We introduce the Random Oscillators Network (RON), a physically-inspired recurrent model derived from a network of heterogeneous oscillators. Unlike traditional recurrent neural networks, RON keeps the connections between oscillators untrained by leveraging on smart random initialisations, leading to exceptional computational efficiency. A rigorous theoretical analysis finds the necessary and sufficient conditions for the stability of RON, highlighting the natural tendency of RON to lie at the edge of stability, a regime of configurations offering particularly powerful and expressive models. Through an extensive empirical evaluation on several benchmarks, we show four main advantages of RON. 1) RON shows excellent long-term memory and sequence classification ability, outperforming other randomised approaches. 2) RON outperforms fully-trained recurrent models and state-of-the-art randomised models in chaotic time series forecasting. 3) RON provides expressive internal representations even in a small parametrisation regime making it amenable to be deployed on low-powered devices and at the edge. 4) RON is up to two orders of magnitude faster than fully-trained models.

Even though a variety of methods have been proposed in the literature, efficient and effective latent-space control (i.e., control in a learned low-dimensional space) of physical systems remains an open challenge. We argue that a promising avenue is to leverage powerful and well-understood closed-form strategies from control theory literature in combination with learned dynamics, such as potential-energy shaping. We identify three fundamental shortcomings in existing latent-space models that have so far prevented this powerful combination: (i) they lack the mathematical structure of a physical system, (ii) they do not inherently conserve the stability properties of the real systems, (iii) these methods do not have an invertible mapping between input and latent-space forcing. This work proposes a novel Coupled Oscillator Network (CON) model that simultaneously tackles all these issues. More specifically, (i) we show analytically that CON is a Lagrangian system - i.e., it possesses well-defined potential and kinetic energy terms. Then, (ii) we provide formal proof of global Input-to-State stability using Lyapunov arguments. Moving to the experimental side, we demonstrate that CON reaches SoA performance when learning complex nonlinear dynamics of mechanical systems directly from images. An additional methodological innovation contributing to achieving this third goal is an approximated closed-form solution for efficient integration of network dynamics, which eases efficient training. We tackle (iii) by approximating the forcing-to-input mapping with a decoder that is trained to reconstruct the input based on the encoded latent space force. Finally, we leverage these three properties and show that they enable latent-space control. We use an integral-saturated PID with potential force compensation and demonstrate high-quality performance on a soft robot using raw pixels as the only feedback information.

For asymptotically optimal sampling-based path planners such as RRT*, path quality improves as the number of samples added to the motion tree increases. However, each additional sample requires a nearest-neighbor search. Calculating state transition costs can be particularly difficult in cases with complex dynamics such as aerial vehicles in non-isotropic cost fields like wind. Computationally costly nearest neighbor searches increase the time required to add new samples to the search tree, thereby reducing the likelihood of finding low-cost paths in a given computational time. In this paper, we propose the use of a lightweight neural network to approximate nearest neighbor cost calculations. The network approach uses a low-dimensional encoding of the cost space along with a start and goal query pair and returns an estimate of the path cost that can be used for nearest neighbor and path validity estimation. We demonstrate our method for a Dubins airplane model in a 3D wind field and show that the network method achieves equivalent path lengths as an existing iterative solver 32% faster and, when given the same search time, up to 10.8% shorter.