Pontryagin Neural Operator for Solving Parametric General-Sum Differential Games

The values of two-player general-sum differential games are viscosity solutions to Hamilton-Jacobi-Isaacs (HJI) equations. Value and policy approximations for such games suffer from the curse of dimensionality (CoD). Alleviating CoD through physics-informed neural networks (PINN) encounters convergence issues when value discontinuity is present due to state constraints. On top of these challenges, it is often necessary to learn generalizable values and policies across a parametric space of games, e.g., for game parameter inference when information is incomplete. To address these challenges, we propose in this paper a Pontryagin-mode neural operator that outperforms existing state-of-the-art (SOTA) on safety performance across games with parametric state constraints. Our key contribution is the introduction of a costate loss defined on the discrepancy between forward and backward costate rollouts, which are computationally cheap. We show that the discontinuity of costate dynamics (in the presence of state constraints) effectively enables the learning of discontinuous values, without requiring manually supervised data as suggested by the current SOTA. More importantly, we show that the close relationship between costates and policies makes the former critical in learning feedback control policies with generalizable safety performance.

Value Approximation for Two-Player General-Sum Differential Games with State Constraints

Solving Hamilton-Jacobi-Isaacs (HJI) PDEs enables equilibrial feedback control in two-player differential games, yet faces the curse of dimensionality (CoD). While physics-informed machine learning has been adopted to address CoD in solving PDEs, this method falls short in learning discontinuous solutions due to its sampling nature, leading to poor safety performance of the resulting controllers in robotics applications where values are discontinuous due to state or other temporal logic constraints. In this study, we explore three potential solutions to this problem: (1) a hybrid learning method that uses both equilibrium demonstrations and the HJI PDE, (2) a value-hardening method where a sequence of HJIs are solved with increasing Lipschitz constant on the constraint violation penalty, and (3) the epigraphical technique that lifts the value to a higher dimensional auxiliary state space where the value becomes continuous. Evaluations through 5D and 9D vehicle simulations and 13D drone simulations reveal that the hybrid method outperforms others in terms of generalization and safety performance.

Solving Two-Player General-Sum Games Between Swarms

Hamilton-Jacobi-Isaacs (HJI) PDEs are the governing equations for the two-player general-sum games. Unlike Reinforcement Learning (RL) methods, which are data-intensive methods for learning value function, learning HJ PDEs provide a guaranteed convergence to the Nash Equilibrium value of the game when it exists. However, a caveat is that solving HJ PDEs becomes intractable when the state dimension increases. To circumvent the curse of dimensionality (CoD), physics-informed machine learning methods with supervision can be used and have been shown to be effective in generating equilibrial policies in two-player general-sum games. In this work, we extend the existing work on agent-level two-player games to a two-player swarm-level game, where two sub-swarms play a general-sum game. We consider the \textit{Kolmogorov forward equation} as the dynamic model for the evolution of the densities of the swarms. Results show that policies generated from the physics-informed neural network (PINN) result in a higher payoff than a Nash Double Deep Q-Network (Nash DDQN) agent and have comparable performance with numerical solvers.

HAT: Hybrid Attention Transformer for Image Restoration

Transformer-based methods have shown impressive performance in image restoration tasks, such as image super-resolution and denoising. However, we find that these networks can only utilize a limited spatial range of input information through attribution analysis. This implies that the potential of Transformer is still not fully exploited in existing networks. In order to activate more input pixels for better restoration, we propose a new Hybrid Attention Transformer (HAT). It combines both channel attention and window-based self-attention schemes, thus making use of their complementary advantages. Moreover, to better aggregate the cross-window information, we introduce an overlapping cross-attention module to enhance the interaction between neighboring window features. In the training stage, we additionally adopt a same-task pre-training strategy to further exploit the potential of the model for further improvement. Extensive experiments have demonstrated the effectiveness of the proposed modules. We further scale up the model to show that the performance of the SR task can be greatly improved. Besides, we extend HAT to more image restoration applications, including real-world image super-resolution, Gaussian image denoising and image compression artifacts reduction. Experiments on benchmark and real-world datasets demonstrate that our HAT achieves state-of-the-art performance both quantitatively and qualitatively. Codes and models are publicly available at https://github.com/XPixelGroup/HAT.

SEAL: A Framework for Systematic Evaluation of Real-World Super-Resolution

Real-world Super-Resolution (real-SR) methods focus on dealing with diverse real-world images and have attracted increasing attention in recent years. The key idea is to use a complex and high-order degradation model to mimic real-world degradations. Although they have achieved impressive results in various scenarios, they are faced with the obstacle of evaluation. Currently, these methods are only assessed by their average performance on a small set of degradation cases randomly selected from a large space, which fails to provide a comprehensive understanding of their overall performance and often yields biased results. To overcome the limitation in evaluation, we propose SEAL, a framework for systematic evaluation of real-SR. In particular, we cluster the extensive degradation space to create a set of representative degradation cases, which serves as a comprehensive test set. Next, we propose a coarse-to-fine evaluation protocol to measure the distributed and relative performance of real-SR methods on the test set. The protocol incorporates two new metrics: acceptance rate (AR) and relative performance ratio (RPR), derived from an acceptance line and an excellence line. Under SEAL, we benchmark existing real-SR methods, obtain new observations and insights into their performance, and develop a new strong baseline. We consider SEAL as the first step towards creating an unbiased and comprehensive evaluation platform, which can promote the development of real-SR.

