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Control barrier functions (CBFs) play a critical role in the design of safe optimization-based controllers for control-affine systems. Given a CBF associated with a desired ``safe'' set, the typical approach consists in embedding CBF-based constraints into the optimization problem defining the control law to enforce forward invariance of the safe set. While this approach effectively guarantees safety for a given CBF, the CBF-based control law can introduce undesirable equilibrium points (i.e., points that are not equilibria of the original system); open questions remain on how the choice of CBF influences the number and locations of undesirable equilibria and, in general, the dynamics of the closed-loop system. This paper investigates how the choice of CBF impacts the dynamics of the closed-loop system and shows that: (i) The CBF does not affect the number, location, and (local) stability properties of the equilibria in the interior of the safe set; (ii) undesirable equilibria only appear on the boundary of the safe set; and, (iii) the number and location of undesirable equilibria for the closed-loop system do not depend of the choice of the CBF. Additionally, for the well-established safety filters and controllers based on both CBF and control Lyapunov functions (CLFs), we show that the stability properties of equilibria of the closed-loop system are independent of the choice of the CBF and of the associated extended class-K function.

Data depth has emerged as an invaluable nonparametric measure for the ranking of multivariate samples. The main contribution of depth-based two-sample comparisons is the introduction of the Q statistic (Liu and Singh, 1993), a quality index. Unlike traditional methods, data depth does not require the assumption of normal distributions and adheres to four fundamental properties. Many existing two-sample homogeneity tests, which assess mean and/or scale changes in distributions often suffer from low statistical power or indeterminate asymptotic distributions. To overcome these challenges, we introduced a DEEPEAST (depth-explored same-attraction sample-to-sample central-outward ranking) technique for improving statistical power in two-sample tests via the same-attraction function. We proposed two novel and powerful depth-based test statistics: the sum test statistic and the product test statistic, which are rooted in Q statistics, share a "common attractor" and are applicable across all depth functions. We further proved the asymptotic distribution of these statistics for various depth functions. To assess the performance of power gain, we apply three depth functions: Mahalanobis depth (Liu and Singh, 1993), Spatial depth (Brown, 1958; Gower, 1974), and Projection depth (Liu, 1992). Through two-sample simulations, we have demonstrated that our sum and product statistics exhibit superior power performance, utilizing a strategic block permutation algorithm and compare favourably with popular methods in literature. Our tests are further validated through analysis on Raman spectral data, acquired from cellular and tissue samples, highlighting the effectiveness of the proposed tests highlighting the effective discrimination between health and cancerous samples.

This paper studies the dynamical properties of closed-loop systems obtained from control barrier function-based safety filters. We provide a sufficient and necessary condition for the existence of undesirable equilibria and show that the Jacobian matrix of the closed-loop system evaluated at an undesirable equilibrium always has a nonpositive eigenvalue. In the special case of linear planar systems and ellipsoidal obstacles, we give a complete characterization of the dynamical properties of the corresponding closed-loop system. We show that for underactuated systems, the safety filter always introduces a single undesirable equilibrium, which is a saddle-point. We prove that all trajectories outside the global stable manifold of such equilibrium converge to the origin. In the fully actuated case, we discuss how the choice of nominal controller affects the stability properties of the closed-loop system. Various simulations illustrate our results.

Recently, data depth has been widely used to rank multivariate data. The study of the depth-based $Q$ statistic, originally proposed by Liu and Singh (1993), has become increasingly popular when it can be used as a quality index to differentiate between two samples. Based on the existing theoretical foundations, more and more variants have been developed for increasing power in the two sample test. However, the asymptotic expansion of the $Q$ statistic in the important foundation work of Zuo and He (2006) currently has an optimal rate $m^{-3/4}$ slower than the target $m^{-1}$, leading to limitations in higher-order expansions for developing more powerful tests. We revisit the existing assumptions and add two new plausible assumptions to obtain the target rate by applying a new proof method based on the Hoeffding decomposition and the Cox-Reid expansion. The aim of this paper is to rekindle interest in asymptotic data depth theory, to place Q-statistical inference on a firmer theoretical basis, to show its variants in current research, to open the door to the development of new theories for further variants requiring higher-order expansions, and to explore more of its potential applications.

