Non-linear model predictive control (nMPC) is a powerful approach to control complex robots (such as humanoids, quadrupeds, or unmanned aerial manipulators (UAMs)) as it brings important advantages over other existing techniques. The full-body dynamics, along with the prediction capability of the optimal control problem (OCP) solved at the core of the controller, allows to actuate the robot in line with its dynamics. This fact enhances the robot capabilities and allows, e.g., to perform intricate maneuvers at high dynamics while optimizing the amount of energy used. Despite the many similarities between humanoids or quadrupeds and UAMs, full-body torque-level nMPC has rarely been applied to UAMs. This paper provides a thorough description of how to use such techniques in the field of aerial manipulation. We give a detailed explanation of the different parts involved in the OCP, from the UAM dynamical model to the residuals in the cost function. We develop and compare three different nMPC controllers: Weighted MPC, Rail MPC, and Carrot MPC, which differ on the structure of their OCPs and on how these are updated at every time step. To validate the proposed framework, we present a wide variety of simulated case studies. First, we evaluate the trajectory generation problem, i.e., optimal control problems solved offline, involving different kinds of motions (e.g., aggressive maneuvers or contact locomotion) for different types of UAMs. Then, we assess the performance of the three nMPC controllers, i.e., closed-loop controllers solved online, through a variety of realistic simulations. For the benefit of the community, we have made available the source code related to this work.

Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important applications such as reservoir modeling and turbulence prediction. We demonstrate that for such PDEs, the spectral bias towards low-frequency components presents a significant challenge for existing neural operators. To address this challenge, we propose a hierarchical attention neural operator (HANO) inspired by the hierarchical matrix approach. HANO features a scale-adaptive interaction range and self-attentions over a hierarchy of levels, enabling nested feature computation with controllable linear cost and encoding/decoding of multiscale solution space. We also incorporate an empirical $H^1$ loss function to enhance the learning of high-frequency components. Our numerical experiments demonstrate that HANO outperforms state-of-the-art (SOTA) methods for representative multiscale problems.

This paper investigates the problem of efficient constrained global optimization of hybrid models that are a composition of a known white-box function and an expensive multi-output black-box function subject to noisy observations, which often arises in real-world science and engineering applications. We propose a novel method, Constrained Upper Quantile Bound (CUQB), to solve such problems that directly exploits the composite structure of the objective and constraint functions that we show leads substantially improved sampling efficiency. CUQB is a conceptually simple, deterministic approach that avoid constraint approximations used by previous methods. Although the CUQB acquisition function is not available in closed form, we propose a novel differentiable sample average approximation that enables it to be efficiently maximized. We further derive bounds on the cumulative regret and constraint violation under a non-parametric Bayesian representation of the black-box function. Since these bounds depend sublinearly on the number of iterations under some regularity assumptions, we establis bounds on the convergence rate to the optimal solution of the original constrained problem. In contrast to most existing methods, CUQB further incorporates a simple infeasibility detection scheme, which we prove triggers in a finite number of iterations when the original problem is infeasible (with high probability given the Bayesian model). Numerical experiments on several test problems, including environmental model calibration and real-time optimization of a reactor system, show that CUQB significantly outperforms traditional Bayesian optimization in both constrained and unconstrained cases. Furthermore, compared to other state-of-the-art methods that exploit composite structure, CUQB achieves competitive empirical performance while also providing substantially improved theoretical guarantees.

Deep learning (DL) approaches are being increasingly used for time-series forecasting, with many efforts devoted to designing complex DL models. Recent studies have shown that the DL success is often attributed to effective data representations, fostering the fields of feature engineering and representation learning. However, automated approaches for feature learning are typically limited with respect to incorporating prior knowledge, identifying interactions among variables, and choosing evaluation metrics to ensure that the models are reliable. To improve on these limitations, this paper contributes a novel visual analytics framework, namely TimeTuner, designed to help analysts understand how model behaviors are associated with localized correlations, stationarity, and granularity of time-series representations. The system mainly consists of the following two-stage technique: We first leverage counterfactual explanations to connect the relationships among time-series representations, multivariate features and model predictions. Next, we design multiple coordinated views including a partition-based correlation matrix and juxtaposed bivariate stripes, and provide a set of interactions that allow users to step into the transformation selection process, navigate through the feature space, and reason the model performance. We instantiate TimeTuner with two transformation methods of smoothing and sampling, and demonstrate its applicability on real-world time-series forecasting of univariate sunspots and multivariate air pollutants. Feedback from domain experts indicates that our system can help characterize time-series representations and guide the feature engineering processes.

