Autonomous drone pursuit requires not only detecting drones but also predicting their trajectories in a manner that enables kinematically feasible interception. Existing tracking methods optimize for prediction accuracy but ignore pursuit feasibility, resulting in trajectories that are physically impossible to intercept 99.9% of the time. We propose Perception-to-Pursuit (P2P), a track-centric temporal reasoning framework that bridges detection and actionable pursuit planning. Our method represents drone motion as compact 8-dimensional tokens capturing velocity, acceleration, scale, and smoothness, enabling a 12-frame causal transformer to reason about future behavior. We introduce the Intercept Success Rate (ISR) metric to measure pursuit feasibility under realistic interceptor constraints. Evaluated on the Anti-UAV-RGBT dataset with 226 real drone sequences, P2P achieves 28.12 pixel average displacement error and 0.597 ISR, representing a 77% improvement in trajectory prediction and 597x improvement in pursuit feasibility over tracking-only baselines, while maintaining perfect drone classification accuracy (100%). Our work demonstrates that temporal reasoning over motion patterns
Scientists do not merely choose to accept fully formed theories, they also have to decide which models to work on before they are fully developed and tested. Since decisive empirical evidence in favour of a model will not yet have been gathered, other criteria must play determining roles. I examine the case of modern high-energy physics where the experimental context that once favoured the pursuit of beautiful, simple, and general theories now favours the pursuit of models that are ad hoc, narrow in scope, and complex; in short, ugly models. The lack of new discoveries since the Higgs boson, together with the lack of a new higher energy collider, has left searches for new physics conceptually and empirically wide open. Physicists must make use of the experiment at hand while also creatively exploring alternatives that have not yet been explored. This encourages the pursuit of models that have at least one of two key features: i) they take radically novel approaches, or ii) are easily testable. I present four cases, neutralino dark matter, the relaxion, repulsive gravity, and models of lepton flavour universality violation, and show that even if they do not exhibit traditional epist
This paper studies a multiplayer reach-avoid differential game in the presence of general polygonal obstacles that block the players' motions. The pursuers cooperate to protect a convex region from the evaders who try to reach the region. We propose a multiplayer onsite and close-to-goal (MOCG) pursuit strategy that can tell and achieve an increasing lower bound on the number of guaranteed defeated evaders. This pursuit strategy fuses the subgame outcomes for multiple pursuers against one evader with hierarchical optimal task allocation in the receding-horizon manner. To determine the qualitative subgame outcomes that who is the game winner, we construct three pursuit winning regions and strategies under which the pursuers guarantee to win against the evader, regardless of the unknown evader strategy. First, we utilize the expanded Apollonius circles and propose the onsite pursuit winning that achieves the capture in finite time. Second, we introduce convex goal-covering polygons (GCPs) and propose the close-to-goal pursuit winning for the pursuers whose visibility region contains the whole protected region, and the goal-visible property will be preserved afterwards. Third, we empl
Basis pursuit is the problem of finding a vector with smallest $\ell_1$-norm among the solutions of a given linear system of equations. It is a well-known convex relaxation of the sparse affine feasibility problem, where sparse solutions to underdetermined systems are sought. Since basis pursuit admits a linear programming reformulation, standard LP solvers are directly applicable. We instead address the basis pursuit directly in its $\ell_1$-minimization form, without LP reformulation, via a scheme that uses alternating projections in its subproblems. These subproblems are designed to be inconsistent in the sense that they relate to two non-intersecting sets. Recently in [R. Behling, Y. Bello-Cruz and L.-R. Santos, SIAM J. Optim., 31 (2021), pp. 2863-2892], inconsistency coming from infeasibility has been shown to accelerate convergence of alternating projections. We deliberately enforce this inconsistency by constructing subproblems whose feasible sets are disjoint by design. We prove that the resulting $\ell_1$-radii converge linearly to the optimal value, and that when the solution is unique, all generated sequences converge linearly to it at a rate governed by a natural error
Greedy first-order methods, such as coordinate descent with Gauss-Southwell rule or matching pursuit, have become popular in optimization due to their natural tendency to propose sparse solutions and their refined convergence guarantees. In this work, we propose a principled approach to generating (regularized) matching pursuit algorithms adapted to the geometry of the problem at hand, as well as their convergence guarantees. Building on these results, we derive approximate convergence guarantees and describe a transition phenomenon in the convergence of (regularized) matching pursuit from underparametrized to overparametrized models.
