natural valley does not offer. In these cases, the satellite might get trapped in a local dip, unable to reach the true destination, or it might approach the target from the wrong side, missing the docking port entirely.

The new method addresses this by adding a layer of control that acts like a series of invisible, temporary magnets placed along the desired path. These are not physical objects, but rather mathematical points of attraction introduced into the guidance system. By carefully positioning these fictitious attractors, the researchers can shape the invisible landscape of forces, carving out a specific corridor that the satellite is compelled to follow. This allows the chaser to bypass obstacles and approach the target from a specific direction, such as a radial line pointing toward Earth, which might be necessary for a safe docking or to satisfy lighting conditions for an inspection camera. The key to this strategy is that it requires the mission planners to know the starting position and the desired path in advance. Because the positions of these invisible magnets must be calculated before the maneuver begins, the method is best suited for scenarios where the environment is predictable, such as a planned rendezvous with a known target or a pre-mapped inspection flight.

The team tested this approach through detailed computer simulations of two distinct scenarios. In the first, a chaser satellite attempted to dock with a target while avoiding a nearby monitoring satellite that acted as a moving obstacle. The target had a specific docking port located on its side, requiring the chaser to approach from a precise angle. When using the traditional navigation method, the chaser was pushed away from the obstacle but ended up approaching the target from the opposite side, missing the docking corridor entirely. In contrast, the new method successfully guided the chaser through a narrow, preferential corridor, forcing it to pass near a specific point in space before aligning with the docking port. The simulation showed that while this new path required slightly more fuel—about 19 percent more than the traditional method—it achieved the critical goal of a safe, aligned approach that the older method could not guarantee. The extra fuel cost was a calculated trade-off for the ability to navigate a constrained, safe path.

The second scenario involved a monitoring satellite that needed to switch positions to maintain a continuous view of a target, a maneuver often required to keep a spacecraft illuminated by the sun. In this case, the satellite started on one side of the target and needed to move to the other. The traditional navigation system struggled here because the forces pulling the satellite toward its new position were balanced in a way that allowed it to drift in either direction, creating a risk of moving the wrong way. By introducing a single, strategically placed attractor, the researchers were able to break this symmetry. The satellite was gently but firmly guided along a specific arc, ensuring it moved in the intended direction without getting lost or colliding with the target. The simulation confirmed that the satellite could complete the orbital switch autonomously, following the pre-defined corridor without human intervention.

These findings suggest that the Multiple Attractors Potential Field offers a robust solution for missions where safety and specific approach angles are paramount. The method does not rely on complex, real-time calculations that might overwhelm a satellite's computer, making it a practical tool for autonomous operations. However, the researchers are clear about its limitations: the technique works best when the initial setup is known and the path can be planned ahead of time. It is not a magic wand for chaotic, unpredictable environments where obstacles appear suddenly. Instead, it is a precise instrument for shaping the journey, ensuring that when a satellite moves in the crowded space around a target, it follows a path that has been carefully designed for safety and success. The work highlights a shift in how space navigation is conceived, moving from simple avoidance of danger to the active shaping of a safe, preferential route through the void.

Technical Summary: Preferential Corridor Shaping for Satellite Proximity Maneuvers via Multiple Attractors Potential Field

Problem Statement
Autonomous rendezvous, proximity operations, and docking (RPOD) are critical for future space sustainability, including on-orbit servicing and cargo transportation. While traditional guidance and control methods exist, they often face a trade-off between computational complexity and real-time applicability. Artificial Potential Field (APF) algorithms are favored for their low computational cost and real-time capabilities but suffer from a significant limitation: they often fail to satisfy "preferential movement corridor" requirements. These corridors are necessary to enhance mission safety (e.g., avoiding specific approach angles) or achieve mission objectives (e.g., satisfying illumination constraints for inspection). Standard APF methods, which rely on a global attractor (target) and repulsive obstacles, lack the mechanism to enforce a specific trajectory path when the initial configuration and desired maneuvering direction are known in advance.

Methodology
The authors propose a novel guidance and control strategy within the Hill-Clohessy-Wiltshire (HCW) dynamic model, termed the Multiple Attractors Potential Field (MAPF). This method modifies the classical APF by introducing fictitious local attractors to delineate preferential movement corridors.