In multi-agent reinforcement learning (MARL), the Centralized Training with Decentralized Execution (CTDE) framework is pivotal but struggles due to a gap: global state guidance in training versus reliance on local observations in execution, lacking global signals. Inspired by human societal consensus mechanisms, we introduce the Hierarchical Consensus-based Multi-Agent Reinforcement Learning (HC-MARL) framework to address this limitation. HC-MARL employs contrastive learning to foster a global consensus among agents, enabling cooperative behavior without direct communication. This approach enables agents to form a global consensus from local observations, using it as an additional piece of information to guide collaborative actions during execution. To cater to the dynamic requirements of various tasks, consensus is divided into multiple layers, encompassing both short-term and long-term considerations. Short-term observations prompt the creation of an immediate, low-layer consensus, while long-term observations contribute to the formation of a strategic, high-layer consensus. This process is further refined through an adaptive attention mechanism that dynamically adjusts the influence of each consensus layer. This mechanism optimizes the balance between immediate reactions and strategic planning, tailoring it to the specific demands of the task at hand. Extensive experiments and real-world applications in multi-robot systems showcase our framework's superior performance, marking significant advancements over baselines., Comment: 8 pages, 10 figures. Accepted for presentation at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2024)

Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality. However, the estimated transition probability matrix derived from MLE lacks accuracy compared to the real one, and LRT is inefficient in high-dimensional Markov chains. In this study, we extended the adaptive Lasso technique from linear models to Markov chains and proposed a novel model by applying penalized maximum likelihood estimation to optimize the estimation of the transition probability matrix. Meanwhile, we demonstrated that the new model enjoys oracle properties, which means the estimated transition probability matrix has the same performance as the real one when given. Simulations show that our new method behave very well overall in comparison with various competitors. Real data analysis further convince the value of our proposed method.

Visual object tracking aims to localize the target object of each frame based on its initial appearance in the first frame. Depending on the input modility, tracking tasks can be divided into RGB tracking and RGB+X (e.g. RGB+N, and RGB+D) tracking. Despite the different input modalities, the core aspect of tracking is the temporal matching. Based on this common ground, we present a general framework to unify various tracking tasks, termed as OneTracker. OneTracker first performs a large-scale pre-training on a RGB tracker called Foundation Tracker. This pretraining phase equips the Foundation Tracker with a stable ability to estimate the location of the target object. Then we regard other modality information as prompt and build Prompt Tracker upon Foundation Tracker. Through freezing the Foundation Tracker and only adjusting some additional trainable parameters, Prompt Tracker inhibits the strong localization ability from Foundation Tracker and achieves parameter-efficient finetuning on downstream RGB+X tracking tasks. To evaluate the effectiveness of our general framework OneTracker, which is consisted of Foundation Tracker and Prompt Tracker, we conduct extensive experiments on 6 popular tracking tasks across 11 benchmarks and our OneTracker outperforms other models and achieves state-of-the-art performance., Comment: Accepted to CVPR 2024

This paper considers the problem of controlling inverter-interfaced distributed energy resources (DERs) in a distribution grid to solve an AC optimal power flow (OPF) problem in real time. The AC OPF includes voltage constraints, and seeks to minimize costs associated with the economic operation, power losses, or the power curtailment from renewables. We develop an online feedback optimization method to drive the DERs' power setpoints to solutions of an AC OPF problem based only on voltage measurements (and without requiring measurements of the power consumption of non-controllable assets). The proposed method - grounded on the theory of control barrier functions - is based on a continuous approximation of the projected gradient flow, appropriately modified to accommodate measurements from the power network. We provide results in terms of local exponential stability, and assess the robustness to errors in the measurements and in the system Jacobian matrix. We show that the proposed method ensures anytime satisfaction of the voltage constraints when no model and measurement errors are present; if these errors are present and are small, the voltage violation is practically negligible. We also discuss extensions of the framework to virtual power plant setups and to cases where constraints on power flows and currents must be enforced. Numerical experiments on a 93-bus distribution system and with realistic load and production profiles show a superior performance in terms of voltage regulation relative to existing methods.