A greedy pursuit strategy which finds a common basis for approximating a set of similar signals is proposed. The strategy extends the Optimized Orthogonal Matching Pursuit approach to selecting the subspace containing the approximation of all the signals in the set. The method, called Simultaneous Optimized Orthogonal Matching Pursuit, is stepwise optimal in the sense of minimizing at each iteration the mean error norm of the joint approximation. When applied to compression of electrocardiograms, significant gains over other transformation based compression techniques are demonstrated on the MIT-BIH Arrhythmia dataset.
The accelerated deployment of service robots have spawned a number of algorithm variations to better handle real-world conditions. Many local trajectory planning techniques have been deployed on practical robot systems successfully. While most formulations of Dynamic Window Approach and Model Predictive Control can progress along paths and optimize for additional criteria, the use of pure path tracking algorithms is still commonplace. Decades later, Pure Pursuit and its variants continues to be one of the most commonly utilized classes of local trajectory planners. However, few Pure Pursuit variants have been proposed with schema for variable linear velocities - they either assume a constant velocity or fails to address the point at all. This paper presents a variant of Pure Pursuit designed with additional heuristics to regulate linear velocities, built atop the existing Adaptive variant. The Regulated Pure Pursuit algorithm makes incremental improvements on state of the art by adjusting linear velocities with particular focus on safety in constrained and partially observable spaces commonly negotiated by deployed robots. We present experiments with the Regulated Pure Pursuit algo
Unmanned aerial vehicles (UAVs) have become increasingly prevalent in various domains, ranging from military operations to civilian applications. However, the proliferation of UAVs has also given rise to concerns regarding their potential misuse and security threats. As a result, the search and pursuit of UAVs have become crucial tasks for law enforcement agencies and security organizations. In this paper, we use a game theoretic approach to explore the problem of searching for and pursuing submarines and translate the problem into a UAV search and pursuit problem. Game theory provides a mathematical framework for modeling and analyzing strategic interactions among multiple decision makers. By applying game theoretic principles to the search and pursuit problem, we aim to improve the effectiveness of UAV detection and capture strategies. We begin by formulating the problem as a game, where the UAV represents the evader, and the search and pursuit team represents the pursuers. Each player's objective is to optimize their own utility while considering the actions and strategies of the other players. By leveraging game theory, we can gain insights into the optimal decision-making stra
The pursuit problem is a historical issue of the application of mathematics in physics, which has been discussed for centuries since the time of Leonardo Da Vinci, and its applications are wide ranging from military and industrial to recreational, but its place of interest is nowhere but nature and inspiration from the way of migration of birds and hunting of archer fish. The pursuit problem involves one or more pursuers trying to catch a target that is moving in a certain direction. In this article, we delve into two modes of movement: movement on a straight line and movement on a curve. Our primary focus is on the latter. Within the context of movement on a straight line, we explore two methods and compare their respective results. Furthermore, we investigate the movement of two particles chasing each other and extend these findings to N particles that are chasing each other in pairs. By leveraging these two modes of movement, we present a novel relationship for two-particle and N-particle systems in pursuit. Lastly, we analyze the movement of moths around a lamp and evaluate their motion in relation to two-particle and N-particle systems in pursuit. The results of this analysis
When faced with a new customer, many factors contribute to an insurance firm's decision of what offer to make to that customer. In addition to the expected cost of providing the insurance, the firm must consider the other offers likely to be made to the customer, and how sensitive the customer is to differences in price. Moreover, firms often target a specific portfolio of customers that could depend on, e.g., age, location, and occupation. Given such a target portfolio, firms may choose to modulate an individual customer's offer based on whether the firm desires the customer within their portfolio. We term the problem of modulating offers to achieve a desired target portfolio the portfolio pursuit problem. Having formulated the portfolio pursuit problem as a sequential decision making problem, we devise a novel reinforcement learning algorithm for its solution. We test our method on a complex synthetic market environment, and demonstrate that it outperforms a baseline method which mimics current industry approaches to portfolio pursuit.
