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Motion prediction for traffic participants is essential for a safe and robust automated driving system, especially in cluttered urban environments. However, it is highly challenging due to the complex road topology as well as the uncertain intentions of the other agents. In this paper, we present a graph-based trajectory prediction network named the Dual Scale Predictor (DSP), which encodes both the static and dynamical driving context in a hierarchical manner. Different from methods based on a rasterized map or sparse lane graph, we consider the driving context as a graph with two layers, focusing on both geometrical and topological features. Graph neural networks (GNNs) are applied to extract features with different levels of granularity, and features are subsequently aggregated with attention-based inter-layer networks, realizing better local-global feature fusion. Following the recent goal-driven trajectory prediction pipeline, goal candidates with high likelihood for the target agent are extracted, and predicted trajectories are generated conditioned on these goals. Thanks to the proposed dual-scale context fusion network, our DSP is able to generate accurate and human-like multi-modal trajectories. We evaluate the proposed method on the large-scale Argoverse motion forecasting benchmark, and it achieves promising results, outperforming the recent state-of-the-art methods.

In recent years, deep learning technology has been used to solve partial differential equations (PDEs), among which the physics-informed neural networks (PINNs) emerges to be a promising method for solving both forward and inverse PDE problems. PDEs with a point source that is expressed as a Dirac delta function in the governing equations are mathematical models of many physical processes. However, they cannot be solved directly by conventional PINNs method due to the singularity brought by the Dirac delta function. We propose a universal solution to tackle this problem with three novel techniques. Firstly the Dirac delta function is modeled as a continuous probability density function to eliminate the singularity; secondly a lower bound constrained uncertainty weighting algorithm is proposed to balance the PINNs losses between point source area and other areas; and thirdly a multi-scale deep neural network with periodic activation function is used to improve the accuracy and convergence speed of the PINNs method. We evaluate the proposed method with three representative PDEs, and the experimental results show that our method outperforms existing deep learning-based methods with respect to the accuracy, the efficiency and the versatility.

We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural features of the system. We introduce approaches that incorporate regularization together with prudent selection of interpolation data. We focus on linear time-invariant systems and present a systematic treatment of a variety of model classes that include combinations of index-$1$ and index-$2$ systems, describing in particular how constraints may be represented in the transfer function and then preserved with interpolatory methods. We propose an algorithm to generate effective interpolation data and illustrate its effectiveness via two numerical examples.

Online 3-dimensional bin packing problem (O3D-BPP) is getting renewed prominence due to the industrial automation brought by Industry 4.0. However, due to limited attention in the past and its challenging nature, a good approximate algorithm is in scarcity as compared to 1D or 2D problems. This paper considers real-time O$3$D-BPP of cuboidal boxes with partial information (look-ahead) in an automated robotic sorting center. We present two rolling-horizon mixed-integer linear programming (MILP) cum-heuristic based algorithms: MPack (for bench-marking) and MPackLite (for real-time deployment). Additionally, we present a framework OPack that adapts and improves the performance of BP heuristics by utilizing information in an online setting with a look-ahead. We then perform a comparative analysis of BP heuristics (with and without OPack), MPack, and MPackLite on synthetic and industry provided data with increasing look-ahead. MPackLite and the baseline heuristics perform within bounds of robot operations and thus, can be used in real-time.

Deep learning-based models, such as recurrent neural networks (RNNs), have been applied to various sequence learning tasks with great success. Following this, these models are increasingly replacing classic approaches in object tracking applications for motion prediction. On the one hand, these models can capture complex object dynamics with less modeling required, but on the other hand, they depend on a large amount of training data for parameter tuning. Towards this end, we present an approach for generating synthetic trajectory data of unmanned-aerial-vehicles (UAVs) in image space. Since UAVs, or rather quadrotors are dynamical systems, they can not follow arbitrary trajectories. With the prerequisite that UAV trajectories fulfill a smoothness criterion corresponding to a minimal change of higher-order motion, methods for planning aggressive quadrotors flights can be utilized to generate optimal trajectories through a sequence of 3D waypoints. By projecting these maneuver trajectories, which are suitable for controlling quadrotors, to image space, a versatile trajectory data set is realized. To demonstrate the applicability of the synthetic trajectory data, we show that an RNN-based prediction model solely trained on the generated data can outperform classic reference models on a real-world UAV tracking dataset. The evaluation is done on the publicly available ANTI-UAV dataset.

This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise condition numbers of the TLSE problem are derived. Computable expressions and upper bounds for these condition numbers are also given to avoid the costly Kronecker product-based operations. The results unify the ones for the TLS problem. For TLSE problems with equilibratory input data, numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, mixed and componentwise condition numbers-based estimates are much tighter.

Road networks exist in the form of polylines with attributes within the GIS databases. Such a representation renders the geographic data impracticable for 3D road traffic simulation. In this work, we propose a method to transform raw GIS data into a realistic, operational model for real-time road traffic simulation. For instance, the proposed raw to simulation ready data transformation is achieved through several curvature estimation, interpolation/approximation, and clustering schemes. The obtained results show the performance of our approach and prove its adequacy to real traffic simulation scenario as can be seen in this video 1 .

Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we make an attempt along this line by reformulating the training procedure from the trajectory optimization perspective. We first show that most widely-used algorithms for training DNNs can be linked to the Differential Dynamic Programming (DDP), a celebrated second-order trajectory optimization algorithm rooted in the Approximate Dynamic Programming. In this vein, we propose a new variant of DDP that can accept batch optimization for training feedforward networks, while integrating naturally with the recent progress in curvature approximation. The resulting algorithm features layer-wise feedback policies which improve convergence rate and reduce sensitivity to hyper-parameter over existing methods. We show that the algorithm is competitive against state-ofthe-art first and second order methods. Our work opens up new avenues for principled algorithmic design built upon the optimal control theory.

We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given distribution, only by observing the reward signals and following feasibility rules. Our model represents a parameterized stochastic policy, and by applying a policy gradient algorithm to optimize its parameters, the trained model produces the solution as a sequence of consecutive actions in real time, without the need to re-train for every new problem instance. On capacitated VRP, our approach outperforms classical heuristics and Google's OR-Tools on medium-sized instances in solution quality with comparable computation time (after training). We demonstrate how our approach can handle problems with split delivery and explore the effect of such deliveries on the solution quality. Our proposed framework can be applied to other variants of the VRP such as the stochastic VRP, and has the potential to be applied more generally to combinatorial optimization problems.

Deep reinforcement learning (RL) methods generally engage in exploratory behavior through noise injection in the action space. An alternative is to add noise directly to the agent's parameters, which can lead to more consistent exploration and a richer set of behaviors. Methods such as evolutionary strategies use parameter perturbations, but discard all temporal structure in the process and require significantly more samples. Combining parameter noise with traditional RL methods allows to combine the best of both worlds. We demonstrate that both off- and on-policy methods benefit from this approach through experimental comparison of DQN, DDPG, and TRPO on high-dimensional discrete action environments as well as continuous control tasks. Our results show that RL with parameter noise learns more efficiently than traditional RL with action space noise and evolutionary strategies individually.