We present a convex formulation of compliant frictional contact and a robust, performant method to solve it in practice. By analytically eliminating contact constraints, we obtain an unconstrained convex problem. Our solver has proven global convergence and warm-starts effectively, enabling simulation at interactive rates. We develop compact analytical expressions of contact forces allowing us to describe our model in clear physical terms and to rigorously characterize our approximations. Moreover, this enables us not only to model point contact, but also to incorporate sophisticated models of compliant contact patches. Our time stepping scheme includes the midpoint rule, which we demonstrate achieves second order accuracy even with frictional contact. We introduce a number of accuracy metrics and show our method outperforms existing commercial and open source alternatives without sacrificing accuracy. Finally, we demonstrate robust simulation of robotic manipulation tasks at interactive rates, with accurately resolved stiction and contact transitions, as required for meaningful sim-to-real transfer. Our method is implemented in the open source robotics toolkit Drake.

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The generation of feasible adversarial examples is necessary for properly assessing models that work on constrained feature space. However, it remains a challenging task to enforce constraints into attacks that were designed for computer vision. We propose a unified framework to generate feasible adversarial examples that satisfy given domain constraints. Our framework supports the use cases reported in the literature and can handle both linear and non-linear constraints. We instantiate our framework into two algorithms: a gradient-based attack that introduces constraints in the loss function to maximize, and a multi-objective search algorithm that aims for misclassification, perturbation minimization, and constraint satisfaction. We show that our approach is effective on two datasets from different domains, with a success rate of up to 100%, where state-of-the-art attacks fail to generate a single feasible example. In addition to adversarial retraining, we propose to introduce engineered non-convex constraints to improve model adversarial robustness. We demonstrate that this new defense is as effective as adversarial retraining. Our framework forms the starting point for research on constrained adversarial attacks and provides relevant baselines and datasets that future research can exploit.

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We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the state equation, existence of global optimal solutions, differentiability of the control-to-state map and first-order necessary optimality conditions are established. The aforementioned results require the controls to be functions in $H^1$ and subject to pointwise upper and lower bounds. In order to obtain the Newton differentiability of the optimality conditions, we employ a Moreau-Yosida-type penalty approach to treat the control constraints and study its convergence. The first-order optimality conditions of the regularized problems are shown to be Newton diffentiable, and a generalized Newton method is detailed. A discretization of the optimal control problem by piecewise linear finite elements is proposed and numerical results are presented.

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Modern neural networks are able to perform at least as well as humans in numerous tasks involving object classification and image generation. However, small perturbations which are imperceptible to humans may significantly degrade the performance of well-trained deep neural networks. We provide a Distributionally Robust Optimization (DRO) framework which integrates human-based image quality assessment methods to design optimal attacks that are imperceptible to humans but significantly damaging to deep neural networks. Through extensive experiments, we show that our attack algorithm generates better-quality (less perceptible to humans) attacks than other state-of-the-art human imperceptible attack methods. Moreover, we demonstrate that DRO training using our optimally designed human imperceptible attacks can improve group fairness in image classification. Towards the end, we provide an algorithmic implementation to speed up DRO training significantly, which could be of independent interest.

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We develop an autonomous navigation algorithm for a robot operating in two-dimensional environments cluttered with obstacles having arbitrary convex shapes. The proposed navigation approach relies on a hybrid feedback to guarantee global asymptotic stabilization of the robot towards a predefined target location while ensuring the forward invariance of the obstacle-free workspace. The main idea consists in designing an appropriate switching strategy between the move-to-target mode and the obstacle-avoidance mode based on the proximity of the robot with respect to the nearest obstacle. The proposed hybrid controller generates continuous velocity input trajectories when the robot is initialized away from the boundaries of the unsafe regions. Finally, we provide an algorithmic procedure for the sensor-based implementation of the proposed hybrid controller and validate its effectiveness through some simulation results.

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We propose and analyse an augmented mixed finite element method for the Navier--Stokes equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and no-slip boundary conditions. The weak formulation includes least-squares terms arising from the constitutive equation and from the incompressibility condition, and we use a fixed point strategies to show the existence and uniqueness of continuous and discrete solutions under the assumption of sufficiently small data. The method is constructed using any compatible finite element pair (conforming or non-conforming) for velocity and pressure as dictated by Stokes inf-sup stability, while for vorticity any generic discrete space (of arbitrary order) can be used. We establish optimal a priori error estimates. Finally, we provide a set of numerical tests in 2D and 3D illustrating the behaviour of the scheme as well as verifying the theoretical convergence rates.

