Search

The moving target traveling salesman problem with obstacles (MT-TSP-O) is a generalization of the traveling salesman problem (TSP) where, as its name suggests, the targets are moving. A solution to the MT-TSP-O is a trajectory that visits each moving target during a certain time window(s), and this trajectory avoids stationary obstacles. We assume each target moves at a constant velocity during each of its time windows. The agent has a speed limit, and this speed limit is no smaller than any target's speed. This paper presents the first complete algorithm for finding feasible solutions to the MT-TSP-O. Our algorithm builds a tree where the nodes are agent trajectories intercepting a unique sequence of targets within a unique sequence of time windows. We generate each of a parent node's children by extending the parent's trajectory to intercept one additional target, each child corresponding to a different choice of target and time window. This extension consists of planning a trajectory from the parent trajectory's final point in space-time to a moving target. To solve this point-to-moving-target subproblem, we define a novel generalization of a visibility graph called a moving target visibility graph (MTVG). Our overall algorithm is called MTVG-TSP. To validate MTVG-TSP, we test it on 570 instances with up to 30 targets. We implement a baseline method that samples trajectories of targets into points, based on prior work on special cases of the MT-TSP-O. MTVG-TSP finds feasible solutions in all cases where the baseline does, and when the sum of the targets' time window lengths enters a critical range, MTVG-TSP finds a feasible solution with up to 38 times less computation time., Comment: Accepted to WAFR 2024

Autonomous robotic search has important applications in robotics, such as the search for signs of life after a disaster. When \emph{a priori} information is available, for example in the form of a distribution, a planner can use that distribution to guide the search. Ergodic search is one method that uses the information distribution to generate a trajectory that minimizes the ergodic metric, in that it encourages the robot to spend more time in regions with high information and proportionally less time in the remaining regions. Unfortunately, prior works in ergodic search do not perform well in complex environments with obstacles such as a building's interior or a maze. To address this, our work presents a modified ergodic metric using the Laplace-Beltrami eigenfunctions to capture map geometry and obstacle locations within the ergodic metric. Further, we introduce an approach to generate trajectories that minimize the ergodic metric while guaranteeing obstacle avoidance using measure-preserving vector fields. Finally, we leverage the divergence-free nature of these vector fields to generate collision-free trajectories for multiple agents. We demonstrate our approach via simulations with single and multi-agent systems on maps representing interior hallways and long corridors with non-uniform information distribution. In particular, we illustrate the generation of feasible trajectories in complex environments where prior methods fail., Comment: 15 pages, accepted to DARS 2024

Multi-agent proximal policy optimization (MAPPO) has recently demonstrated state-of-the-art performance on challenging multi-agent reinforcement learning tasks. However, MAPPO still struggles with the credit assignment problem, wherein the sheer difficulty in ascribing credit to individual agents' actions scales poorly with team size. In this paper, we propose a multi-agent reinforcement learning algorithm that adapts recent developments in credit assignment to improve upon MAPPO. Our approach leverages partial reward decoupling (PRD), which uses a learned attention mechanism to estimate which of a particular agent's teammates are relevant to its learning updates. We use this estimate to dynamically decompose large groups of agents into smaller, more manageable subgroups. We empirically demonstrate that our approach, PRD-MAPPO, decouples agents from teammates that do not influence their expected future reward, thereby streamlining credit assignment. We additionally show that PRD-MAPPO yields significantly higher data efficiency and asymptotic performance compared to both MAPPO and other state-of-the-art methods across several multi-agent tasks, including StarCraft II. Finally, we propose a version of PRD-MAPPO that is applicable to \textit{shared} reward settings, where PRD was previously not applicable, and empirically show that this also leads to performance improvements over MAPPO., Comment: 20 pages, 5 figures, 12 tables, Reinforcement Learning Journal and Reinforcement Learning Conference 2024

