Successive Convexification for Passively-Safe Spacecraft Rendezvous on Near Rectilinear Halo Orbit

TL;DR

The paper tackles safe, fuel-efficient spacecraft rendezvous with the Gateway on a near-rectilinear halo orbit by formulating a stochastic optimal control problem with continuous-time passive-safety and path constraints. A sequential convex programming framework is developed, employing isoperimetric reformulations of path constraints, a backward-reachable-set-based approximation for safety, and a stabilizing feedback controller to bound uncertainty, along with chance constraints for actuation and measurements. The method is validated on a realistic three-phase NRHO rendezvous scenario, using Monte Carlo simulations to confirm continuous-time safety and constraint satisfaction, with fuel usage in line with state-of-the-art approaches. The work provides a practical, robust tool for NRHO operations and contributes broadly to safe, uncertainty-aware trajectory optimization in nonlinear spaceflight dynamics.

Abstract

We present an optimization-based approach for fuel-efficient spacecraft rendezvous to the Gateway, a space station that will be deployed on a near rectilinear halo orbit (NRHO) around the Moon. The approach: i) ensures passive safety and satisfies path constraints at all times, ii) meets the specifications for critical decision points along the trajectory, iii) accounts for uncertainties that are common in real-world operation, such as due to orbital insertion, actuation, and navigation measurement, via chance constraints and utilizes a stabilizing feedback controller to bound the effect of uncertainties. We leverage sequential convex programming (SCP) and isoperimetric reformulation of path constraints, including passive safety, to eliminate the risk of inter-sample constraint violations that is common in existing methods. We demonstrate the proposed approach on a realistic simulation of a rendezvous to the Gateway.

Figures (5)

• Figure 1: Schematic describing the passively-safe rendezvous maneuver of a visiting spacecraft to the Gateway deployed on a NRHO. The NRHO region where rendezvous is initiated, the avoid sets and approach cone, and the sources of uncertainty are shown.
• Figure 2: SCP-based approach for computing the rendezvous maneuver in problem \ref{['stoc-ocp']}. The iterative part of the algorithm is enclosed in the dashed box.
• Figure 3: Monte Carlo simulation of the NRHO rendezvous maneuver. Position trajectories are shown in the Sun Referenced LVLH frame (with coordinates $\bm{r_1,r_2,r_3}$), where blue curves denote the Monte Carlo samples and light blue curves denote the nominal, with dots indicating the discretization nodes. The avoid sets of the three phases are shown in red.
• Figure 4: Free-drift position trajectories of the Monte Carlo samples.
• Figure 5: Monte Carlo simulation of closed-loop control input magnitudes and total fuel consumption across the three-phase rendezvous maneuver. The first three rows show histograms of control input magnitudes for each phase, while the fourth row presents the histogram of total fuel consumption.