Using Spectral Submanifolds for Nonlinear Periodic Control

Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present computational challenges for direct application to automatic control. While model reduction has seen ubiquitous applications in control, the use of nonlinear model reduction methods in this setting remains difficult. The problem lies in preserving the structure of the nonlinear dynamics in the reduced order model for high-fidelity control. In this work, we leverage recent advances in Spectral Submanifold (SSM) theory to enable model reduction under well-defined assumptions for the purpose of efficiently synthesizing feedback controllers.

Exploring Event Camera-based Odometry for Planetary Robots

Due to their resilience to motion blur and high robustness in low-light and high dynamic range conditions, event cameras are poised to become enabling sensors for vision-based exploration on future Mars helicopter missions. However, existing event-based visual-inertial odometry (VIO) algorithms either suffer from high tracking errors or are brittle, since they cannot cope with significant depth uncertainties caused by an unforeseen loss of tracking or other effects. In this work, we introduce EKLT-VIO, which addresses both limitations by combining a state-of-the-art event-based frontend with a filter-based backend. This makes it both accurate and robust to uncertainties, outperforming event- and frame-based VIO algorithms on challenging benchmarks by 32%. In addition, we demonstrate accurate performance in hover-like conditions (outperforming existing event-based methods) as well as high robustness in newly collected Mars-like and high-dynamic-range sequences, where existing frame-based methods fail. In doing so, we show that event-based VIO is the way forward for vision-based exploration on Mars.