Pursuit-evasion games are ubiquitous in nature and in an artificial world. In nature, pursuer(s) and evader(s) are intelligent agents that can learn from experience, and dynamics (i.e., Newtonian or Lagrangian) is vital for the pursuer and the evader in some scenarios. To this end, this paper addresses the pursuit-evasion game of intelligent agents from the perspective of dynamics. A bio-inspired dynamics formulation of a pursuit-evasion game and baseline pursuit and evasion strategies are introduced at first. Then, reinforcement learning techniques are used to mimic the ability of intelligent agents to learn from experience. Based on the dynamics formulation and reinforcement learning techniques, the effects of improving both pursuit and evasion strategies based on experience on pursuit-evasion games are investigated at two levels 1) individual runs and 2) ranges of the parameters of pursuit-evasion games. Results of the investigation are consistent with nature observations and the natural law - survival of the fittest. More importantly, with respect to the result of a pursuit-evasion game of agents with baseline strategies, this study achieves a different result. It is shown that
Isometry pursuit is a convex algorithm for identifying orthonormal column-submatrices of wide matrices. It consists of a novel normalization method followed by multitask basis pursuit. Applied to Jacobians of putative coordinate functions, it helps identity isometric embeddings from within interpretable dictionaries. We provide theoretical and experimental results justifying this method. For problems involving coordinate selection and diversification, it offers a synergistic alternative to greedy and brute force search.
This report studies the emergent behavior of systems of agents performing cyclic pursuit controlled by an external broadcast signal detected by a random set of the agents. Two types of cyclic pursuit are analyzed: 1)linear cyclic pursuit, where each agent senses the relative position of its target or leading agent 2)non-linear cyclic pursuit, where the agents can sense only bearing to their leading agent and colliding agents merge and continue on the path of the pursued agent (a so-called "bugs" model). Cyclic pursuit is, in both cases, a gathering algorithm, which has been previously analyzed. The novelty of our work is the derivation of emergent behaviours, in both linear and non-linear cyclic pursuit, in the presence of an exogenous broadcast control detected by a random subset of agents. We show that the emergent behavior of the swarm depends on the type of cyclic pursuit. In the linear case, the agents asymptotically align in the desired direction and move with a common speed which is a proportional to the ratio of the number of agents detecting the broadcast control to the total number of agents in the swarm, for any magnitude of input (velocity) signal. In the non-linear cas
Visualization of extremely large datasets in static or dynamic form is a huge challenge because most traditional methods cannot deal with big data problems. A new visualization method for big data is proposed based on Projection Pursuit, Guided Tour and Data Nuggets methods, that will help display interesting hidden structures such as clusters, outliers, and other nonlinear structures in big data. The Guided Tour is a dynamic graphical tool for high-dimensional data combining Projection Pursuit and Grand Tour methods. It displays a dynamic sequence of low-dimensional projections obtained by using Projection Pursuit (PP) index functions to navigate the data space. Different PP indices have been developed to detect interesting structures of multivariate data but there are computational problems for big data using the original guided tour with these indices. A new PP index is developed to be computable for big data, with the help of a data compression method called Data Nuggets that reduces large datasets while maintaining the original data structure. Simulation studies are conducted and a real large dataset is used to illustrate the proposed methodology. Static and dynamic graphical
It is of great challenge, though promising, to coordinate collective robots for hunting an evader in a decentralized manner purely in light of local observations. In this paper, this challenge is addressed by a novel hybrid cooperative pursuit algorithm that combines reinforcement learning with the artificial potential field method. In the proposed algorithm, decentralized deep reinforcement learning is employed to learn cooperative pursuit policies that are adaptive to dynamic environments. The artificial potential field method is integrated into the learning process as predefined rules to improve the data efficiency and generalization ability. It is shown by numerical simulations that the proposed hybrid design outperforms the pursuit policies either learned from vanilla reinforcement learning or designed by the potential field method. Furthermore, experiments are conducted by transferring the learned pursuit policies into real-world mobile robots. Experimental results demonstrate the feasibility and potential of the proposed algorithm in learning multiple cooperative pursuit strategies.