This paper investigates a constrained inverse kinematic (IK) problem that seeks a feasible configuration of an articulated robot under various constraints such as joint limits and obstacle collision avoidance. Due to the high-dimensionality and complex constraints, this problem is often solved numerically via iterative local optimization. Classic local optimization methods take joint angles as the decision variable, which suffers from non-linearity caused by the trigonometric constraints. Recently, distance-based IK methods have been developed as an alternative approach that formulates IK as an optimization over the distances among points attached to the robot and the obstacles. Although distance-based methods have demonstrated unique advantages, they still suffer from low computational efficiency, since these approaches usually ignore the chain structure in the kinematics of serial robots. This paper proposes a new method called propagative distance optimization for constrained inverse kinematics (PDO-IK), which captures and leverages the chain structure in the distance-based formulation and expedites the optimization by computing forward kinematics and the Jacobian propagatively along the kinematic chain. Test results show that PDO-IK runs up to two orders of magnitude faster than the existing distance-based methods under joint limits constraints and obstacle avoidance constraints. It also achieves up to three times higher success rates than the conventional joint-angle-based optimization methods for IK problems. The high runtime efficiency of PDO-IK allows the real-time computation (10$-$1500 Hz) and enables a simulated humanoid robot with 19 degrees of freedom (DoFs) to avoid moving obstacles, which is otherwise hard to achieve with the baselines.

A conjecture of Rosenberger says that a group of the form $\langle x,y|x^p=y^q=W(x,y)^r=1\rangle$ (with $r>1$) is either virtually solvable or contains a non-abelian free subgroup. This note is an account of an attack on the conjecture in the case $(p,q,r)=(2,4,2)$. The results obtained are only partial, but nevertheless provide strong evidence in support of the conjecture in the case in question, in that the word $W$ in any counterexample is shown to satisfy some strong restrictions. The exponent-sums of $x$ and $y$ in $W$ must be even and odd respectively, while its free-product (or syllable) length must be at least 68. There is also a report of computer investigations which yield a stronger lower bound of 196 for the free-product length., Comment: 14 pages

In the realm of robotics, the quest for achieving real-world autonomy, capable of executing large-scale and long-term operations, has positioned place recognition (PR) as a cornerstone technology. Despite the PR community's remarkable strides over the past two decades, garnering attention from fields like computer vision and robotics, the development of PR methods that sufficiently support real-world robotic systems remains a challenge. This paper aims to bridge this gap by highlighting the crucial role of PR within the framework of Simultaneous Localization and Mapping (SLAM) 2.0. This new phase in robotic navigation calls for scalable, adaptable, and efficient PR solutions by integrating advanced artificial intelligence (AI) technologies. For this goal, we provide a comprehensive review of the current state-of-the-art (SOTA) advancements in PR, alongside the remaining challenges, and underscore its broad applications in robotics. This paper begins with an exploration of PR's formulation and key research challenges. We extensively review literature, focusing on related methods on place representation and solutions to various PR challenges. Applications showcasing PR's potential in robotics, key PR datasets, and open-source libraries are discussed. We also emphasizes our open-source package, aimed at new development and benchmark for general PR. We conclude with a discussion on PR's future directions, accompanied by a summary of the literature covered and access to our open-source library, available to the robotics community at: https://github.com/MetaSLAM/GPRS., Comment: 20 pages, 12 figures, under review

We present a fast trajectory optimization algorithm for the soft capture of uncooperative tumbling space objects. Our algorithm generates safe, dynamically feasible, and minimum-fuel trajectories for a six-degree-of-freedom servicing spacecraft to achieve soft capture (near-zero relative velocity at contact) between predefined locations on the servicer spacecraft and target body. We solve a convex problem by enforcing a convex relaxation of the field-of-view constraint, followed by a sequential convex program correcting the trajectory for collision avoidance. The optimization problems can be solved with a standard second-order cone programming solver, making the algorithm both fast and practical for implementation in flight software. We demonstrate the performance and robustness of our algorithm in simulation over a range of object tumble rates up to 10{\deg}/s., Comment: Accepted to ISpaRo24

Addressing the challenges related to data sparsity, cold-start problems, and diversity in recommendation systems is both crucial and demanding. Many current solutions leverage knowledge graphs to tackle these issues by combining both item-based and user-item collaborative signals. A common trend in these approaches focuses on improving ranking performance at the cost of escalating model complexity, reducing diversity, and complicating the task. It is essential to provide recommendations that are both personalized and diverse, rather than solely relying on achieving high rank-based performance, such as Click-through Rate, Recall, etc. In this paper, we propose a hybrid multi-task learning approach, training on user-item and item-item interactions. We apply item-based contrastive learning on descriptive text, sampling positive and negative pairs based on item metadata. Our approach allows the model to better understand the relationships between entities within the knowledge graph by utilizing semantic information from text. It leads to more accurate, relevant, and diverse user recommendations and a benefit that extends even to cold-start users who have few interactions with items. We perform extensive experiments on two widely used datasets to validate the effectiveness of our approach. Our findings demonstrate that jointly training user-item interactions and item-based signals using synopsis text is highly effective. Furthermore, our results provide evidence that item-based contrastive learning enhances the quality of entity embeddings, as indicated by metrics such as uniformity and alignment., Comment: Accepted at LREC-COLING 2024

