We propose a novel and efficient lifting approach for the optimal control of rigid-body systems with contacts to improve the convergence properties of Newton-type methods. To relax the high nonlinearity, we consider the state, acceleration, contact forces, and control input torques, as optimization variables and the inverse dynamics and acceleration constraints on the contact frames as equality constraints. We eliminate the update of the acceleration, contact forces, and their dual variables from the linear equation to be solved in each Newton-type iteration in an efficient manner. As a result, the computational cost per Newton-type iteration is almost identical to that of the conventional non-lifted Newton-type iteration that embeds contact dynamics in the state equation. We conducted numerical experiments on the whole-body optimal control of various quadrupedal gaits subject to the friction cone constraints considered in interior-point methods and demonstrated that the proposed method can significantly increase the convergence speed to more than twice that of the conventional non-lifted approach.
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Graph Pattern Mining (GPM) is an important, rapidly evolving, and computation demanding area. GPM computation relies on subgraph enumeration, which consists in extracting subgraphs that match a given property from an input graph. Graphics Processing Units (GPUs) have been an effective platform to accelerate applications in many areas. However, the irregularity of subgraph enumeration makes it challenging for efficient execution on GPU due to typical uncoalesced memory access, divergence, and load imbalance. Unfortunately, these aspects have not been fully addressed in previous work. Thus, this work proposes novel strategies to design and implement subgraph enumeration efficiently on GPU. We support a depth-first search style search (DFS-wide) that maximizes memory performance while providing enough parallelism to be exploited by the GPU, along with a warp-centric design that minimizes execution divergence and improves utilization of the computing capabilities. We also propose a low-cost load balancing layer to avoid idleness and redistribute work among thread warps in a GPU. Our strategies have been deployed in a system named DuMato, which provides a simple programming interface to allow efficient implementation of GPM algorithms. Our evaluation has shown that DuMato is often an order of magnitude faster than state-of-the-art GPM systems and can mine larger subgraphs (up to 12 vertices).
Motion planning and control in autonomous car racing are one of the most challenging and safety-critical tasks due to high speed and dynamism. The lower-level control nodes are expected to be highly optimized due to resource constraints of onboard embedded processing units, although there are strict latency requirements. Some of these guarantees can be provided at the application level, such as using ROS2's Real-Time executors. However, the performance can be far from satisfactory as many modern control algorithms (such as Model Predictive Control) rely on solving complicated online optimization problems at each iteration. In this paper, we present a simple yet effective multi-threading technique to optimize the throughput of online-control algorithms for resource-constrained autonomous racing platforms. We achieve this by maintaining a systematic pool of worker threads solving the optimization problem in parallel which can improve the system performance by reducing latency between control input commands. We further demonstrate the effectiveness of our method using the Model Predictive Contouring Control (MPCC) algorithm running on Nvidia's Xavier AGX platform.
Temporally consistent depth estimation is crucial for online applications such as augmented reality. While stereo depth estimation has received substantial attention as a promising way to generate 3D information, there is relatively little work focused on maintaining temporal stability. Indeed, based on our analysis, current techniques still suffer from poor temporal consistency. Stabilizing depth temporally in dynamic scenes is challenging due to concurrent object and camera motion. In an online setting, this process is further aggravated because only past frames are available. We present a framework named Consistent Online Dynamic Depth (CODD) to produce temporally consistent depth estimates in dynamic scenes in an online setting. CODD augments per-frame stereo networks with novel motion and fusion networks. The motion network accounts for dynamics by predicting a per-pixel SE3 transformation and aligning the observations. The fusion network improves temporal depth consistency by aggregating the current and past estimates. We conduct extensive experiments and demonstrate quantitatively and qualitatively that CODD outperforms competing methods in terms of temporal consistency and performs on par in terms of per-frame accuracy.
The closure principle is fundamental in multiple testing and has been used to derive many efficient procedures with familywise error rate control. However, it is often not suitable for modern research, as more flexible multiple testing settings are considered where not all hypotheses are known at the beginning of the evaluation. In this paper, we focus on online multiple testing where a possibly infinite sequence of hypotheses is tested over time. At each step, it must be decided on the current hypothesis without having any information about the hypotheses that have not been tested yet. Our main contribution is a new online closure principle which ensures that the resulting closed procedure can be applied in the online setting. We prove that any familywise error rate (FWER) controlling online procedure can be derived by this online closure principle. In addition, we demonstrate how short-cuts of these online closed procedures can be obtained under a suitable consonance property and apply the results in order to construct new online multiple testing methods. Finally, the new online closure principle is used to derive an improvement of the currently most promising online procedure with FWER control, the ADDIS-Spending under local dependence.
