Given a stream of multimodal sensory data, an autonomous robot must continuously refine its understanding of itself and its environment as it makes decisions on how to act to achieve a goal. These are difficult problems that roboticists have attacked using classical tools from mechanics and controls and, more recently, machine learning. However, classical methods and machine learning algorithms are often seen to be at odds, and researchers continue to debate the merits of engineering vs. learning. 

A recurring theme in this talk will be that prior knowledge and domain insights can make learning and inference easier. I will discuss several fundamental robotics problems including continuous-time motion planning, localization, and mapping from a unified probabilistic inference perspective. I will show how models from statistical machine learning like Gaussian Processes can be tightly integrated with insights from engineering expressed as differential equations to solve these problems efficiently. Finally, I will demonstrate the effectiveness of these algorithms on several existent robotics platforms.

In this talk, I will present a new family of computational approaches for learning dynamical system models with a particular focus on problems relevant to robotics. The key insight is that low-order moments of observed data often possess structure that can be revealed by powerful spectral decomposition methods, and, from this structure, model parameters can be directly recovered. Based on this insight, we design highly effective algorithms for learning popular parametric models like Kalman Filters and Hidden Markov Models, as well as an expressive new class of nonparametric models via reproducing kernels. Unlike maximum likelihood-based approaches, these new learning algorithms are statistically consistent, computationally efficient, and easy to implement using established matrix-algebra techniques. The result is a powerful framework for learning dynamical system models with state-of-the-art performance on video, robotics, and biological modeling problems.