This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once within their assigned time-windows, and returns to the depot. The formulation relies on the key idea that when the targets move along lines, their trajectories become convex sets within the space-time coordinate system. The problem then reduces to finding the shortest path within a graph of convex sets, subject to some speed constraints. We compare our formulation with the current state-of-the-art Mixed Integer Conic Program (MICP) solver for the MT-TSP. The experimental results show that our formulation outperforms the MICP for instances with up to 20 targets, with up to two orders of magnitude reduction in runtime, and up to a 60\% tighter optimality gap. We also show that the solution cost from the convex relaxation of our formulation provides significantly tighter lower bounds for the MT-TSP than the ones from the MICP., Comment: 7 pages, 4 figures

Trajectory optimization is a widely used technique in robot motion planning for letting the dynamics and constraints on the system shape and synthesize complex behaviors. Several previous works have shown its benefits in high-dimensional continuous state spaces and under differential constraints. However, long time horizons and planning around obstacles in non-convex spaces pose challenges in guaranteeing convergence or finding optimal solutions. As a result, discrete graph search planners and sampling-based planers are preferred when facing obstacle-cluttered environments. A recently developed algorithm called INSAT effectively combines graph search in the low-dimensional subspace and trajectory optimization in the full-dimensional space for global kinodynamic planning over long horizons. Although INSAT successfully reasoned about and solved complex planning problems, the numerous expensive calls to an optimizer resulted in large planning times, thereby limiting its practical use. Inspired by the recent work on edge-based parallel graph search, we present PINSAT, which introduces systematic parallelization in INSAT to achieve lower planning times and higher success rates, while maintaining significantly lower costs over relevant baselines. We demonstrate PINSAT by evaluating it on 6 DoF kinodynamic manipulation planning with obstacles., Comment: Under review

We are interested in studying sports with robots and starting with the problem of intercepting a projectile moving toward a robot manipulator equipped with a shield. To successfully perform this task, the robot needs to (i) detect the incoming projectile, (ii) predict the projectile's future motion, (iii) plan a minimum-time rapid trajectory that can evade obstacles and intercept the projectile, and (iv) execute the planned trajectory. These four steps must be performed under the manipulator's dynamic limits and extreme time constraints (<350ms in our setting) to successfully intercept the projectile. In addition, we want these trajectories to be smooth to reduce the robot's joint torques and the impulse on the platform on which it is mounted. To this end, we propose a kinodynamic motion planning framework that preprocesses smooth trajectories offline to allow real-time collision-free executions online. We present an end-to-end pipeline along with our planning framework, including perception, prediction, and execution modules. We evaluate our framework experimentally in simulation and show that it has a higher blocking success rate than the baselines. Further, we deploy our pipeline on a robotic system comprising an industrial arm (ABB IRB-1600) and an onboard stereo camera (ZED 2i), which achieves a 78% success rate in projectile interceptions., Comment: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) 2024

Multi-Agent Combinatorial Path Finding (MCPF) seeks collision-free paths for multiple agents from their initial to goal locations, while visiting a set of intermediate target locations in the middle of the paths. MCPF is challenging as it involves both planning collision-free paths for multiple agents and target sequencing, i.e., solving traveling salesman problems to assign targets to and find the visiting order for the agents. Recent work develops methods to address MCPF while minimizing the sum of individual arrival times at goals. Such a problem formulation may result in paths with different arrival times and lead to a long makespan, the maximum arrival time, among the agents. This paper proposes a min-max variant of MCPF, denoted as MCPF-max, that minimizes the makespan of the agents. While the existing methods (such as MS*) for MCPF can be adapted to solve MCPF-max, we further develop two new techniques based on MS* to defer the expensive target sequencing during planning to expedite the overall computation. We analyze the properties of the resulting algorithm Deferred MS* (DMS*), and test DMS* with up to 20 agents and 80 targets. We demonstrate the use of DMS* on differential-drive robots., Comment: 9 pages, 6 figures