To control humanoid robots, the reference pose of end effector(s) is planned in task space, then mapped into the reference joints by IK. By viewing that problem as approximate quadratic programming (QP), recent QP solvers can be applied to solve it precisely, but iterative numerical IK solvers based on Jacobian are still in high demand due to their low computational cost. However, the conventional Jacobian-based IK usually clamps the obtained joints during iteration according to the constraints in practice, causing numerical instability due to non-smoothed objective function. To alleviate the clamping problem, this study explicitly considers the joint constraints, especially the box constraints in this paper, inside the new IK solver. Specifically, instead of clamping, a mirror descent (MD) method with box-constrained real joint space and no-constrained mirror space is integrated with the Jacobian-based IK, so-called MD-IK. In addition, to escape local optima nearly on the boundaries of constraints, a heuristic technique, called $\epsilon$-clamping, is implemented as margin in software level. Finally, to increase convergence speed, the acceleration method for MD is integrated assuming continuity of solutions at each time. As a result, the accelerated MD-IK achieved more stable and enough fast tracking performance compared to the conventional IK solvers. The low computational cost of the proposed method mitigated the time delay until the solution is obtained in real-time humanoid gait control, achieving a more stable gait.
Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the linear system is frequently approximated through so-called mass lumping, which consists in replacing the mass matrix by some diagonal approximation. Mass lumping has been widely used in engineering practice for decades already and has a sound mathematical theory supporting it for finite element methods using the classical Lagrange basis. However, the theory for more general basis functions is still missing. Our paper partly addresses this shortcoming. Some special and practically relevant properties of lumped mass matrices are proved and we discuss how these properties naturally extend to banded and Kronecker product matrices whose structure allows to solve linear systems very efficiently. Our theoretical results are applied to isogeometric discretizations but are not restricted to them.
Simulating rigid collisions among arbitrary shapes is notoriously difficult due to complex geometry and the strong non-linearity of the interactions. While graph neural network (GNN)-based models are effective at learning to simulate complex physical dynamics, such as fluids, cloth and articulated bodies, they have been less effective and efficient on rigid-body physics, except with very simple shapes. Existing methods that model collisions through the meshes' nodes are often inaccurate because they struggle when collisions occur on faces far from nodes. Alternative approaches that represent the geometry densely with many particles are prohibitively expensive for complex shapes. Here we introduce the Face Interaction Graph Network (FIGNet) which extends beyond GNN-based methods, and computes interactions between mesh faces, rather than nodes. Compared to learned node- and particle-based methods, FIGNet is around 4x more accurate in simulating complex shape interactions, while also 8x more computationally efficient on sparse, rigid meshes. Moreover, FIGNet can learn frictional dynamics directly from real-world data, and can be more accurate than analytical solvers given modest amounts of training data. FIGNet represents a key step forward in one of the few remaining physical domains which have seen little competition from learned simulators, and offers allied fields such as robotics, graphics and mechanical design a new tool for simulation and model-based planning.
In this paper, we consider the problem where a drone has to collect semantic information to classify multiple moving targets. In particular, we address the challenge of computing control inputs that move the drone to informative viewpoints, position and orientation, when the information is extracted using a "black-box" classifier, e.g., a deep learning neural network. These algorithms typically lack of analytical relationships between the viewpoints and their associated outputs, preventing their use in information-gathering schemes. To fill this gap, we propose a novel attention-based architecture, trained via Reinforcement Learning (RL), that outputs the next viewpoint for the drone favoring the acquisition of evidence from as many unclassified targets as possible while reasoning about their movement, orientation, and occlusions. Then, we use a low-level MPC controller to move the drone to the desired viewpoint taking into account its actual dynamics. We show that our approach not only outperforms a variety of baselines but also generalizes to scenarios unseen during training. Additionally, we show that the network scales to large numbers of targets and generalizes well to different movement dynamics of the targets.
A platoon refers to a group of vehicles traveling together in very close proximity. It has received significant attention from the autonomous vehicle research community due to its strong potential to significantly enhance fuel efficiency, driving safety, and driver comfort. Despite these advantages, recent research has revealed a detrimental effect of the extremely small intra-platoon gap on traffic flow for highway on-ramp merging. While existing control-based methods allow for adaptation of the intra-platoon gap to improve traffic flow, making an optimal control decision under the complex dynamics of traffic conditions remains a significant challenge due to the massive computational complexity. To this end, we present the design, implementation, and evaluation of a novel reinforcement learning framework that adaptively adjusts the intra-platoon gap of an individual platoon member to maximize traffic flow in response to dynamically changing, complex traffic conditions for highway on-ramp merging. The state space of the framework is carefully designed in consultation with the transportation literature to incorporate critical traffic parameters relevant to merging efficiency. A deep deterministic policy gradient algorithm is adopted to account for the continuous action space to ensure precise and continuous adjustment of the intra-platoon gap. An extensive simulation study demonstrates the effectiveness of the reinforcement learning-based approach for significantly improving traffic flow in various highway merging scenarios.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
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