We present Kinodynamic RRT*, an incremental sampling-based approach for asymptotically optimal motion planning for robots with linear differential constraints. Our approach extends RRT*, which was introduced for holonomic robots [8], by using a fixed-final-state-free-final-time controller that exactly and optimally connects any pair of states, where the cost function is expressed as a trade-off between the duration of a trajectory and the expended control effort. Our approach generalizes earlier work on extending RRT* to kinodynamic systems, as it guarantees asymptotic optimality for any system with controllable linear dynamics, in state spaces of any dimension. Our approach can be applied to non-linear dynamics as well by using their first-order Taylor approximations. In addition, we show that for the rich subclass of systems with a nilpotent dynamics matrix, closed-form solutions for optimal trajectories can be derived, which keeps the computational overhead of our algorithm compared to traditional RRT* at a minimum. We demonstrate the potential of our approach by computing asymptotically optimal trajectories in three challenging motion planning scenarios: (i) a planar robot with a 4-D state space and double integrator dynamics, (ii) an aerial vehicle with a 10-D state space and linearized quadrotor dynamics, and (iii) a carlike robot with a 5-D state space and non-linear dynamics.

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Kernel learning is the problem of determining the best kernel (either from a dictionary of fixed kernels, or from a smooth space of kernel representations) for a given task. In this paper, we describe a new approach to kernel learning that establishes connections between the Fourier-analytic representation of kernels arising out of Bochner's theorem and a specific kind of feed-forward network using cosine activations. We analyze the complexity of this space of hypotheses and demonstrate empirically that our approach provides scalable kernel learning superior in quality to prior approaches.

As the complexity of our neural network models grow, so too do the data and computation requirements for successful training. One proposed solution to this problem is training on a distributed network of computational devices, thus distributing the computational and data storage loads. This strategy has already seen some adoption by the likes of Google and other companies. In this paper we propose a new method of distributed, decentralized learning that allows a network of computation nodes to coordinate their training using asynchronous updates over an unreliable network while only having access to a local dataset. This is achieved by taking inspiration from Distributed Averaging Consensus algorithms to coordinate the various nodes. Sharing the internal model instead of the training data allows the original raw data to remain with the computation node. The asynchronous nature and lack of centralized coordination allows this paradigm to function with limited communication requirements. We demonstrate our method on the MNIST, Fashion MNIST, and CIFAR10 datasets. We show that our coordination method allows models to be learned on highly biased datasets, and in the presence of intermittent communication failure.Preprint. Under review.

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