To Collide or Not To Collide -- Exploiting Passive Deformable Quadrotors for Contact-Rich Tasks

With an increase in aerial vehicle applications, passive deformable quadrotors are getting significant attention in the research community due to their potential to perform physical interaction tasks. Such quadrotors are capable of undergoing collisions, both planned and unplanned, which are harnessed to induce deformation and retain stability by dissipating collision energies. In this article, we utilize one such passive deforming quadrotor, XPLORER, to complete various contact-rich tasks by exploiting its compliant chassis via various impact-aware planning and control algorithms. At the core of these algorithms is a novel external wrench estimation technique developed specifically for the unique multi-linked structure of XPLORER's chassis. The external wrench information is then employed for designing interaction controllers to obtain three additional flight modes: static-wrench application, disturbance rejection and yielding to the disturbance. These modes are then incorporated into a novel online exploration scheme to enable navigation in unknown flight spaces with only tactile feedback and generate a map of the environment without requiring additional sensors. Experiments show the efficacy of this scheme to generate maps of the previously unexplored flight space with an accuracy of 96.72%. Finally, we develop a novel collision-aware trajectory planner (CATAAN) to generate minimum time maneuvers for waypoint tracking by integrating collision-induced state jumps for both elastic and inelastic cases. We experimentally validate that minimum time trajectories can be obtained with CATAAN leading to a 40.38% reduction of settling time accompanied by improved tracking performance of a root mean squared error in position within 0.5cm as compared to 3cm of conventional methods.

Recon: Reducing Conflicting Gradients from the Root for Multi-Task Learning

A fundamental challenge for multi-task learning is that different tasks may conflict with each other when they are solved jointly, and a cause of this phenomenon is conflicting gradients during optimization. Recent works attempt to mitigate the influence of conflicting gradients by directly altering the gradients based on some criteria. However, our empirical study shows that ``gradient surgery'' cannot effectively reduce the occurrence of conflicting gradients. In this paper, we take a different approach to reduce conflicting gradients from the root. In essence, we investigate the task gradients w.r.t. each shared network layer, select the layers with high conflict scores, and turn them to task-specific layers. Our experiments show that such a simple approach can greatly reduce the occurrence of conflicting gradients in the remaining shared layers and achieve better performance, with only a slight increase in model parameters in many cases. Our approach can be easily applied to improve various state-of-the-art methods including gradient manipulation methods and branched architecture search methods. Given a network architecture (e.g., ResNet18), it only needs to search for the conflict layers once, and the network can be modified to be used with different methods on the same or even different datasets to gain performance improvement. The source code is available at https://github.com/moukamisama/Recon.

Improving Responsiveness to Robots for Tacit Human-Robot Interaction via Implicit and Naturalistic Team Status Projection

Fluent human-human teaming is often characterized by tacit interaction without explicit communication. This is because explicit communication, such as language utterances and gestures, are inherently interruptive. On the other hand, tacit interaction requires team situation awareness (TSA) to facilitate, which often relies on explicit communication to maintain, creating a paradox. In this paper, we consider implicit and naturalistic team status projection for tacit human-robot interaction. Implicitness minimizes interruption while naturalness reduces cognitive demand, and they together improve responsiveness to robots. We introduce a novel process for such Team status Projection via virtual Shadows, or TPS. We compare our method with two baselines that use explicit projection for maintaining TSA. Results via human factors studies demonstrate that TPS provides a more fluent human-robot interaction experience by significantly improving human responsiveness to robots in tacit teaming scenarios, which suggests better TSA. Participants acknowledged robots implementing TPS as more acceptable as a teammate and favorable. Simultaneously, we demonstrate that TPS is comparable to, and sometimes better than, the best-performing baseline in maintaining accurate TSA

Configuration Tracking Control of a Multi-Segment Soft Robotic Arm Using a Cosserat Rod Model

Controlling soft continuum robotic arms is challenging due to their hyper-redundancy and dexterity. In this paper we demonstrate, for the first time, closed-loop control of the configuration space variables of a soft robotic arm, composed of independently controllable segments, using a Cosserat rod model of the robot and the distributed sensing and actuation capabilities of the segments. Our controller solves the inverse dynamic problem by simulating the Cosserat rod model in MATLAB using a computationally efficient numerical solution scheme, and it applies the computed control output to the actual robot in real time. The position and orientation of the tip of each segment are measured in real time, while the remaining unknown variables that are needed to solve the inverse dynamics are estimated simultaneously in the simulation. We implement the controller on a multi-segment silicone robotic arm with pneumatic actuation, using a motion capture system to measure the segments' positions and orientations. The controller is used to reshape the arm into configurations that are achieved through different combinations of bending and extension deformations in 3D space. The resulting tracking performance indicates the effectiveness of the controller and the accuracy of the simulated Cosserat rod model that is used to estimate the unmeasured variables.

Adaptive Attitude Control for Foldable Quadrotors

Recent quadrotor vehicles transcended conventional designs, emphasizing more on foldable and reconfigurable bodies. However, the state of the art still focuses on the mechanical feasibility of such designs with limited discussions on the tracking performance of the vehicle during configuration switching. In this paper, we propose a complete control and planning framework for attitude tracking during configuration switching and curbs any switch-based disturbances, which can lead to violation of safety constraints and cause crashes. The control framework includes a morphology-aware adaptive controller with a estimator to account for parameter variation and a minimum-jerk trajectory planner to achieve stable flights while switching. Stability analysis for attitude tracking is presented by employing the theory of switched systems and simulation results validate the proposed framework for a foldable quadrotor's flight through a passageway.