This paper considers the problem of regulating a dynamical system to equilibria that are defined as solutions of an input- and state-constrained optimization problem. To solve this regulation task, we design a state feedback controller based on a continuous approximation of the projected gradient flow. We first show that the equilibria of the interconnection between the plant and the proposed controller correspond to critical points of the constrained optimization problem. We then derive sufficient conditions to ensure that, for the closed-loop system, isolated locally optimal solutions of the optimization problem are locally exponentially stable and show that input constraints are satisfied at all times by identifying an appropriate forward-invariant set., Comment: This paper has been accepted for publication on IEEE Control Systems Letters

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

Grasping is a fundamental skill for robots to interact with their environment. While grasp execution requires coordinated movement of the hand and arm to achieve a collision-free and secure grip, many grasp synthesis studies address arm and hand motion planning independently, leading to potentially unreachable grasps in practical settings. The challenge of determining integrated arm-hand configurations arises from its computational complexity and high-dimensional nature. We address this challenge by presenting a novel differentiable robot neural distance function. Our approach excels in capturing intricate geometry across various joint configurations while preserving differentiability. This innovative representation proves instrumental in efficiently addressing downstream tasks with stringent contact constraints. Leveraging this, we introduce an adaptive grasp synthesis framework that exploits the full potential of the unified arm-hand system for diverse grasping tasks. Our neural joint space distance function achieves an 84.7% error reduction compared to baseline methods. We validated our approaches on a unified robotic arm-hand system that consists of a 7-DoF robot arm and a 16-DoF multi-fingered robotic hand. Results demonstrate that our approach empowers this high-DoF system to generate and execute various arm-hand grasp configurations that adapt to the size of the target objects while ensuring whole-body movements to be collision-free., Comment: Under review

Efficient and accurate 3D object shape reconstruction contributes significantly to the success of a robot's physical interaction with its environment. Acquiring accurate shape information about unknown objects is challenging, especially in unstructured environments, e.g. the vision sensors may only be able to provide a partial view. To address this issue, tactile sensors could be employed to extract local surface information for more robust unknown object shape estimation. In this paper, we propose a novel approach for efficient unknown 3D object shape exploration and reconstruction using a multi-fingered hand equipped with tactile sensors and a depth camera only providing a partial view. We present a multi-finger sliding touch strategy for efficient shape exploration using a Bayesian Optimization approach and a single-leader-multi-follower strategy for multi-finger smooth local surface perception. We evaluate our proposed method by estimating the 3D shape of objects from the YCB and OCRTOC datasets based on simulation and real robot experiments. The proposed approach yields successful reconstruction results relying on only a few continuous sliding touches. Experimental results demonstrate that our method is able to model unknown objects in an efficient and accurate way., Comment: 8 pages, 11 figures. Accepted by IROS 2023

In this letter, we propose a novel statistical method to measure which system is better suited to probe small deviations from the usual quantum behavior. Such deviations are motivated by a number of theoretical and phenomenological motivations, and various systems have been proposed to test them. We propose that measuring deviations from quantum mechanics for a system would be easier if it has a higher Kullback Leibler divergence. We show this explicitly for a nonlocal Schrodinger equation and argue that it will hold for any modification to standard quantum behaviour. Thus, the results of this letter can be used to classify a wide range of theoretical and phenomenological models., Comment: 13 pages , 2 figures , 8 authors

Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data depth-based tests for this problem, but they may not be very powerful, or have unknown asymptotic distributions, or have slow convergence rates to asymptotic distributions. Given the recent development of data depth as an important measure in quality assurance, we propose three new test statistics for multivariate two-sample homogeneity tests. The proposed minimum test statistics have simple asymptotic half-normal distribution. We also discuss the generalization of the proposed tests to multiple samples. The simulation study demonstrates the superior performance of the proposed tests. The test procedure is illustrated by two real data examples.

