Pol Mesalles-Ripoll, SpaceNav; Edward Herrick-Reynolds, SpaceNav; Matt Duncan, SpaceNav
Keywords: space situational awareness, risk mitigation maneuver, maneuver pairs, orbit raising, low thrust
Abstract:
With the increasing number of objects in low-Earth orbit, there is a growing need for satellites of any size and thrust capability to be able to perform collision avoidance maneuvers when the likelihood of a collision event exceeds a predetermined threshold. To determine the most optimal risk mitigation maneuver (RMM), SpaceNav creates a maneuver trade space (MTS) that encapsulates all possible maneuver times and durations before the conjunction.
Each grid point in the MTS represents a potential maneuver of a given duration starting at a certain time. An ephemeris is propagated for each possible maneuver and screened against all known active conjunction events in the planning window. These events are defined as distinct close approaches with secondary objects as obtained from processing conjunction data messages. For each propagated maneuver ephemeris and each close encounter, the probability of collision and relative geometry are recalculated by propagating the secondary object to the new time of closest approach.
Once a full trade space grid has been generated, we can proceed with the maneuver optimization process. The point with the lowest collision probability is first found through a global search, followed by a local search using the Nelder–Mead optimization algorithm. In descending relative weighting, the cost function uses miss distance, collision probability and maneuver magnitude to assign a cost to each point in the MTS.
Maneuver times and durations in the MTS can be further limited based on additional constraints, such as burning during eclipse or daylight, as well as geodetic location and local time of day. Eclipse constraints can be of particular importance for satellites with limited power resources as they allow for control over whether the maneuver will take place when the Sun is visible or not. For large MTS time intervals, local time constraints are beneficial if the user wishes to specify burn times when more support staff would be available, such as maneuvering only during business hours at a particular location. To prevent service interruptions to ground users, satellite constellations may want to only maneuver over the oceans or only at certain latitudes and longitudes; this can be accomplished through geodetic location constraints.
In traditional maneuver planning, if no solution is found that mitigates the risk to an acceptable level, the trade space is expanded to consider a larger span of maneuver durations. This expansion process will continue until a satisfactory solution is found or the spacecraft thruster limits are reached. However, for low-thrust space systems, the maximum possible maneuver duration will not always be enough to reduce the collision risk. In this paper, we present an approach where maneuver pairs can be constructed to allow optimization to look for an RMM in which two separate maneuvers would be performed, allowing for a larger change in trajectory while still meeting the spacecraft operational constraints. Maneuver pairing allows for specification of minimum and maximum durations for both maneuvers individually, the ratio between maneuver durations, and the number of revolutions between the maneuvers.
Conjunction events can occur at any time during the life of a satellite. In this paper, we explore how we can extend the same maneuver trade space framework to work with satellites during low-thrust orbit raising; close approaches occuring during this time present an interesting inversion of the standard RMM approach where risk can be mitigated by not performing a section of the nominal ascent maneuver plan. The exact time and duration to stop maneuvering will be determined by the same optimization process outlined above, but in this case it will minimize changes from the nominal plan instead of the RMM duration or Δv while still mitigating the collision risk.
As mentioned, the presented methodology centers around finding an optimal time and duration to stop maneuvering. The optimization can be constrained based on user input such as minimum time before the time of closest approach to modify maneuvers, as well as a maximum acceptable Δv change from the nominal maneuver plan. Planned maneuvers that satisfy the constraints are mapped into a shifted time domain, in which all planed maneuvers occur consecutively. From here, the trade space gets generated with user-defined step sizes and axes of shifted time vs. shifted stop duration, where the same global search and Nelder–Mead optimization algorithm can be applied.
Testing has shown that this novel approach to risk mitigation during orbit raising can reduce the risk with minimum deviations from the nominal maneuver plan. In a test case with an ascent plan of four maneuvers per day for five days and maneuver trade space limits set to 24 hours before a high-interest event with Pc = 8.25e-2, it was found that risk was reduced to Pc < 6e-8 by trimming the original maneuver plan by just 10 minutes. This demonstrates the capability of mitigating collision risk during ascent through small changes to the original maneuver plan.
Date of Conference: September 19-22, 2023
Track: Conjunction/RPO