User:Abcdefghwater/sandbox/Collision Avoidance (Spacecraft)

Collision avoidance is the study of preventing collisions of spacecraft with external objects, which includes both space debris and other spacecraft. It is estimated that there are more than 500,000 pieces of space debris orbiting earth. In addition, there are over 2,000 satellites orbiting earth. Space debris poses a threat to the operation of satellites in both low earth orbit and geostationary orbit. Collision avoidance, as an area of study, refers to the techniques of tracking external objects, quantifying the risk of colliding with these objects, and performing avoidance maneuvers. There are a variety of maneuvers used to prevent collisions, each involving thrusting to modify the spacecraft’s orbital path. Tracking objects in space is essential for quantifying the probability of collision and also for performing the correct avoidance maneuver. Modern collision avoidance research involves control systems, machine learning, and astrodynamics.

Techniques

Collision avoidance involves tracking external objects, calculating collision probability, and executing avoidance maneuvers. To accomplish each of these tasks, various techniques have been developed and implemented.

Tracking External Objects

To calculate collision probability and perform avoidance maneuvers, the trajectory of external objects must be known. Trajectory data is provided by the Joint Space Operations Center (JSpOC). JSpOC uses a combination conventional radar, phased array radar, ground-based optical sensors, and space-based infrared sensors. The combination of various tracking technologies enables JSpOC to provide reliable trajectory data to spacecraft operators. These tracking technologies are used to calculate both the position and velocity of tracked objects. Using both these parameters, a set of standardized data can be generated to calculate collision probability.

Collision Probability

To determine the necessity of performing an avoidance maneuver, the probability of a tracked object colliding with the spacecraft must be calculated. To calculate the probability of collision, a conjunction data message is sent to the spacecraft operator. A conjunction data message includes the following set of data provided by JSpOC:

• The estimated time that the spacecraft passes by the object (when the distance between the spacecraft and the object is smallest). This is known as the time of closest approach (TCA).
• Covariance matrix of both the spacecraft and the external object, which can be represented by an ellipsoid.
• Relative speed at TCA

The covariance matrix is used as a way to express the uncertainty of measuring the exact position of each object. This uncertainty is the result of potential errors in the process of determining the location of the spacecraft. The ellipsoid representing the covariance matrix of each object contains all the potential positions that the object can be in based on the location tracking data. If the ellipsoids indicated by each object's covariance matrix intersect with each other, then there is a non-zero probability of collision. Specifically, the volume bound by both ellipsoids is the probability of collision. This volume can be calculated using a heuristic that utilizes the following set of assumptions :

• The uncertainty of position associated with the external object is independent of that of the spacecraft
• Predicted velocities during the time of approach are treated as absolute, certain values
• The uncertainty doesn't change through the course of the approach between the external object and the spacecraft (the size of the ellipsoids remains constant during the approach)
• Rectilinear motion is assumed

Alternatively, Monte Carlo simulations are also used to calculate collision probability, but it often requires more computing time than calculating the double integral heuristic described above. However, it is also regarded as being more accurate at calculating collision probability than other methods because it does not rely on the assumption of rectilinear motion nor the assumption of certain velocities. In Monte Carlo simulations, trials are use to calculate the probability of collision. In each trial, the probability of collision is calculated by randomly sampling a specific set of position and velocity parameters. These position and velocity parameters are calculated from the covariance matrix. After all trials have been performed, the average of these probabilities is found, which is equal to the estimated probability of collision.

If the probability of collision is greater than a minimum threshold value set by the spacecraft operator, then a collision avoidance maneuver is performed. If the probability is less than this threshold value, then a collision avoidance maneuver is not performed. Unnecessary maneuvers are avoided because they use up the spacecraft's finite fuel and may affect the functionality of the spacecraft.

Once the collision probability is determined to be above a defined threshold value (accepted collision probability level), then the spacecraft operator performs an appropriate collision avoidance maneuver. The threshold value is determined by a variety of factors including :

• Remaining fuel
• Uncertainty of trajectory dataset
• Size of the spacecraft

Avoidance Maneuvers

Conventional avoidance maneuvers involve changing a satellite's orbit using thrusting. Thrusting is achievable in the cross-track direction, in-track direction, and radial direction. However, the in-track direction is preferred due to its relative simplicity and fuel efficiency. In-track thrusting involves changing speed in the direction tangent to that of the orbit. As a result, the angular momentum of the spacecraft changes and the length of the orbit's semi-major axis is altered. The other thrusting directions affect other parameters of the spacecraft's orbital elements, including perigee, inclination, eccentricity. After the maneuver is performed, the spacecraft can be maneuvered back to its original orbit.

Notable Incidents

On September 2nd, 2019, the ESA's Aeolus Earth observation satellite had to maneuver out of a collision path with a SpaceX Starlink satellite. There was approximately a 1 in 1,000 chance of collision. This incident drew criticism against SpaceX, due to their inaction.

In February of 2009, a US Iridium satellite collided with a non-operational Russian satellite, which created thousands of pieces of space debris. This was also the first incident of two whole spacecraft colliding with each other.

Research

Optimization algorithms are currently in development to optimize fuel consumption of avoidance maneuvers and trajectory change minimization. Thrusting relies on the use of fuel to generate thrust. These methods are often based on machine learning techniques. These machine learning models use a cost function to compare the efficiency of a potential maneuver in a specific collision avoidance scenario to a desired efficiency. Efficiency is determined by fuel constraints.

Alternatives to fuel-based avoidance maneuvers have also been proposed. One such proposed method involves using electrostatic forces for satellites in geostationary orbit. In this method, naturally-accumulating electrons (electrons accumulate as a result of the plasma environment of space) on the spacecraft's body are ejected to change the charge on the surfaces of a spacecraft. The ejection of electrons decreases the magnitude of the negative charge present on the spacecraft's surface. By specifically tuning the charge of a spacecraft, the extent to which it repels other spacecraft can be varied. This method is especially useful for satellite clusters, where conventional thrusting may damage nearby satellites in the cluster.

Research into high accuracy mathematical models is also being performed. SpOCK is a model which takes into account the effects of large gravitational bodies such as the moon and the sun and drag in the thermosphere. Atmospheric effects are thought to be a source of uncertainty that is generally unaccounted for when calculating the collision probability, which is why SpOCK was developed. SpOCK uses Monte Carlo simulations to calculate the probability of collision. It is implemented in C, and supports multicore, parallel processing. This enables efficient computation of the model, even though it uses more parameters to calculate the probability of collision than more traditional methods.