Guidance and Control Networks with Periodic Activation Functions

TL;DR

This work investigates replacing traditional hidden-layer activations in Guidance & Control Networks (G&CNETs) with periodic sine activations (SIREN) to improve learning from behavioral cloning of optimal trajectories. By enforcing $ω_0=30$, careful input scaling to $[-1,1]$, and specialized weight initializations, SIREN-based G&CNETs train faster and achieve lower training losses than ReLU/Softplus baselines across three challenging control problems (drone racing, asteroid landing, interplanetary transfer). The results show that SIREN networks often yield the best final-state accuracy and can attain comparable performance with far fewer parameters, suggesting a significant efficiency advantage. The findings point to a mechanism where periodic activations exploit oscillatory structure in the control and state spaces, with practical implications for deploying accurate, data-efficient guidance policies in aerospace systems.

Abstract

Inspired by the versatility of sinusoidal representation networks (SIRENs), we present a modified Guidance & Control Networks (G&CNETs) variant using periodic activation functions in the hidden layers. We demonstrate that the resulting G&CNETs train faster and achieve a lower overall training error on three different control scenarios on which G&CNETs have been tested previously. A preliminary analysis is presented in an attempt to explain the superior performance of the SIREN architecture for the particular types of tasks that G&CNETs excel on.

Figures (6)

• Figure 1: Drone racing: Training loss for different control policies and hidden layer activation functions.
• Figure 2: Asteroid landing: Final position and velocity errors over 500 initial conditions from validation dataset.
• Figure 3: Interplanetary transfer: Final position and velocity errors over 500 initial conditions from validation dataset.
• Figure 4: Coordinate frames (Body x-axis points to the front of the drone) origer2023guidance.
• Figure 5: Bundle of 2,000 optimal trajectories from training dataset origer2024closing. Landing on Psyche shown in rotating frame $\mathcal{R}$. Axis unit is km.