Ian Connerney, Virginia Polytechnic Institute and State University; Alejandro Sosa, Virginia Tech; Kevin Schroeder, Virginia Polytechnic Institute and State University; Jonathan Black, Virginia Polytechnic Institute and State University
Keywords: Trajectory, Optimization, Optimal Control, Collocation, RPO, Collision Avoidance, Rendezvous, Proximity, SSA, Inspection
Abstract:
The capability to perform in-space inspection and characterization of space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints.
This paper investigates and compares solution methods used to find optimal trajectories for a variety of potential inspection maneuvers subject to complex constraints. The two solution methods investigated are a randomness-based adapted A* Search method and a nonlinear optimization method based on direct collocation. Maneuvers studied include transfers between fixed relative position inspection locations and long term minimal thrust station keeping via natural motion trajectories. Estimates for minimum time of flight and total fuel use for each of the proximity maneuvers as obtained from the different solution methods described here are compared.
Constrained optimization can be applied to more complicated trajectory design problems for which analytical solutions are not feasible. Direct collocation, a method used to discretize and solve nonlinear optimal control problems, has seen recent success when used for complex trajectory optimization problems. This method converts the trajectory problem into a nonlinear constrained optimization problem by discretizing the trajectory into N number of nodes representing the state and control variables at each timestep. The objective function, fuel or time-of-flight is minimized at each of the nodal points subject to dynamics constraints by a nonlinear programming solver that provides an optimal solution to the trajectory optimization problem.
Another class of promising solution methods for the rapid generation of optimal relative motion trajectories is motion planning using random sampling or grid search-based algorithms. We describe here an adapted A* Search algorithm that utilizes a newly developed admissible heuristic for minimum delta-V trajectories to bias the path planning search towards optimal minimum fuel trajectories.
We apply both solution methods to generate relative motion trajectories for a free-flying companion vehicle conducting inspection tasks and assess delta-V, time of flight, and computational time impacts with an additional focus on the nonlinear and non-convex constraints that these solution methods can accommodate.
We investigate trajectories utilizing impulsive burns, continuous thrusting, variable thrusting, as well as problems including additional constraints, such as those with complex keep-out-regions and thruster plume limitations that might be required for inspection of a specific target area in a complex environment. The benefits of close and far range inspection maneuvers will be assessed with effects on fuel, time of flight, and relative orbital motion where applicable.
This work is widely applicable and can be expanded to apply to a variety of relative trajectory problems. One such example involves with multiple inspector satellites working together in need of efficient computation of complicated relative motion trajectories for in-space inspection maneuvers.
Date of Conference: September 14-17, 2021
Track: Conjunction/RPO