Control Barrier functions (CBFs) have attracted extensive attention for designing safe controllers for their deployment in real-world safety-critical systems. However, the perception of the surrounding environment is often subject to stochasticity and further distributional shift from the nominal one. In this paper, we present distributional robust CBF (DR-CBF) to achieve resilience under distributional shift while keeping the advantages of CBF, such as computational efficacy and forward invariance. To achieve this goal, we first propose a single-level convex reformulation to estimate the conditional value at risk (CVaR) of the safety constraints under distributional shift measured by a Wasserstein metric, which is by nature tri-level programming. Moreover, to construct a control barrier condition to enforce the forward invariance of the CVaR, the technique of differentiable convex programming is applied to enable differentiation through the optimization layer of CVaR estimation. We also provide an approximate variant of DR-CBF for higher-order systems. Simulation results are presented to validate the chance-constrained safety guarantee under the distributional shift in both first and second-order systems.

Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to ideal approximation of high-level performance goals is a challenging task. In this work, we propose Neural Metamaterial Networks (NMN) -- smooth neural representations that encode the nonlinear mechanics of entire metamaterial families. Given structure parameters as input, NMN return continuously differentiable strain energy density functions, thus guaranteeing conservative forces by construction. Though trained on simulation data, NMN do not inherit the discontinuities resulting from topological changes in finite element meshes. They instead provide a smooth map from parameter to performance space that is fully differentiable and thus well-suited for gradient-based optimization. On this basis, we formulate inverse material design as a nonlinear programming problem that leverages neural networks for both objective functions and constraints. We use this approach to automatically design materials with desired strain-stress curves, prescribed directional stiffness and Poisson ratio profiles. We furthermore conduct ablation studies on network nonlinearities and show the advantages of our approach compared to native-scale optimization.

We investigate the problem of training models that are robust to shifts caused by changes in the distribution of class-priors or group-priors. The presence of skewed training priors can often lead to the models overfitting to spurious features. Unlike existing methods, which optimize for either the worst or the average performance over classes or groups, our work is motivated by the need for finer control over the robustness properties of the model. We present an extremely lightweight post-hoc approach that performs scaling adjustments to predictions from a pre-trained model, with the goal of minimizing a distributionally robust loss around a chosen target distribution. These adjustments are computed by solving a constrained optimization problem on a validation set and applied to the model during test time. Our constrained optimization objective is inspired from a natural notion of robustness to controlled distribution shifts. Our method comes with provable guarantees and empirically makes a strong case for distributional robust post-hoc classifiers.

The intention of the target can help us to estimate its future motion state more accurately. This paper proposes an intention-aware planner to enhance safety and robustness in aerial tracking applications. Firstly, we utilize the Mediapipe framework to estimate target's pose. A risk assessment function and a state observation function are designed to predict the target intention. Afterwards, an intention-driven hybrid A* method is proposed for target motion prediction, ensuring that the target's future positions align with its intention. Finally, an intention-aware optimization approach, in conjunction with particular penalty formulations, is designed to generate a spatial-temporal optimal trajectory. Benchmark comparisons validate the superior performance of our proposed methodology across diverse scenarios. This is attributed to the integration of the target intention into the planner through coupled formulations.

Generating motion for robots that interact with objects of various shapes is a complex challenge, further complicated when the robot's own geometry and multiple desired behaviors are considered. To address this issue, we introduce a new framework based on Geometric Projectors (GeoPro) for constrained optimization. This novel framework allows for the generation of task-agnostic behaviors that are compliant with geometric constraints. GeoPro streamlines the design of behaviors in both task and configuration spaces, offering diverse functionalities such as collision avoidance and goal-reaching, while maintaining high computational efficiency. We validate the efficacy of our work through simulations and Franka Emika robotic experiments, comparing its performance against state-of-the-art methodologies. This comprehensive evaluation highlights GeoPro's versatility in accommodating robots with varying dynamics and precise geometric shapes. For additional materials, please visit: https://www.xueminchi.com/publications/geopro

In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality constraints in the configuration space, which are difficult for trajectory optimizers. In addition, the set of feasible configurations becomes a measure zero set, which presents a challenge to sampling-based motion planners. We leverage an analytic solution to the inverse kinematics problem to parametrize the configuration space, resulting in a lower-dimensional representation where the set of valid configurations has positive measure. We describe how to use this parametrization with existing algorithms for motion planning, including sampling-based approaches, trajectory optimizers, and techniques that plan through convex inner-approximations of collision-free space.