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Trajectory forecasting plays a pivotal role in the field of intelligent vehicles or social robots. Recent works focus on modeling spatial social impacts or temporal motion attentions, but neglect inherent properties of motions, i.e. moving trends and driving intentions. This paper proposes a context-free Hierarchical Motion Encoder-Decoder Network (HMNet) for vehicle trajectory prediction. HMNet first infers the hierarchical difference on motions to encode physically compliant patterns with high expressivity of moving trends and driving intentions. Then, a goal (endpoint)-embedded decoder hierarchically constructs multimodal predictions depending on the location-velocity-acceleration-related patterns. Besides, we present a modified social pooling module which considers certain motion properties to represent social interactions. HMNet enables to make the accurate, unimodal/multimodal and physically-socially-compliant prediction. Experiments on three public trajectory prediction datasets, i.e. NGSIM, HighD and Interaction show that our model achieves the state-of-the-art performance both quantitatively and qualitatively. We will release our code here: https://github.com/xuedashuai/HMNet.

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Smart contracts written in Solidity are programs used in blockchain networks, such as Etherium, for performing transactions. However, as with any piece of software, they are prone to errors and may present vulnerabilities, which malicious attackers could then use. This paper proposes a solidity frontend for the efficient SMT-based context-bounded model checker (ESBMC), named ESBMC-Solidity, which provides a way of verifying such contracts with its framework. A benchmark suite with vulnerable smart contracts was also developed for evaluation and comparison with other verification tools. The experiments performed here showed that ESBMC-Solidity detected all vulnerabilities, was the fastest tool, and provided a counterexample for each benchmark. A demonstration is available at https://youtu.be/3UH8_1QAVN0.

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Active inference is a unifying theory for perception and action resting upon the idea that the brain maintains an internal model of the world by minimizing free energy. From a behavioral perspective, active inference agents can be seen as self-evidencing beings that act to fulfill their optimistic predictions, namely preferred outcomes or goals. In contrast, reinforcement learning requires human-designed rewards to accomplish any desired outcome. Although active inference could provide a more natural self-supervised objective for control, its applicability has been limited because of the shortcomings in scaling the approach to complex environments. In this work, we propose a contrastive objective for active inference that strongly reduces the computational burden in learning the agent's generative model and planning future actions. Our method performs notably better than likelihood-based active inference in image-based tasks, while also being computationally cheaper and easier to train. We compare to reinforcement learning agents that have access to human-designed reward functions, showing that our approach closely matches their performance. Finally, we also show that contrastive methods perform significantly better in the case of distractors in the environment and that our method is able to generalize goals to variations in the background.

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Despite the impressive quality improvements yielded by neural machine translation (NMT) systems, controlling their translation output to adhere to user-provided terminology constraints remains an open problem. We describe our approach to constrained neural decoding based on finite-state machines and multi-stack decoding which supports target-side constraints as well as constraints with corresponding aligned input text spans. We demonstrate the performance of our framework on multiple translation tasks and motivate the need for constrained decoding with attentions as a means of reducing misplacement and duplication when translating user constraints.

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We present a challenging and realistic novel dataset for evaluating 6-DOF object tracking algorithms. Existing datasets show serious limitations---notably, unrealistic synthetic data, or real data with large fiducial markers---preventing the community from obtaining an accurate picture of the state-of-the-art. Our key contribution is a novel pipeline for acquiring accurate ground truth poses of real objects w.r.t a Kinect V2 sensor by using a commercial motion capture system. A total of 100 calibrated sequences of real objects are acquired in three different scenarios to evaluate the performance of trackers in various scenarios: stability, robustness to occlusion and accuracy during challenging interactions between a person and the object. We conduct an extensive study of a deep 6-DOF tracking architecture and determine a set of optimal parameters. We enhance the architecture and the training methodology to train a 6-DOF tracker that can robustly generalize to objects never seen during training, and demonstrate favorable performance compared to previous approaches trained specifically on the objects to track.

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