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Automated vehicles require the ability to cooperate with humans for smooth integration into today's traffic. While the concept of cooperation is well known, developing a robust and efficient cooperative trajectory planning method is still a challenge. One aspect of this challenge is the uncertainty surrounding the state of the environment due to limited sensor accuracy. This uncertainty can be represented by a Partially Observable Markov Decision Process. Our work addresses this problem by extending an existing cooperative trajectory planning approach based on Monte Carlo Tree Search for continuous action spaces. It does so by explicitly modeling uncertainties in the form of a root belief state, from which start states for trees are sampled. After the trees have been constructed with Monte Carlo Tree Search, their results are aggregated into return distributions using kernel regression. We apply two risk metrics for the final selection, namely a Lower Confidence Bound and a Conditional Value at Risk. It can be demonstrated that the integration of risk metrics in the final selection policy consistently outperforms a baseline in uncertain environments, generating considerably safer trajectories.

Free-space-oriented roadmaps typically generate a series of convex geometric primitives, which constitute the safe region for motion planning. However, a static environment is assumed for this kind of roadmap. This assumption makes it unable to deal with dynamic obstacles and limits its applications. In this paper, we present a dynamic free-space roadmap, which provides feasible spaces and a navigation graph for safe quadrotor motion planning. Our roadmap is constructed by continuously seeding and extracting free regions in the environment. In order to adapt our map to environments with dynamic obstacles, we incrementally decompose the polyhedra intersecting with obstacles into obstacle-free regions, while the graph is also updated by our well-designed mechanism. Extensive simulations and real-world experiments demonstrate that our method is practically applicable and efficient.

For autonomous quadruped robot navigation in various complex environments, a typical SOTA system is composed of four main modules -- mapper, global planner, local planner, and command-tracking controller -- in a hierarchical manner. In this paper, we build a robust and safe local planner which is designed to generate a velocity plan to track a coarsely planned path from the global planner. Previous works used waypoint-based methods (e.g. Proportional-Differential control and pure pursuit) which simplify the path tracking problem to local point-goal navigation. However, they suffer from frequent collisions in geometrically complex and narrow environments because of two reasons; the global planner uses a coarse and inaccurate model and the local planner is unable to track the global plan sufficiently well. Currently, deep learning methods are an appealing alternative because they can learn safety and path feasibility from experience more accurately. However, existing deep learning methods are not capable of planning for a long horizon. In this work, we propose a learning-based fully autonomous navigation framework composed of three innovative elements: a learned forward dynamics model (FDM), an online sampling-based model-predictive controller, and an informed trajectory sampler (ITS). Using our framework, a quadruped robot can autonomously navigate in various complex environments without a collision and generate a smoother command plan compared to the baseline method. Furthermore, our method can reactively handle unexpected obstacles on the planned path and avoid them. Project page //awesomericky.github.io/projects/FDM_ITS_navigation/.

Recent work has demonstrated that motion planners' performance can be significantly improved by retrieving past experiences from a database. Typically, the experience database is queried for past similar problems using a similarity function defined over the motion planning problems. However, to date, most works rely on simple hand-crafted similarity functions and fail to generalize outside their corresponding training dataset. To address this limitation, we propose (FIRE), a framework that extracts local representations of planning problems and learns a similarity function over them. To generate the training data we introduce a novel self-supervised method that identifies similar and dissimilar pairs of local primitives from past solution paths. With these pairs, a Siamese network is trained with the contrastive loss and the similarity function is realized in the network's latent space. We evaluate FIRE on an 8-DOF manipulator in five categories of motion planning problems with sensed environments. Our experiments show that FIRE retrieves relevant experiences which can informatively guide sampling-based planners even in problems outside its training distribution, outperforming other baselines.