As large language models (LLMs) like GPT become increasingly prevalent, it is essential that we assess their capabilities beyond language processing. This paper examines the economic rationality of GPT by instructing it to make budgetary decisions in four domains: risk, time, social, and food preferences. We measure economic rationality by assessing the consistency of GPT's decisions with utility maximization in classic revealed preference theory. We find that GPT's decisions are largely rational in each domain and demonstrate higher rationality score than those of human subjects in a parallel experiment and in the literature. Moreover, the estimated preference parameters of GPT are slightly different from human subjects and exhibit a lower degree of heterogeneity. We also find that the rationality scores are robust to the degree of randomness and demographic settings such as age and gender, but are sensitive to contexts based on the language frames of the choice situations. These results suggest the potential of LLMs to make good decisions and the need to further understand their capabilities, limitations, and underlying mechanisms.

Learning on graphs, where instance nodes are inter-connected, has become one of the central problems for deep learning, as relational structures are pervasive and induce data inter-dependence which hinders trivial adaptation of existing approaches that assume inputs to be i.i.d.~sampled. However, current models mostly focus on improving testing performance of in-distribution data and largely ignore the potential risk w.r.t. out-of-distribution (OOD) testing samples that may cause negative outcome if the prediction is overconfident on them. In this paper, we investigate the under-explored problem, OOD detection on graph-structured data, and identify a provably effective OOD discriminator based on an energy function directly extracted from graph neural networks trained with standard classification loss. This paves a way for a simple, powerful and efficient OOD detection model for GNN-based learning on graphs, which we call GNNSafe. It also has nice theoretical properties that guarantee an overall distinguishable margin between the detection scores for in-distribution and OOD samples, which, more critically, can be further strengthened by a learning-free energy belief propagation scheme. For comprehensive evaluation, we introduce new benchmark settings that evaluate the model for detecting OOD data from both synthetic and real distribution shifts (cross-domain graph shifts and temporal graph shifts). The results show that GNNSafe achieves up to $17.0\%$ AUROC improvement over state-of-the-arts and it could serve as simple yet strong baselines in such an under-developed area., Comment: Published at ICLR 2023, the implementation code is available at https://github.com/qitianwu/GraphOOD-GNNSafe

This paper presents a system identification framework -- inspired by multi-task learning -- to estimate the dynamics of a given number of linear time-invariant (LTI) systems jointly by leveraging structural similarities across the systems. In particular, we consider LTI systems that model networked systems with similar connectivity, or LTI systems with small differences in their matrices. The system identification task involves the minimization of the least-squares (LS) fit for individual systems, augmented with a regularization function that enforces structural similarities. The proposed method is particularly suitable for cases when the recorded trajectories for one or more LTI systems are not sufficiently rich, leading to ill-conditioning of LS methods. We analyze the performance of the proposed method when the matrices of the LTI systems feature a common sparsity pattern (i.e., similar connectivity), and provide simulations based on real data for the estimation of the brain dynamics. We show that the proposed method requires a significantly smaller number of fMRI scans to achieve similar error levels of the LS., Comment: Paper to appear in the proceedings of 62nd IEEE Conference on Decision and Control (CDC 2023)

This letter describes an approach to achieve well-known Chinese cooking art stir-fry on a bimanual robot system. Stir-fry requires a sequence of highly dynamic coordinated movements, which is usually difficult to learn for a chef, let alone transfer to robots. In this letter, we define a canonical stir-fry movement, and then propose a decoupled framework for learning this deformable object manipulation from human demonstration. First, the dual arms of the robot are decoupled into different roles (a leader and follower) and learned with classical and neural network-based methods separately, then the bimanual task is transformed into a coordination problem. To obtain general bimanual coordination, we secondly propose a Graph and Transformer based model -- Structured-Transformer, to capture the spatio-temporal relationship between dual-arm movements. Finally, by adding visual feedback of content deformation, our framework can adjust the movements automatically to achieve the desired stir-fry effect. We verify the framework by a simulator and deploy it on a real bimanual Panda robot system. The experimental results validate our framework can realize the bimanual robot stir-fry motion and have the potential to extend to other deformable objects with bimanual coordination., Comment: 8 pages, 8 figures, published to RA-L

