Photons x Force: Differentiable Radiation Pressure Modeling

TL;DR

This work tackles the challenge of efficiently and differentiably modeling solar radiation pressure (SRP) for spacecraft across large design spaces. It combines a parallel Monte Carlo SRP simulator, a neural proxy that makes SRP forces differentiable and fast, and an adjoint-based optimization framework to solve inverse SRP design problems. The approach yields accurate SRP force mappings, fast design-space queries, and robust results across tasks such as waypoint interception, attitude control, formation flight, and inference of geometry from trajectory data, highlighting potential gains in automated spacecraft design and space situational awareness. The methodology promises practical impact by enabling large-scale, differentiable, SRP-aware optimization that can inform materials, geometry, and operational decisions in space missions.

Abstract

We propose a system to optimize parametric designs subject to radiation pressure, \ie the effect of light on the motion of objects. This is most relevant in the design of spacecraft, where radiation pressure presents the dominant non-conservative forcing mechanism, which is the case beyond approximately 800 km altitude. Despite its importance, the high computational cost of high-fidelity radiation pressure modeling has limited its use in large-scale spacecraft design, optimization, and space situational awareness applications. We enable this by offering three innovations in the simulation, in representation and in optimization: First, a practical computer graphics-inspired Monte-Carlo (MC) simulation of radiation pressure. The simulation is highly parallel, uses importance sampling and next-event estimation to reduce variance and allows simulating an entire family of designs instead of a single spacecraft as in previous work. Second, we introduce neural networks as a representation of forces from design parameters. This neural proxy model, learned from simulations, is inherently differentiable and can query forces orders of magnitude faster than a full MC simulation. Third, and finally, we demonstrate optimizing inverse radiation pressure designs, such as finding geometry, material or operation parameters that minimizes travel time, maximizes proximity given a desired end-point, minimize thruster fuel, trains mission control policies or allocated compute budget in extraterrestrial compute.

Figures (16)

• Figure 1: Main flow of our system: The input is a design space of spacecraft, shown here with different panel configurations as well as a design goal symbolized as a star. In the first step, we simulate and store the force resulting from many directions of illumination under many different designs. In the second step, a neural model of light direction and design parameters is learned which predicts force. The final part is an optimization step that computes orbits of the given spacecraft (shown as spirals) using the forces of the neural model under a certain radiation, adjusting the design parameters so as to arrive at the goal (star). The output are these optimal design parameters.
• Figure 2: Radiation pressure converting light to force: Radiation arrives from one direction $\TextOrMath{$$\xspace}{\bm\upomega}_\mathrm{in}$$\bm\upomega$_in and is reflected to another random direction $\TextOrMath{$$\xspace}{\bm\upomega}_\mathrm{out}$$\bm\upomega$_out at a position $\mathbf x$ x, with a probability that depends on the material and the incoming direction. The resulting force $F$F is the negated weighted half-vector of these.
• Figure 3: Evaluation dependency. Edges are works-if relationships. Nodes are evaluation steps. Grey components are parts of the system, but we trust they were verified elsewhere.
• Figure 4: Force maps for different spacecraft geometry and materials. In a force map, each pixel corresponds to one light direction in the spacecraft-fixed latitude-longitude (as defined in montenbruck2015gnssbhattarai2019demonstrating) and the color corresponds to the resulting 3D force, mapped from signed 3D to unsigned RGB. For each, we show four different force maps (top to bottom): First, the neural proxy used for design. We use no design parameters for this visualization. Second, the immediate simulator output. Third and fourth, the direct, resp. indirect force, split and tone-mapped separately. We see that force maps depend on geometry and that the neural proxy captures the function. Convergence plots of the neural proxy are show in the neural row for each column, where blue is train and orange is test. The ground truth of the NN is our simulation, while for simulation, the ground truth is unknown.
• Figure 5: Visualization of sampling a one-dimensional design space of changing solar array width (from left to right). At a single pixel, the radiance is a random one out of many designs. When integrating over a thousand samples, we see the variation in a Schrödinger-style image where all designs are present at the same time. We train a neural network from that information (more precisely, from force, not radiance shown here for visualization) that can then be queried at random-access designs. The third and fourth row show the positional and rotational force map of the minimal solar array width (left) and the maximal one (right).