Advanced Techniques for Trajectory Design and Optimization

Traditional multi-body mission design and trajectory optimization processes are notorious for their laborious and time-intensive nature, requiring weeks or even months to generate a single reference trajectory for these multifaceted missions. This underscores the critical necessity for novel techniques and tools capable of expediting and enhancing the trajectory design and optimization process. Not only is the design space infinite, system uncertainties in this complex and sensitive dynamical environment are not yet well understood. For this phase I effort, Navigation Uncertainty ANalysis in the Cislunar Environment (NUANCE) aims to partner with Purdue University to analyze spacecraft system uncertainties in a multi-body dynamical environment through the evaluation of two relevant test cases. This effort proposes to introduce Gaussian uncertainty by employing sigma sampling techniques to the initial conditions of deterministically-optimized transfer scenarios. By propagating the trajectories from these sampled points using the originally optimized maneuver values (∆V, transfer time), this study aims to observe the position uncertainty over time during orbit transfers in cislunar space. Taking another approach of analyzing the sigma-like points, maneuver errors will be assessed by re-optimizing the transfers from these sampled points and observing the spread in ∆V and transfer time. Test case options include transfers along unstable manifolds transferring to and from periodic or quasi-periodic orbits and utilizing “free” ∆V transfers between orbits around L1 and L3 via “Cycler” orbits, which offer a unique case to compare propagated sigma-point trajectories. Target markets include NASA missions beyond the Earth, small commercial spacecraft companies and universities that would benefit from lower propellant requirements and increased navigation/maneuver knowledge, and the military organizations interested in cislunar space operations.

This is the overarching goal of the proposed effort is to inform the trajectory design and optimization process by providing insight on how ∆V and time uncertainties respond to navigation and maneuver errors. Choice of novel test cases and exploring of the use of invariant manifolds to/from Quasi-Periodic Orbits (QPOs) and Cycler orbits will also provide pioneering solutions in this design space, especially when determining first guess trajectories for QPOs with innovative techniques. In addition to Purdue’s cutting-edge deterministic trajectory design research, the results of NUANCE will give valuable information about the errors associated with specific areas of the design trade space when choosing initial conditions of trajectory design optimization problems. A primary focus of NUANCE is to examine navigation and maneuver errors through Gaussian uncertainty in relevant trajectory optimization test cases. The uncertainty characterization aspects of NUANCE will provide insight into “better” or “worse” choices of initial guesses based on the observed spread of ∆V and timing uncertainty in the test cases. The investigators are familiar with the existing GMAT, CSALT, EMTG, MONTE, and OTIS tools, and thus can integrate the newly developed techniques for NASA needs as an add-on feature to the appropriate tool. A stability or sensitivity visualization feature, trajectory optimization add-on, system uncertainty analysis function, or (Phase II/III) stochastic control aspect could fit into one or more of these tool suites. Along with traditional beyond-Earth NASA missions, the proposed work will benefit the commercial market, universities, as well as the military. Universities and smaller commercial companies, typically interested in cubesat and smallsat missions, can greatly benefit from NUANCE technology due to the anticipated increased efficiency in spacecraft propellant use and creative mission trajectory designs. Leveraging this work’s advanced analysis of complex dynamical features and understanding maneuver possibilities, these companies and groups may be able to deploy less precise yet cost-effective instruments and minimize propellant requirements by implementing low- (or no-) ∆V solutions. Since the Air Force Research Laboratory’s Space Vehicles Directorate co-published a “primer” on cislunar space in 2021, there has been a noticeable increase in the military’s interest in cislunar space. The 19th Space Defense Squadron (19 SDS) was established to lead space domain awareness in cislunar and extra-geosynchronous areas. Knowledge of system uncertainties and advanced mission design techniques in the dynamical space that serves as the focus for the establishment of the 19 SDS would be vital to inform future military space programs and missions in this space. Other likely end-users include several of the US Space Force Deltas, including Delta 2 (Space Domain Awareness), Delta 5 (Command and Control), and Delta 7 (Intelligence, Surveillance, and Reconnaissance). In supporting the Space Deltas, the customer is anticipated to be the Space Systems Command program offices, Space Development Agency, or Space Rapid Capabilities Office. These agencies and offices oversee procurement of technologies used by the Space Deltas.

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