Trajectory Design and Guidance for Far-range Proximity Operations of Active Debris Removal Missions with Angles-only Navigation and Safety Considerations

Abstract

Observability of the target, safety, and robustness are often recognized as critical factors in ensuring successful far-range proximity operations. The application of angles-only (AO) navigation for proximity operations is often met with hesitancy due to its inherent limitations in determining range, leading to issues in target observability and consequently, mission safety. However, this form of navigation remains highly appealing due to its low cost. This work employs Particle Swarm Optimization (PSO) and Reinforcement Learning (RL) for the design and guidance of such far-range trajectories, assuring observability, safety and robustness under angles-only navigation. Firstly, PSO is used to design a nominal trajectory that is observable, robust and safe. Subsequently, Proximal Policy Optimization (PPO), a cutting-edge RL algorithm, is utilized to develop a guidance controller capable of maintaining observability while steering the spacecraft from an initial perturbed state to a target state. The fidelity of the guidance controller is then tested in a Monte-Carlo (MC) manner by varying the initial relative spacecraft state. The observability of the nominal trajectory and the perturbed trajectories with guidance are validated using an Extended Kalman Filter (EKF). The perturbed trajectories are also shown to adhere to the safety requirements satisfied by the nominal trajectory. Results demonstrate that the trained controller successfully determines maneuvers that maintain observability and safety and reaches the target end state.

Figures (13)

• Figure 1: Nominal $\Delta \overline{v}$ metric: implementation of nominal $\Delta v$s to reach the target.
• Figure 2: Observability metric: $\bm{\bar{r}}_1(t),\bm{\bar{r}}_2(t),\bm{\bar{r}}_3(t),\bm{\bar{r}}_{(n-1)}(t)$ are the maneuvred nominal trajectory position vectors, $\bm{\bar{r}}_{1,bal}(t),\bm{\bar{r}}_{2,bal}(t),\bm{\bar{r}}_{3,bal}(t),\bm{\bar{r}}_{(n-1),bal}(t)$ are the ballistic trajectory position vectors.
• Figure 3: Safety penalty function.
• Figure 4: Safety metric: The point-wise safety is calculated on the trajectory (orange), and passive safety is calculated for the resultant ballistic trajectory (dotted blue) if an impulse is missed.
• Figure 5: Reinforcement learning guidance.