Controlling the interaction forces between a human and an exoskeleton is crucial for providing transparency or adjusting assistance or resistance levels. However, it is an open problem to control the interaction forces of lower-limb exoskeletons designed for unrestricted overground walking. For these types of exoskeletons, it is challenging to implement force/torque sensors at every contact between the user and the exoskeleton for direct force measurement. Moreover, it is important to compensate for the exoskeleton's whole-body gravitational and dynamical forces, especially for heavy lower-limb exoskeletons. Previous works either simplified the dynamic model by treating the legs as independent double pendulums, or they did not close the loop with interaction force feedback. The proposed whole-exoskeleton closed-loop compensation (WECC) method calculates the interaction torques during the complete gait cycle by using whole-body dynamics and joint torque measurements on a hip-knee exoskeleton. Furthermore, it uses a constrained optimization scheme to track desired interaction torques in a closed loop while considering physical and safety constraints. We evaluated the haptic transparency and dynamic interaction torque tracking of WECC control on three subjects. We also compared the performance of WECC with a controller based on a simplified dynamic model and a passive version of the exoskeleton. The WECC controller results in a consistently low absolute interaction torque error during the whole gait cycle for both zero and nonzero desired interaction torques. In contrast, the simplified controller yields poor performance in tracking desired interaction torques during the stance phase.
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We provide a variety of lower bounds for the well-known shortcut set problem: how much can one decrease the diameter of a directed graph on $n$ vertices and $m$ edges by adding $O(n)$ or $O(m)$ of shortcuts from the transitive closure of the graph. Our results are based on a vast simplification of the recent construction of Bodwin and Hoppenworth [FOCS 2023] which was used to show an $\widetilde{\Omega}(n^{1/4})$ lower bound for the $O(n)$-sized shortcut set problem. We highlight that our simplification completely removes the use of the convex sets by B\'ar\'any and Larman [Math. Ann. 1998] used in all previous lower bound constructions. Our simplification also removes the need for randomness and further removes some log factors. This allows us to generalize the construction to higher dimensions, which in turn can be used to show the following results. For $O(m)$-sized shortcut sets, we show an $\Omega(n^{1/5})$ lower bound, improving on the previous best $\Omega(n^{1/8})$ lower bound. For all $\varepsilon > 0$, we show that there exists a $\delta > 0$ such that there are $n$-vertex $O(n)$-edge graphs $G$ where adding any shortcut set of size $O(n^{2-\varepsilon})$ keeps the diameter of $G$ at $\Omega(n^\delta)$. This improves the sparsity of the constructed graph compared to a known similar result by Hesse [SODA 2003]. We also consider the sourcewise setting for shortcut sets: given a graph $G=(V,E)$, a set $S\subseteq V$, how much can we decrease the sourcewise diameter of $G$, $\max_{(s, v) \in S \times V, \text{dist}(s, v) < \infty} \text{dist}(s,v)$ by adding a set of edges $H$ from the transitive closure of $G$? We show that for any integer $d \ge 2$, there exists a graph $G=(V, E)$ on $n$ vertices and $S \subseteq V$ with $|S| = \widetilde{\Theta}(n^{3/(d+3)})$, such that when adding $O(n)$ or $O(m)$ shortcuts, the sourcewise diameter is $\widetilde{\Omega}(|S|^{1/3})$.
The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common - but very different - ways to measure the satisfaction of a voter consider (i) the number of approved projects and (ii) the total cost of approved projects, respectively. In general, it is difficult to decide which measure of satisfaction best reflects the voters' true utilities. In this paper, we study proportionality axioms with respect to large classes of approval-based satisfaction functions. We establish logical implications among our axioms and related notions from the literature, and we ask whether outcomes can be achieved that are proportional with respect to more than one satisfaction function. We show that this is impossible for the two commonly used satisfaction functions when considering proportionality notions based on extended justified representation, but achievable for a notion based on proportional justified representation. For the latter result, we introduce a strengthening of priceability and show that it is satisfied by several polynomial-time computable rules, including the Method of Equal Shares and Phragm\`en's sequential rule.
