## Session

Technical Session XI: Orbital Manuvering

## Abstract

The deviations in the injection orbital parameters, resulting from launcher dispersions, need to be corrected through a set of acquisition maneuvers to achieve the desired nominal parameters. When multiple satellites are injected into a single orbital plane, as a part of constellation establishment, they have to positioned in the plane with appropriate semi-major axis ‘a’ and mean anomaly ‘M’. In this paper, three strategies are studied for achieving orbit acquisition. The first strategy is by deriving an analogy to the Linear Quadratic Regulator (LQR). The state dynamics and the control law are of the form X&= AX + BU and U = −KX . The feedback gain K is calculated by minimizing the cost function. Under this strategy the thrust (N) and velocity increment ( ÄV ) are functions of time and only the matrix K needs to be up-linked. Any revision in the current or the target states, will then lead to a simple re-calculation of K and up-linking them. The second strategy assumes that ÄV is same for each maneuver and calculates the number of maneuvers and the ÄV required for each maneuver. If the maneuvers are stopped for reasons like orbit assessment, and thruster performance evaluation, the strategy can be restarted easily without having any penalty on the overall ÄV. Besides these two strategies, a third strategy based on the application of Fuzzy Modified Potential Function is also studied for autonomous orbit acquisition with constraints in the path. By adding Fuzzy logic to the potential function it is shown that, maneuvers can be changed gradually ahead of the constraints. Onboard implementation related aspects are also briefly addressed for all the strategies.

Suitable Strategies for In-plane Orbit Acquisition using Micro-thrusters

The deviations in the injection orbital parameters, resulting from launcher dispersions, need to be corrected through a set of acquisition maneuvers to achieve the desired nominal parameters. When multiple satellites are injected into a single orbital plane, as a part of constellation establishment, they have to positioned in the plane with appropriate semi-major axis ‘a’ and mean anomaly ‘M’. In this paper, three strategies are studied for achieving orbit acquisition. The first strategy is by deriving an analogy to the Linear Quadratic Regulator (LQR). The state dynamics and the control law are of the form X&= AX + BU and U = −KX . The feedback gain K is calculated by minimizing the cost function. Under this strategy the thrust (N) and velocity increment ( ÄV ) are functions of time and only the matrix K needs to be up-linked. Any revision in the current or the target states, will then lead to a simple re-calculation of K and up-linking them. The second strategy assumes that ÄV is same for each maneuver and calculates the number of maneuvers and the ÄV required for each maneuver. If the maneuvers are stopped for reasons like orbit assessment, and thruster performance evaluation, the strategy can be restarted easily without having any penalty on the overall ÄV. Besides these two strategies, a third strategy based on the application of Fuzzy Modified Potential Function is also studied for autonomous orbit acquisition with constraints in the path. By adding Fuzzy logic to the potential function it is shown that, maneuvers can be changed gradually ahead of the constraints. Onboard implementation related aspects are also briefly addressed for all the strategies.