State-of-the-art neural networks require extreme computational power to train. It is therefore natural to wonder whether they are optimally trained. Here we apply a recent advancement in stochastic thermodynamics which allows bounding the speed at which one can go from the initial weight distribution to the final distribution of the fully trained network, based on the ratio of their Wasserstein-2 distance and the entropy production rate of the dynamical process connecting them. Considering both gradient-flow and Langevin training dynamics, we provide analytical expressions for these speed limits for linear and linearizable neural networks e.g. Neural Tangent Kernel (NTK). Remarkably, given some plausible scaling assumptions on the NTK spectra and spectral decomposition of the labels -- learning is optimal in a scaling sense. Our results are consistent with small-scale experiments with Convolutional Neural Networks (CNNs) and Fully Connected Neural networks (FCNs) on CIFAR-10, showing a short highly non-optimal regime followed by a longer optimal regime.

This paper introduces Borinot, an open-source aerial robotic platform designed to conduct research on hybrid agile locomotion and manipulation using flight and contacts. This platform features an agile and powerful hexarotor that can be outfitted with torque-actuated limbs of diverse architecture, allowing for whole-body dynamic control. As a result, Borinot can perform agile tasks such as aggressive or acrobatic maneuvers with the participation of the whole-body dynamics. The limbs attached to Borinot can be utilized in various ways; during contact, they can be used as legs to create contact-based locomotion, or as arms to manipulate objects. In free flight, they can be used as tails to contribute to dynamics, mimicking the movements of many animals. This allows for any hybridization of these dynamic modes, making Borinot an ideal open-source platform for research on hybrid aerial-contact agile motion. To demonstrate the key capabilities of Borinot in terms of agility with hybrid motion modes, we have fitted a planar 2DoF limb and implemented a whole-body torque-level model-predictive-control. The result is a capable and adaptable platform that, we believe, opens up new avenues of research in the field of agile robotics. Interesting links\footnote{Documentation: \url{www.iri.upc.edu/borinot}}\footnote{Video: \url{https://youtu.be/Ob7IIVB6P_A}}.

This extended abstract provides a short introduction on our recently developed perception-based controller for quadrupedal locomotion. Compared to our previous approach based on Visual Foothold Adaptation (VFA) and Model Predictive Control (MPC), our new framework combines a fast approximation of the safe foothold regions based on Neural Network regression, followed by a convex decomposition routine in order to generate safe landing areas where the controller can freely optimize the footholds location. The aforementioned framework, which combines prediction, convex decomposition, and MPC solution, is tested in simulation on our 140kg hydraulic quadruped robot (HyQReal).

Operating in the near-vicinity of marine energy devices poses significant challenges to the control of underwater vehicles, predominantly due to the presence of large magnitude wave disturbances causing hazardous state perturbations. Approaches to tackle this problem have varied, but one promising solution is to adopt predictive control methods. Given the predictable nature of ocean waves, the potential exists to incorporate disturbance estimations directly within the plant model; this requires inclusion of a wave predictor to provide online preview information. To this end, this paper presents a Nonlinear Model Predictive Controller with an integrated Deterministic Sea Wave Predictor for trajectory tracking of underwater vehicles. State information is obtained through an Extended Kalman Filter, forming a complete closed-loop strategy and facilitating online wave load estimations. The strategy is compared to a similar feed-forward disturbance mitigation scheme, showing mean performance improvements of 51% in positional error and 44.5% in attitude error. The preliminary results presented here provide strong evidence of the proposed method's high potential to effectively mitigate disturbances, facilitating accurate tracking performance even in the presence of high wave loading.

We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized emergence of macroscopic patterns from microscopic interactions between self-propelled particles can be widely observed nature. Although hydrodynamic theories help us better understand the physical basis of this phenomenon, identifying a sufficient set of local interactions that shape, regulate, and sustain self-organized structures in active particle systems remains challenging. We investigate a classic hydrodynamic model of self-propelled particles that produces a wide variety of patterns, like asters and moving density bands. Our data-driven analysis shows that propagating bands are formed by local alignment interactions driven by density gradients, while steady-state asters are shaped by a mechanism of splay-induced negative compressibility arising from strong particle interactions. Our method also reveals analogous physical principles of pattern formation in a system where the speed of the particle is influenced by local density. This demonstrates the ability of our method to reveal physical commonalities across models. The physical mechanisms inferred from the data are in excellent agreement with analytical scaling arguments and experimental observations.

The processing of information is an indispensable property of living systems realized by networks of active processes with enormous complexity. They have inspired many variants of modern machine learning one of them being reservoir computing, in which stimulating a network of nodes with fading memory enables computations and complex predictions. Reservoirs are implemented on computer hardware, but also on unconventional physical substrates such as mechanical oscillators, spins, or bacteria often summarized as physical reservoir computing. Here we demonstrate physical reservoir computing with a synthetic active microparticle system that self-organizes from an active and passive component into inherently noisy nonlinear dynamical units. The self-organization and dynamical response of the unit is the result of a delayed propulsion of the microswimmer to a passive target. A reservoir of such units with a self-coupling via the delayed response can perform predictive tasks despite the strong noise resulting from Brownian motion of the microswimmers. To achieve efficient noise suppression, we introduce a special architecture that uses historical reservoir states for output. Our results pave the way for the study of information processing in synthetic self-organized active particle systems.