Multi-objective optimization problems are ubiquitous in robotics, e.g., the optimization of a robot manipulation task requires a joint consideration of grasp pose configurations, collisions and joint limits. While some demands can be easily hand-designed, e.g., the smoothness of a trajectory, several task-specific objectives need to be learned from data. This work introduces a method for learning data-driven SE(3) cost functions as diffusion models. Diffusion models can represent highly-expressive multimodal distributions and exhibit proper gradients over the entire space due to their score-matching training objective. Learning costs as diffusion models allows their seamless integration with other costs into a single differentiable objective function, enabling joint gradient-based motion optimization. In this work, we focus on learning SE(3) diffusion models for 6DoF grasping, giving rise to a novel framework for joint grasp and motion optimization without needing to decouple grasp selection from trajectory generation. We evaluate the representation power of our SE(3) diffusion models w.r.t. classical generative models, and we showcase the superior performance of our proposed optimization framework in a series of simulated and real-world robotic manipulation tasks against representative baselines.
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Tracking and following objects of interest is critical to several robotics use cases, ranging from industrial automation to logistics and warehousing, to healthcare and security. In this paper, we present a robotic system to detect, track, and follow any object in real-time. Our approach, dubbed ``follow anything'' (FAn), is an open-vocabulary and multimodal model -- it is not restricted to concepts seen at training time and can be applied to novel classes at inference time using text, images, or click queries. Leveraging rich visual descriptors from large-scale pre-trained models (foundation models), FAn can detect and segment objects by matching multimodal queries (text, images, clicks) against an input image sequence. These detected and segmented objects are tracked across image frames, all while accounting for occlusion and object re-emergence. We demonstrate FAn on a real-world robotic system (a micro aerial vehicle) and report its ability to seamlessly follow the objects of interest in a real-time control loop. FAn can be deployed on a laptop with a lightweight (6-8 GB) graphics card, achieving a throughput of 6-20 frames per second. To enable rapid adoption, deployment, and extensibility, we open-source all our code on our project webpage at //github.com/alaamaalouf/FollowAnything . We also encourage the reader the watch our 5-minutes explainer video in this //www.youtube.com/watch?v=6Mgt3EPytrw .
The ability of robots to autonomously navigate through 3D environments depends on their comprehension of spatial concepts, ranging from low-level geometry to high-level semantics, such as objects, places, and buildings. To enable such comprehension, 3D scene graphs have emerged as a robust tool for representing the environment as a layered graph of concepts and their relationships. However, building these representations using monocular vision systems in real-time remains a difficult task that has not been explored in depth. This paper puts forth a real-time spatial perception system Mono-Hydra, combining a monocular camera and an IMU sensor setup, focusing on indoor scenarios. However, the proposed approach is adaptable to outdoor applications, offering flexibility in its potential uses. The system employs a suite of deep learning algorithms to derive depth and semantics. It uses a robocentric visual-inertial odometry (VIO) algorithm based on square-root information, thereby ensuring consistent visual odometry with an IMU and a monocular camera. This system achieves sub-20 cm error in real-time processing at 15 fps, enabling real-time 3D scene graph construction using a laptop GPU (NVIDIA 3080). This enhances decision-making efficiency and effectiveness in simple camera setups, augmenting robotic system agility. We make Mono-Hydra publicly available at: //github.com/UAV-Centre-ITC/Mono_Hydra
The discovery of equations with knowledge of the process origin is a tempting prospect. However, most equation discovery tools rely on gradient methods, which offer limited control over parameters. An alternative approach is the evolutionary equation discovery, which allows modification of almost every optimization stage. In this paper, we examine the modifications that can be introduced into the evolutionary operators of the equation discovery algorithm, taking inspiration from directed evolution techniques employed in fields such as chemistry and biology. The resulting approach, dubbed directed equation discovery, demonstrates a greater ability to converge towards accurate solutions than the conventional method. To support our findings, we present experiments based on Burgers', wave, and Korteweg--de Vries equations.
We develop a data-driven optimal shrinkage algorithm for matrix denoising in the presence of high-dimensional noise with a separable covariance structure; that is, the noise is colored and dependent across samples. The algorithm, coined {\em extended OptShrink} (eOptShrink) depends on the asymptotic behavior of singular values and singular vectors of the random matrix associated with the noisy data. Based on the developed theory, including the sticking property of non-outlier singular values and delocalization of the non-outlier singular vectors associated with weak signals with a convergence rate, and the spectral behavior of outlier singular values and vectors, we develop three estimators, each of these has its own interest. First, we design a novel rank estimator, based on which we provide an estimator for the spectral distribution of the pure noise matrix, and hence the optimal shrinker called eOptShrink. In this algorithm we do not need to estimate the separable covariance structure of the noise. A theoretical guarantee of these estimators with a convergence rate is given. On the application side, in addition to a series of numerical simulations with a comparison with various state-of-the-art optimal shrinkage algorithms, we apply eOptShrink to extract maternal and fetal electrocardiograms from the single channel trans-abdominal maternal electrocardiogram.