Achieving high performance for Sparse MatrixMatrix Multiplication (SpMM) has received increasing research attention, especially on multi-core CPUs, due to the large input data size in applications such as graph neural networks (GNNs). Most existing solutions for SpMM computation follow the aheadof-time (AOT) compilation approach, which compiles a program entirely before it is executed. AOT compilation for SpMM faces three key limitations: unnecessary memory access, additional branch overhead, and redundant instructions. These limitations stem from the fact that crucial information pertaining to SpMM is not known until runtime. In this paper, we propose JITSPMM, a just-in-time (JIT) assembly code generation framework to accelerated SpMM computation on multi-core CPUs with SIMD extensions. First, JITSPMM integrates the JIT assembly code generation technique into three widely-used workload division methods for SpMM to achieve balanced workload distribution among CPU threads. Next, with the availability of runtime information, JITSPMM employs a novel technique, coarse-grain column merging, to maximize instruction-level parallelism by unrolling the performance-critical loop. Furthermore, JITSPMM intelligently allocates registers to cache frequently accessed data to minimizing memory accesses, and employs selected SIMD instructions to enhance arithmetic throughput. We conduct a performance evaluation of JITSPMM and compare it two AOT baselines. The first involves existing SpMM implementations compiled using the Intel icc compiler with auto-vectorization. The second utilizes the highly-optimized SpMM routine provided by Intel MKL. Our results show that JITSPMM provides an average improvement of 3.8x and 1.4x, respectively.

We introduce a new bounding approach called Continuity* (C*) that provides optimality guarantees to the Moving-Target Traveling Salesman Problem (MT-TSP). Our approach relies on relaxing the continuity constraints on the agent's tour. This is done by partitioning the targets' trajectories into small sub-segments and allowing the agent to arrive at any point in one of the sub-segments and depart from any point in the same sub-segment when visiting each target. This lets us pose the bounding problem as a Generalized Traveling Salesman Problem (GTSP) in a graph where the cost of traveling an edge requires us to solve a new problem called the Shortest Feasible Travel (SFT). We also introduce C*-lite, which follows the same approach as C*, but uses simple and easy to compute lower-bounds to the SFT. We first prove that the proposed algorithms provide lower bounds to the MT-TSP. We also provide computational results to corroborate the performance of C* and C*-lite for instances with up to 15 targets. For the special case where targets travel along lines, we compare our C* variants with the SOCP based method, which is the current state-of-the-art solver for MT-TSP. While the SOCP based method performs well for instances with 5 and 10 targets, C* outperforms the SOCP based method for instances with 15 targets. For the general case, on average, our approaches find feasible solutions within ~4% of the lower bounds for the tested instances., Comment: 17 pages, 12 figures

Segmenting a moving needle in ultrasound images is challenging due to the presence of artifacts, noise, and needle occlusion. This task becomes even more demanding in scenarios where data availability is limited. In this paper, we present a novel approach for needle segmentation for 2D ultrasound that combines classical Kalman Filter (KF) techniques with data-driven learning, incorporating both needle features and needle motion. Our method offers three key contributions. First, we propose a compatible framework that seamlessly integrates into commonly used encoder-decoder style architectures. Second, we demonstrate superior performance compared to recent state-of-the-art needle segmentation models using our novel convolutional neural network (CNN) based KF-inspired block, achieving a 15\% reduction in pixel-wise needle tip error and an 8\% reduction in length error. Third, to our knowledge we are the first to implement a learnable filter to incorporate non-linear needle motion for improving needle segmentation., Comment: 7 pages, 4 figures, accepted at ISBI 2024

We discover that many natural-language prompts can be replaced by corresponding prompts that are unintelligible to humans but that provably elicit similar behavior in language models. We call these prompts "evil twins" because they are obfuscated and uninterpretable (evil), but at the same time mimic the functionality of the original natural-language prompts (twins). Remarkably, evil twins transfer between models. We find these prompts by solving a maximum-likelihood problem which has applications of independent interest., Comment: Preprint. Under review

