Model-Based Control Using Koopman Operators

This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting model-based control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis. Simulated results show that with increasing complexity in the choice of the basis functions, a closed-loop controller is able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore, the specification of the basis function are shown to be of importance when generating a Koopman operator for specific robotic systems. Experimental results with the Sphero SPRK robot explore the utility of the Koopman operator in a reduced state representation setting where increased complexity in the basis function improve open- and closed-loop controller performance in various terrains, including sand.Comment: 8 page

Safety-Critical Ergodic Exploration in Cluttered Environments via Control Barrier Functions

In this paper, we address the problem of safe trajectory planning for autonomous search and exploration in constrained, cluttered environments. Guaranteeing safe navigation is a challenging problem that has garnered significant attention. This work contributes a method that generates guaranteed safety-critical search trajectories in a cluttered environment. Our approach integrates safety-critical constraints using discrete control barrier functions (DCBFs) with ergodic trajectory optimization to enable safe exploration. Ergodic trajectory optimization plans continuous exploratory trajectories that guarantee full coverage of a space. We demonstrate through simulated and experimental results on a drone that our approach is able to generate trajectories that enable safe and effective exploration. Furthermore, we show the efficacy of our approach for safe exploration of real-world single- and multi- drone platforms

DEUX: Active Exploration for Learning Unsupervised Depth Perception

Depth perception models are typically trained on non-interactive datasets with predefined camera trajectories. However, this often introduces systematic biases into the learning process correlated to specific camera paths chosen during data acquisition. In this paper, we investigate the role of how data is collected for learning depth completion, from a robot navigation perspective, by leveraging 3D interactive environments. First, we evaluate four depth completion models trained on data collected using conventional navigation techniques. Our key insight is that existing exploration paradigms do not necessarily provide task-specific data points to achieve competent unsupervised depth completion learning. We then find that data collected with respect to photometric reconstruction has a direct positive influence on model performance. As a result, we develop an active, task-informed, depth uncertainty-based motion planning approach for learning depth completion, which we call DEpth Uncertainty-guided eXploration (DEUX). Training with data collected by our approach improves depth completion by an average greater than 18% across four depth completion models compared to existing exploration methods on the MP3D test set. We show that our approach further improves zero-shot generalization, while offering new insights into integrating robot learning-based depth estimation