To enable the computation of effective randomized patrol routes for single- or multi-robot teams, we present RoSSO, a Python package designed for solving Markov chain optimization problems. We exploit machine-learning techniques such as reverse-mode automatic differentiation and constraint parametrization to achieve superior efficiency compared to general-purpose nonlinear programming solvers. Additionally, we supplement a game-theoretic stochastic surveillance formulation in the literature with a novel greedy algorithm and multi-robot extension. We close with numerical results for a police district in downtown San Francisco that demonstrate RoSSO's capabilities on our new formulations and the prior work.

We present an approach to estimating camera rotation in crowded, real-world scenes from handheld monocular video. While camera rotation estimation is a well-studied problem, no previous methods exhibit both high accuracy and acceptable speed in this setting. Because the setting is not addressed well by other datasets, we provide a new dataset and benchmark, with high-accuracy, rigorously verified ground truth, on 17 video sequences. Methods developed for wide baseline stereo (e.g., 5-point methods) perform poorly on monocular video. On the other hand, methods used in autonomous driving (e.g., SLAM) leverage specific sensor setups, specific motion models, or local optimization strategies (lagging batch processing) and do not generalize well to handheld video. Finally, for dynamic scenes, commonly used robustification techniques like RANSAC require large numbers of iterations, and become prohibitively slow. We introduce a novel generalization of the Hough transform on SO(3) to efficiently and robustly find the camera rotation most compatible with optical flow. Among comparably fast methods, ours reduces error by almost 50\% over the next best, and is more accurate than any method, irrespective of speed. This represents a strong new performance point for crowded scenes, an important setting for computer vision. The code and the dataset are available at https://fabiendelattre.com/robust-rotation-estimation.

Efficient navigation in unknown and dynamic environments is crucial for expanding the application domain of mobile robots. The core challenge stems from the nonavailability of a feasible global path for guiding optimization-based local planners. As a result, existing local planners often get trapped in poor local minima. In this paper, we present a novel optimizer that can explore multiple homotopies to plan high-quality trajectories over long horizons while still being fast enough for real-time applications. We build on the gradient-free paradigm by augmenting the trajectory sampling strategy with a projection optimization that guides the samples toward a feasible region. As a result, our approach can recover from the frequently encountered pathological cases wherein all the sampled trajectories lie in the high-cost region. Furthermore, we also show that our projection optimization has a highly parallelizable structure that can be easily accelerated over GPUs. We push the state-of-the-art in the following respects. Over the navigation stack of the Robot Operating System (ROS), we show an improvement of 7-13% in success rate and up to two times in total travel time metric. On the same benchmarks and metrics, our approach achieves up to 44% improvement over MPPI and its recent variants. On simple point-to-point navigation tasks, our optimizer is up to two times more reliable than SOTA gradient-based solvers, as well as sampling-based approaches such as the Cross-Entropy Method (CEM) and VPSTO. Codes: https://github.com/fatemeh-rastgar/PRIEST

Weakly supervised learning aims to empower machine learning when the perfect supervision is unavailable, which has drawn great attention from researchers. Among various types of weak supervision, one of the most challenging cases is to learn from multiple unlabeled (U) datasets with only a little knowledge of the class priors, or U$^m$ learning for short. In this paper, we study the problem of building an AUC (area under ROC curve) optimization model from multiple unlabeled datasets, which maximizes the pairwise ranking ability of the classifier. We propose U$^m$-AUC, an AUC optimization approach that converts the U$^m$ data into a multi-label AUC optimization problem, and can be trained efficiently. We show that the proposed U$^m$-AUC is effective theoretically and empirically.