Imitation learning is a powerful tool for training robot manipulation policies, allowing them to learn from expert demonstrations without manual programming or trial-and-error. However, common methods of data collection, such as human supervision, scale poorly, as they are time-consuming and labor-intensive. In contrast, Task and Motion Planning (TAMP) can autonomously generate large-scale datasets of diverse demonstrations. In this work, we show that the combination of large-scale datasets generated by TAMP supervisors and flexible Transformer models to fit them is a powerful paradigm for robot manipulation. To that end, we present a novel imitation learning system called OPTIMUS that trains large-scale visuomotor Transformer policies by imitating a TAMP agent. OPTIMUS introduces a pipeline for generating TAMP data that is specifically curated for imitation learning and can be used to train performant transformer-based policies. In this paper, we present a thorough study of the design decisions required to imitate TAMP and demonstrate that OPTIMUS can solve a wide variety of challenging vision-based manipulation tasks with over 70 different objects, ranging from long-horizon pick-and-place tasks, to shelf and articulated object manipulation, achieving 70 to 80% success rates. Video results and code at //mihdalal.github.io/optimus/
Neural tangent kernels (NTKs) provide a theoretical regime to analyze the learning and generalization behavior of over-parametrized neural networks. For a supervised learning task, the association between the eigenvectors of the NTK kernel and given data (a concept referred to as alignment in this paper) can govern the rate of convergence of gradient descent, as well as generalization to unseen data. Building upon this concept, we investigate NTKs and alignment in the context of graph neural networks (GNNs), where our analysis reveals that optimizing alignment translates to optimizing the graph representation or the graph shift operator in a GNN. Our results further establish the theoretical guarantees on the optimality of the alignment for a two-layer GNN and these guarantees are characterized by the graph shift operator being a function of the cross-covariance between the input and the output data. The theoretical insights drawn from the analysis of NTKs are validated by our experiments focused on a multi-variate time series prediction task for a publicly available dataset. Specifically, they demonstrate that GNNs with cross-covariance as the graph shift operator indeed outperform those that operate on the covariance matrix from only the input data.
We consider a simple setting in neuroevolution where an evolutionary algorithm optimizes the weights and activation functions of a simple artificial neural network. We then define simple example functions to be learned by the network and conduct rigorous runtime analyses for networks with a single neuron and for a more advanced structure with several neurons and two layers. Our results show that the proposed algorithm is generally efficient on two example problems designed for one neuron and efficient with at least constant probability on the example problem for a two-layer network. In particular, the so-called harmonic mutation operator choosing steps of size $j$ with probability proportional to $1/j$ turns out as a good choice for the underlying search space. However, for the case of one neuron, we also identify situations with hard-to-overcome local optima. Experimental investigations of our neuroevolutionary algorithm and a state-of-the-art CMA-ES support the theoretical findings.
There is a wide availability of methods for testing normality under the assumption of independent and identically distributed data. When data are dependent in space and/or time, however, assessing and testing the marginal behavior is considerably more challenging, as the marginal behavior is impacted by the degree of dependence. We propose a new approach to assess normality for dependent data by non-linearly incorporating existing statistics from normality tests as well as sample moments such as skewness and kurtosis through a neural network. We calibrate (deep) neural networks by simulated normal and non-normal data with a wide range of dependence structures and we determine the probability of rejecting the null hypothesis. We compare several approaches for normality tests and demonstrate the superiority of our method in terms of statistical power through an extensive simulation study. A real world application to global temperature data further demonstrates how the degree of spatio-temporal aggregation affects the marginal normality in the data.
Accurate reorientation and segmentation of the left ventricular (LV) is essential for the quantitative analysis of myocardial perfusion imaging (MPI), in which one critical step is to reorient the reconstructed transaxial nuclear cardiac images into standard short-axis slices for subsequent image processing. Small-scale LV myocardium (LV-MY) region detection and the diverse cardiac structures of individual patients pose challenges to LV segmentation operation. To mitigate these issues, we propose an end-to-end model, named as multi-scale spatial transformer UNet (MS-ST-UNet), that involves the multi-scale spatial transformer network (MSSTN) and multi-scale UNet (MSUNet) modules to perform simultaneous reorientation and segmentation of LV region from nuclear cardiac images. The proposed method is trained and tested using two different nuclear cardiac image modalities: 13N-ammonia PET and 99mTc-sestamibi SPECT. We use a multi-scale strategy to generate and extract image features with different scales. Our experimental results demonstrate that the proposed method significantly improves the reorientation and segmentation performance. This joint learning framework promotes mutual enhancement between reorientation and segmentation tasks, leading to cutting edge performance and an efficient image processing workflow. The proposed end-to-end deep network has the potential to reduce the burden of manual delineation for cardiac images, thereby providing multimodal quantitative analysis assistance for physicists.
Continuum robots have gained widespread popularity due to their inherent compliance and flexibility, particularly their adjustable levels of stiffness for various application scenarios. Despite efforts to dynamic modeling and control synthesis over the past decade, few studies have incorporated stiffness regulation into their feedback control design; however, this is one of the initial motivations to develop continuum robots. This paper addresses the crucial challenge of controlling both the position and stiffness of underactuated continuum robots actuated by antagonistic tendons. We begin by presenting a rigid-link dynamical model that can analyze the open-loop stiffening of tendon-driven continuum robots. Based on this model, we propose a novel passivity-based position-and-stiffness controller that adheres to the non-negative tension constraint. Comprehensive experiments on our continuum robot validate the theoretical results and demonstrate the efficacy and precision of this approach.
While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.
Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.
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