In this paper, we consider the challenging task of simultaneously locating and recovering multiple hands from single 2D image. Previous studies either focus on single hand reconstruction or solve this problem in a multi-stage way. Moreover, the conventional two-stage pipeline firstly detects hand areas, and then estimates 3D hand pose from each cropped patch. To reduce the computational redundancy in preprocessing and feature extraction, we propose a concise but efficient single-stage pipeline. Specifically, we design a multi-head auto-encoder structure for multi-hand reconstruction, where each head network shares the same feature map and outputs the hand center, pose and texture, respectively. Besides, we adopt a weakly-supervised scheme to alleviate the burden of expensive 3D real-world data annotations. To this end, we propose a series of losses optimized by a stage-wise training scheme, where a multi-hand dataset with 2D annotations is generated based on the publicly available single hand datasets. In order to further improve the accuracy of the weakly supervised model, we adopt several feature consistency constraints in both single and multiple hand settings. Specifically, the keypoints of each hand estimated from local features should be consistent with the re-projected points predicted from global features. Extensive experiments on public benchmarks including FreiHAND, HO3D, InterHand2.6M and RHD demonstrate that our method outperforms the state-of-the-art model-based methods in both weakly-supervised and fully-supervised manners.

We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modelling poro- and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in space and time with inf-sup stable pairs of finite elements for the spatial approximation of the unknowns are investigated. Optimal order error estimates of energy-type are proven. Superconvergence at the time nodes is addressed briefly. The error analysis can be extended to discontinuous and enriched Galerkin space discretizations. The error estimates are confirmed by numerical experiments.

Multi-scale problems, where variables of interest evolve in different time-scales and live in different state-spaces. can be found in many fields of science. Here, we introduce a new recursive methodology for Bayesian inference that aims at estimating the static parameters and tracking the dynamic variables of these kind of systems. Although the proposed approach works in rather general multi-scale systems, for clarity we analyze the case of a heterogeneous multi-scale model with 3 time-scales (static parameters, slow dynamic state variables and fast dynamic state variables). The proposed scheme, based on nested filtering methodology of P\'erez-Vieites et al. (2018), combines three intertwined layers of filtering techniques that approximate recursively the joint posterior probability distribution of the parameters and both sets of dynamic state variables given a sequence of partial and noisy observations. We explore the use of sequential Monte Carlo schemes in the first and second layers while we use an unscented Kalman filter to obtain a Gaussian approximation of the posterior probability distribution of the fast variables in the third layer. Some numerical results are presented for a stochastic two-scale Lorenz 96 model with unknown parameters.

The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory.

5G applications have become increasingly popular in recent years as the spread of fifth-generation (5G) network deployment has grown. For vehicular networks, mmWave band signals have been well studied and used for communication and sensing. In this work, we propose a new dynamic ray tracing algorithm that exploits spatial and temporal coherence. We evaluate the performance by comparing the results on typical vehicular communication scenarios with GEMV^2, which uses a combination of deterministic and stochastic models, and WinProp, which utilizes the deterministic model for simulations with given environment information. We also compare the performance of our algorithm on complex, urban models and observe a reduction in computation time by 36% compared to GEMV^2 and by 30% compared to WinProp, while maintaining similar prediction accuracy.

Recently, deep multiagent reinforcement learning (MARL) has become a highly active research area as many real-world problems can be inherently viewed as multiagent systems. A particularly interesting and widely applicable class of problems is the partially observable cooperative multiagent setting, in which a team of agents learns to coordinate their behaviors conditioning on their private observations and commonly shared global reward signals. One natural solution is to resort to the centralized training and decentralized execution paradigm. During centralized training, one key challenge is the multiagent credit assignment: how to allocate the global rewards for individual agent policies for better coordination towards maximizing system-level's benefits. In this paper, we propose a new method called Q-value Path Decomposition (QPD) to decompose the system's global Q-values into individual agents' Q-values. Unlike previous works which restrict the representation relation of the individual Q-values and the global one, we leverage the integrated gradient attribution technique into deep MARL to directly decompose global Q-values along trajectory paths to assign credits for agents. We evaluate QPD on the challenging StarCraft II micromanagement tasks and show that QPD achieves the state-of-the-art performance in both homogeneous and heterogeneous multiagent scenarios compared with existing cooperative MARL algorithms.