We propose a new model to address the overlooked problem of node clustering in simple hypergraphs. Simple hypergraphs are suitable when a node may not appear multiple times in the same hyperedge, such as in co-authorship datasets. Our model assumes the existence of latent node groups and hyperedges are conditionally independent given these groups. We first establish the generic identifiability of the model parameters. We then develop a variational approximation Expectation-Maximization algorithm for parameter inference and node clustering, and derive a statistical criterion for model selection. To illustrate the performance of our R package HyperSBM, we compare it with other node clustering methods using synthetic data generated from the model, as well as from a line clustering experiment and a co-authorship dataset. As a by-product, our synthetic experiments demonstrate that the detectability thresholds for non-uniform sparse hypergraphs cannot be deduced from the uniform case.
This paper addresses the issues of controlling and analyzing the population diversity in quantum-behaved particle swarm optimization (QPSO), which is an optimization approach motivated by concepts in quantum mechanics and PSO. In order to gain an in-depth understanding of the role the diversity plays in the evolving process, we first define the genotype diversity by the distance to the average point of the particles' positions and the phenotype diversity by the fitness values for the QPSO. Then, the correlations between the two types of diversities and the search performance are tested and analyzed on several benchmark functions, and the distance-to-average-point diversity is showed to have stronger association with the search performance during the evolving processes. Finally, in the light of the performed diversity analyses, two strategies for controlling the distance-to-average-point diversities are proposed for the purpose of improving the search ability of the QPSO algorithm. Empirical studies on the QPSO with the introduced diversity control methods are performed on a set of benchmark functions from the CEC 2005 benchmark suite. The performance of the proposed methods are evaluated and compared with the original QPSO and other PSO variants.
This paper describes a purely functional library for computing level-$p$-complexity of Boolean functions, and applies it to two-level iterated majority. Boolean functions are simply functions from $n$ bits to one bit, and they can describe digital circuits, voting systems, etc. An example of a Boolean function is majority, which returns the value that has majority among the $n$ input bits for odd $n$. The complexity of a Boolean function $f$ measures the cost of evaluating it: how many bits of the input are needed to be certain about the result of $f$. There are many competing complexity measures but we focus on level-$p$-complexity -- a function of the probability $p$ that a bit is 1. The level-$p$-complexity $D_p(f)$ is the minimum expected cost when the input bits are independent and identically distributed with Bernoulli($p$) distribution. We specify the problem as choosing the minimum expected cost of all possible decision trees -- which directly translates to a clearly correct, but very inefficient implementation. The library uses thinning and memoization for efficiency and type classes for separation of concerns. The complexity is represented using (sets of) polynomials, and the order relation used for thinning is implemented using polynomial factorisation and root-counting. Finally we compute the complexity for two-level iterated majority and improve on an earlier result by J.~Jansson.
Ghost, or fictitious points allow to capture boundary conditions that are not located on the finite difference grid discretization. We explore in this paper the impact of ghost points on the stability of the explicit Euler finite difference scheme in the context of the diffusion equation. In particular, we consider the case of a one-touch option under the Black-Scholes model. The observations and results are however valid for a much wider range of financial contracts and models.
This article presents the openCFS submodule scattered data reader for coupling multi-physical simulations performed in different simulation programs. For instance, by considering a forward-coupling of a surface vibration simulation (mechanical system) to an acoustic propagation simulation using time-dependent acoustic absorbing material as a noise mitigation measure. The nearest-neighbor search of the target and source points from the interpolation is performed using the FLANN or the CGAL library. In doing so, the coupled field (e.g., surface velocity) is interpolated from a source representation consisting of field values physically stored and organized in a file directory to a target representation being the quadrature points in the case of the finite element method. A test case of the functionality is presented in the "testsuite" module of the openCFS software called "Abc2dcsvt". This scattered data reader module was successfully applied in numerous studies on flow-induced sound generation. Within this short article, the functionality, and usability of this module are described.
The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular situation of a solid with inhomogeneities. Description of the fracture processes are based on the theory of material damage. It introduces two independent damage parameters to distinguish between interface and internal cracks. The parameter responsible for interface cracks is defined in a thin adhesive layer of the interface and renders relation between stress and strain quantities in fashion of cohesive zone models.The second parameter is defined inside material domains and it is founded on the theory of phase-field fracture guaranteeing the material damage to occur in a thin material strip introducing a regularised model of internal cracks. Additional property of both interface and phase-field damage is their capability to distinguish between fracture modes which is useful if the structures is subjected to combined loading. The solution methodology is based on a variational approach which allows implementation of non-linear programming optimisation into standard methods of finite-element discretisation and time stepping method.Computational implementation is prepared in MATLAB whose numerical data validate developed formulation for analysis of problems of fracture in multi-domain elements of structures.
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