Dynamic Model: The relative motion of a chaser satellite with respect to a target in a circular orbit is governed by the linearized HCW equations.
Potential Function Formulation: The total guidance potential $U_{MAPF}$ $U_{M A P F}$ is constructed as the sum of three components:
1. Global Attractor ( $U_f$ ): A quadratic term driving the chaser toward the origin (target).
2. Obstacle Repulsion ( $U_{obs}$ ): Gaussian-like repulsive terms modeling monitoring satellites or obstacles as point masses to prevent collisions.
3. Local Attractors ( $U_{att}$ ): Gaussian-like attractive terms centered at virtual points ( $r_{att,j}$ ). These are the core innovation, designed to pull the chaser through a specific corridor, bypassing obstacles or adhering to approach constraints.
Stability and Tuning: The stability of the system is analyzed using the second method of Lyapunov. The guidance law applies impulsive velocity changes ( $\Delta v$ $Δ v$ ) to ensure the time derivative of the Lyapunov function remains negative.
- The paper provides rigorous analytical tuning procedures for the MAPF parameters (specifically $\gamma$ , $\beta$ , $\alpha$ , and design ratios $\lambda$ and $\mu$ ).
- These procedures utilize the Lambert $W$ function to define "active radii" for obstacles and attractors, ensuring that the potential field does not create undesired local minima (traps) or saddle points that could stall the chaser.
- A specific condition is derived to ensure the local attractor coefficient ( $\alpha_{att}$ ) is small enough to prevent the formation of critical points near the local attractor itself, while large enough to influence the trajectory.
Close-Range Transition: For the final approach phase (within a critical distance $d_{cr}$ ), the MAPF potential is replaced by a cardioid-shaped repulsive potential. This ensures the chaser aligns with the specific docking port orientation, modeled as a stable minimum with an unstable saddle point.

Key Contributions

Introduction of MAPF: The paper formalizes the use of multiple virtual attractors within an APF framework to enforce preferential trajectories, addressing the "path ambiguity" inherent in standard APF when obstacles and targets are collinear or symmetric.
Analytical Tuning Framework: The authors provide a comprehensive set of analytical results (Recalls #1–#4) for tuning the MAPF parameters. This includes formulas for determining the active radius of obstacles and attractors and calculating the maximum allowable strength of local attractors to avoid local critical points.
Application to Specific Scenarios: The method is applied to two distinct cases where initial configurations are known:
- Rendezvous and Docking: Enforcing an approach along a specific radial direction (negative x-axis) to avoid late-stage fly-around maneuvers.
- Fly-Around Inspection: Defining a preferential orbital switch direction for a monitoring satellite to satisfy illumination requirements, resolving directional ambiguity where standard APF might fail.

Numerical Results
The paper validates the methodology through two numerical case studies:

Case 1 (Rendezvous and Docking): A single chaser approaches a target with an obstacle located at $(0, -250, 0)$ $(0, - 250, 0)$ m.
- MAPF Performance: The chaser successfully navigates through a preferential corridor defined by a local attractor, approaching the target along the desired negative x-axis docking corridor.
- Comparison: Compared to classical APF, the MAPF strategy required approximately 19% more total $\Delta v$ ( $3.98 \times 10^{-4}$ km/s vs. $3.35 \times 10^{-4}$ km/s) and a slightly longer time of flight. However, this cost is traded for a trajectory that strictly adheres to the safety corridor, whereas the classical APF approached from an undesired side.
Case 2 (Orbital Switch/Inspection): A monitoring satellite ( $M_1$ $M_{1}$ ) must relocate from $(0, -500, 0)$ $(0, - 500, 0)$ m to $(0, 500, 0)$ $(0, 500, 0)$ m while avoiding the target.
- Result: The classical APF failed to resolve the directional ambiguity, potentially moving the satellite in the wrong direction. The MAPF, utilizing a local attractor on the negative x-axis, successfully guided the satellite along the preferential corridor to the target position.

Significance and Claims
The authors claim that the MAPF strategy offers a viable solution for autonomous proximity operations in scenarios where:

Computational resources are limited: The algorithm relies on analytical potential functions and impulsive maneuvers, avoiding the high computational cost of optimal control or model predictive control.
Initial configuration is known: The method is specifically suited for cases where the positions of obstacles and the desired maneuvering direction are available in advance, allowing for the pre-calculation of local attractor positions.
Safety and Mission Constraints are critical: The method effectively enforces preferential corridors to satisfy safety constraints (collision avoidance) and mission objectives (illumination, docking alignment) that standard APF cannot guarantee.

The paper concludes that while MAPF may incur a slight penalty in propellant consumption compared to classical APF, it provides the necessary control authority to shape trajectories according to mission-specific corridor requirements, thereby supporting safer and more reliable autonomous space operations.

Technical Summary: Preferential Corridor Shaping for Satellite Proximity Maneuvers via Multiple Attractors Potential Field

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