Ph.D Thesis

Ph.D StudentDenenberg Elad
SubjectSatellite Cluster Collision Awareness and Avoidance
DepartmentDepartment of Autonomous Systems and Robotics
Supervisor PROF. Pinchas Gurfil


A satellite cluster is a group of satellites operating under distance constraints. Spacecraft formation flying and satellite cluster flight have seen growing interest in the last decade. However, the problem of finding the optimal debris Collision Avoidance Maneuvers (CAM) for a satellite in a cluster has received little attention. The calculation of  CAM for a cluster of spacecraft should be as computationally efficient as possible, because the spacecraft are expected to have a certain degree of autonomy. This work contributes to the process of calculating a CAM on two levels: First, it offers improvements to the computation of conjunction. Second, this work develops new CAM methods.

To assess the probability of collision, the Time of Closest Approach (TCA) between the spacecraft and the debris must first be calculated. This work presents three improvements to the calculation of the TCA.

The first is a Surrogate Based Optimization (SBO) algorithm, using the Alfano Negron Close Approach Software (ANCAS) as the underlying model. ANCAS is a numerical method for calculating the TCA. It is very common, and is implemented on many platforms. SBO is a state-of-the-art optimization technique, utilizing simple functions in lieu of the original ones for which the optimum is sought. Using SBO to find the TCA allows a compromise between calculation speed and accuracy.

The second improvement to the TCA calculation is a generalization of TCA, treating a cloud of debris as a continuous object, and searching for the TCA over initial conditions as well as time. This method accelerates the search.

The third improvement uses the TCA generalization as a model for SBO. Using the third method, a strategy for safe operation of a spacecraft cluster in a debris-rich environment is proposed.

All methods are demonstrated and compared. It is shown that TCA and the generalization thereof are very fast in estimating the TCA, and that the SBO-based

algorithms are somewhat slower, but are highly accurate.

For the calculation of the optimal CAM, this work develops a method for choosing the timing of conducting minimum-fuel avoidance maneuvers, without the need for calculating the possible violation of the cluster inter-satellite  maximal distance limits. In addition, three techniques for finding optimal maneuvers under the constraints of cluster keeping after the critical timing are developed.

The first is an execution of an additional cluster keeping maneuver at the debris time of closest approach.  The second is a global all-cluster maneuver, and the third is a fuel-optimal maneuver, which incorporates the cluster keeping constraints into the calculation of the evasive maneuver. The methods are demonstrated and compared.

The first methodology proves to be the most efficient. The global maneuver guarantees boundedness of the inter-satellite distances, as well as fuel and mass balance. However, it is rather fuel-expensive. The last method proves to be useful at certain timings, and is a compromise between fuel consumption, and the number of maneuvers.