The one constant in real-world perception and planning is uncertainty. Robots perceive the world indirectly through imperfect sensors like cameras and LIDAR, and plan using imperfect models of their own dynamics. Machine learning models are constrained by limited training data and imperfect model classes. Robust intelligent systems must be able to accurate estimate their own uncertainty—they must know what they do not know.
Accurately quantifying uncertainty in real time for complex continuous systems is difficult. In this body of work we show that the computationally simple framework of generalized kernel estimation demonstrates good empirical performance and has strong theoretical guarantees. We store a sequence of observed input-output pairs for a system like a controller, mapping system, state estimator, or planner. At runtime, given a new input, we build a model of the distribution of outputs corresponding to similar inputs. By considering a restricted class of output distributions (the exponential family), this inference problem can be solved in time logarithmic in the number of training examples, allowing us to scale to very large data sets.
We show this technique can be used to estimate the covariance of the velocity estimated from laser scan-matching and VIO systems, leading to more robust and accurate state estimates; the distribution over reprojection error in a stereo odometry systems, improving the accuracy of feature tracking; and the probability a motion plan will result in collision in an unknown map, leading to faster navigation. We also show that this learning can be done without ground truth, i.e. without knowing the true output corresponding to each training input, and that we can combine this technique with recent advances in deep learning to model more complex phenomena. For example, we can dynamically decide if a frame in a video stream is likely to lead to poor tracking, perhaps because of the presence of moving objects.