This paper provides a unified view to explain different adversarial attacks and defense methods, \emph{i.e.} the view of multi-order interactions between input variables of DNNs. Based on the multi-order interaction, we discover that adversarial attacks mainly affect high-order interactions to fool the DNN. Furthermore, we find that the robustness of adversarially trained DNNs comes from category-specific low-order interactions. Our findings provide a potential method to unify adversarial perturbations and robustness, which can explain the existing defense methods in a principle way. Besides, our findings also make a revision of previous inaccurate understanding of the shape bias of adversarially learned features., Comment: the previous version is arXiv:2103.07364, but I mistakenly apply a new ID for the paper

Medical ultrasound has become a routine examination approach nowadays and is widely adopted for different medical applications, so it is desired to have a robotic ultrasound system to perform the ultrasound scanning autonomously. However, the ultrasound scanning skill is considerably complex, which highly depends on the experience of the ultrasound physician. In this paper, we propose a learning-based approach to learn the robotic ultrasound scanning skills from human demonstrations. First, the robotic ultrasound scanning skill is encapsulated into a high-dimensional multi-modal model, which takes the ultrasound images, the pose/position of the probe and the contact force into account. Second, we leverage the power of imitation learning to train the multi-modal model with the training data collected from the demonstrations of experienced ultrasound physicians. Finally, a post-optimization procedure with guided explorations is proposed to further improve the performance of the learned model. Robotic experiments are conducted to validate the advantages of our proposed framework and the learned models.

With the potential applications of capsule robots in medical endoscopy, accurate dynamic control of the capsule robot is becoming more and more important. In the scale of a capsule robot, the friction between capsule and the environment plays an essential role in the dynamic model, which is usually difficult to model beforehand. In the paper, a tethered capsule robot system driven by a robot manipulator is built, where a strong magnetic Halbach array is mounted on the robot's end-effector to adjust the state of the capsule. To increase the control accuracy, the friction between capsule and the environment is learned with demonstrated trajectories. With the learned friction model, experimental results demonstrate an improvement of 5.6% in terms of tracking error., Comment: ICRAE 2021 Conference paper

The rise of deep learning has greatly transformed the pipeline of robotic grasping from model-based approach to data-driven stream. Along this line, a large scale of grasping data either collected from simulation or from real world examples become extremely important. In this paper, we present our recent work on data generation in simulation for a bin-picking scene. 77 objects from the YCB object data sets are used to generate the dataset with PyBullet, where different environment conditions are taken into account including lighting, camera pose, sensor noise and so on. In all, 100K data samples are collected in terms of ground truth segmentation, RGB, 6D pose and point cloud. All the data examples including the source code are made available online., Comment: 3 pages, workshop

The ability to segment unknown objects in cluttered scenes has a profound impact on robot grasping. The rise of deep learning has greatly transformed the pipeline of robotic grasping from model-based approach to data-driven stream, which generally requires a large scale of grasping data either collected in simulation or from real-world examples. In this paper, we proposed a sim-to-real framework to transfer the object segmentation model learned in simulation to the real-world. First, data samples are collected in simulation, including RGB, 6D pose, and point cloud. Second, we also present a GAN-based unknown object segmentation method through domain adaptation, which consists of an image translation module and an image segmentation module. The image translation module is used to shorten the reality gap and the segmentation module is responsible for the segmentation mask generation. We used the above method to perform segmentation experiments on unknown objects in a bin-picking scenario. Finally, the experimental result shows that the segmentation model learned in simulation can be used for real-world data segmentation., Comment: 6 pages