Modern cyber attackers use advanced zero-day exploits, highly targeted spear phishing, and other social engineering techniques to gain access and also use evasion techniques to maintain a prolonged presence within the victim network while working gradually towards the objective. To minimize the damage, it is necessary to detect these Advanced Persistent Threats as early in the campaign as possible. This paper proposes, Prov2Vec, a system for the continuous monitoring of enterprise host's behavior to detect attackers' activities. It leverages the data provenance graph built using system event logs to get complete visibility into the execution state of an enterprise host and the causal relationship between system entities. It proposes a novel provenance graph kernel to obtain the canonical representation of the system behavior, which is compared against its historical behaviors and that of other hosts to detect the deviation from the normality. These representations are used in several machine learning models to evaluate their ability to capture the underlying behavior of an endpoint host. We have empirically demonstrated that the provenance graph kernel produces a much more compact representation compared to existing methods while improving prediction ability.

We consider a search problem where a robot has one or more types of sensors, each suited to detecting different types of targets or target information. Often, information in the form of a distribution of possible target locations, or locations of interest, may be available to guide the search. When multiple types of information exist, then a distribution for each type of information must also exist, thereby making the search problem that uses these distributions to guide the search a multi-objective one. In this paper, we consider a multi-objective search problem when the cost to use a sensor is limited. To this end, we leverage the ergodic metric, which drives agents to spend time in regions proportional to the expected amount of information there. We define the multi-objective sparse sensing ergodic (MO-SS-E) metric in order to optimize when and where each sensor measurement should be taken while planning trajectories that balance the multiple objectives. We observe that our approach maintains coverage performance as the number of samples taken considerably degrades. Further empirical results on different multi-agent problem setups demonstrate the applicability of our approach for both homogeneous and heterogeneous multi-agent teams.

This paper considers a generalization of the Path Finding (PF) with refueling constraints referred to as the Refuelling Path Finding (RF-PF) problem. Just like PF, the RF-PF problem is defined over a graph, where vertices are gas stations with known fuel prices, and edge costs depend on the gas consumption between the corresponding vertices. RF-PF seeks a minimum-cost path from the start to the goal vertex for a robot with a limited gas tank and a limited number of refuelling stops. While RF-PF is polynomial-time solvable, it remains a challenge to quickly compute an optimal solution in practice since the robot needs to simultaneously determine the path, where to make the stops, and the amount to refuel at each stop. This paper develops a heuristic search algorithm called Refuel A* (RF-A* ) that iteratively constructs partial solution paths from the start to the goal guided by a heuristic function while leveraging dominance rules for state pruning during planning. RF-A* is guaranteed to find an optimal solution and runs more than an order of magnitude faster than the existing state of the art (a polynomial time algorithm) when tested in large city maps with hundreds of gas stations., Comment: 7 pages, 6 figures, ICRA 2024 submission, path planning, robotics

This paper addresses a Multi-Agent Collective Construction (MACC) problem that aims to build a three-dimensional structure comprised of cubic blocks. We use cube-shaped robots that can carry one cubic block at a time, and move forward, reverse, left, and right to an adjacent cell of the same height or climb up and down one cube height. To construct structures taller than one cube, the robots must build supporting stairs made of blocks and remove the stairs once the structure is built. Conventional techniques solve for the entire structure at once and quickly become intractable for larger workspaces and complex structures, especially in a multi-agent setting. To this end, we present a decomposition algorithm that computes valid substructures based on intrinsic structural dependencies. We use Mixed Integer Linear Programming (MILP) to solve for each of these substructures and then aggregate the solutions to construct the entire structure. Extensive testing on 200 randomly generated structures shows an order of magnitude improvement in the solution computation time compared to an MILP approach without decomposition. Additionally, compared to Reinforcement Learning (RL) based and heuristics-based approaches drawn from the literature, our solution indicates orders of magnitude improvement in the number of pick-up and drop-off actions required to construct a structure. Furthermore, we leverage the independence between substructures to detect which sub-structures can be built in parallel. With this parallelization technique, we illustrate a further improvement in the number of time steps required to complete building the structure. This work is a step towards applying multi-agent collective construction for real-world structures by significantly reducing solution computation time with a bounded increase in the number of time steps required to build the structure., Comment: Presented at the Multi-agent Path Finding Workshop at AAAI 2023