Optimal Experimental Learning and Infinite Linear Embeddings

Abraham, Ian

doi:https://doi.org/10.21985/n2-b2gf-9b90

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Optimal Experimental Learning and Infinite Linear Embeddings

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In the current state of robotics, the systems we create are heavily reliant on our consistent guidance, programming of tasks, and oracle information that allow them to operate in the world that we inhabit. What happens to our robotic systems when we are unable to perform as an oracle, creating the absence of information about what is known and unknown to our robots? Can we expect our robotic systems to operate in our world? And what are the necessary requirements for them to explore and navigate the increasing complexities that we face in an unknown world? In this thesis, I argue that robotic systems are required to have the ability to intentionally learn, model, and explore what is unknown about the world for them to be less reliant on the oracle information that we as the developers provide. This thesis establishes the stated problems as one of active robot learning and decision making. Through the use of existing methods and tools from hybrid control theory, this thesis first looks to enhance the capabilities of the current approaches for robot learning and lays the groundwork for subsequent theoretical advancements for learning and control. Active learning through automated experimental design is then motivated as an approach that enables robotic systems to develop actions that intentionally seek out informative measurements for learning what is unknown. Coupled with methods from ergodicity and ergodic exploration, active learning is shown to be a promising approach for modeling complex and spatially sparse environments using only rudimentary contact sensing. These results are extended to the case of safe exploration and active learning in dynamic state-spaces where robot safety and the quality of informative measurements are provably balanced through Lyapunov attractiveness and hybrid control theoretic analysis. Last, I argue that we should not only care about active learning, but also how we model and represent what robotic systems are learning. The class of infinite linear embeddings is presented as a candidate model that simplifies and improves the control and active learning capabilities of robotic systems. Through simulated and experimental application, I illustrate the potential of the presented approaches for pushing the boundaries of robotic systems towards being more capable, self-sufficient, and curious systems that intentionally learns the unknown and complex nature of interacting in our world.

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