Learning strategic robot behavior -- like that required in pursuit-evasion interactions -- under real-world constraints is extremely challenging. It requires exploiting the dynamics of the interaction, and planning through both physical state and latent intent uncertainty. In this paper, we transform this intractable problem into a supervised learning problem, where a fully-observable robot policy generates supervision for a partially-observable one. We find that the quality of the supervision signal for the partially-observable pursuer policy depends on two key factors: the balance of diversity and optimality of the evader's behavior and the strength of the modeling assumptions in the fully-observable policy. We deploy our policy on a physical quadruped robot with an RGB-D camera on pursuit-evasion interactions in the wild. Despite all the challenges, the sensing constraints bring about creativity: the robot is pushed to gather information when uncertain, predict intent from noisy measurements, and anticipate in order to intercept. Project webpage: https://abajcsy.github.io/vision-based-pursuit/
We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a $k$-dimensional non-Gaussian subspace of interesting features. We use a projection pursuit approach -- we search for mutually orthogonal unit directions which maximise the 2-Wasserstein distance of the empirical distribution of data-projections along these directions from a standard Gaussian. Under a generative model, where there is a underlying (unknown) low-dimensional non-Gaussian subspace, we prove rigorous statistical guarantees on the accuracy of approximating this unknown subspace by the directions found by our projection pursuit approach. Our results operate in the regime where the data dimensionality is comparable to the sample size, and thus supplement the recent literature on the non-feasibility of locating interesting directions via projection pursuit in the complementary regime where the data dimensionality is much larger than the sample size.
Integrating rule-based policies into reinforcement learning promises to improve data efficiency and generalization in cooperative pursuit problems. However, most implementations do not properly distinguish the influence of neighboring robots in observation embedding or inter-robot interaction rules, leading to information loss and inefficient cooperation. This paper proposes a cooperative pursuit algorithm named Decentralized Adaptive COOperative Pursuit via Attention (DACOOP-A) by empowering reinforcement learning with artificial potential field and attention mechanisms. An attention-based framework is developed to emphasize important neighbors by concurrently integrating the learned attention scores into observation embedding and inter-robot interaction rules. A KL divergence regularization is introduced to alleviate the resultant learning stability issue. Improvements in data efficiency and generalization are demonstrated through numerical simulations. Extensive quantitative analysis and ablation studies are performed to illustrate the advantages of the proposed modules. Real-world experiments are performed to justify the feasibility of deploying DACOOP-A in physical systems.
The properties of biological microswimmers are to a large extent determined by fluid-mediated interactions, which govern their propulsion, perception of their surrounding, and the steering of their motion for feeding or in pursuit. Transferring similar functionalities to synthetic microswimmers poses major challenges, and the design of favorable steering and pursuit strategies is fundamental in such an endeavor. Here, we apply a squirmer model to investigate the pursuit of pursuer-target pairs with an implicit sensing mechanism and limited hydrodynamic steering abilities of the pursuer. Two hydrodynamic steering strategies are applied for the pursuer's propulsion direction by adaptation of its surface flow field, (i) reorientation toward the target with limited maneuverability, and (ii) alignment with the target's propulsion direction combined with speed adaptation. Depending on the nature of the microswimmer propulsion (puller, pusher) and the velocity-adaptation scheme, stable cooperatively moving states can be achieved, characterized by specific squirmer arrangements and controllable trajectories. Importantly, pursuer and target mutually affect their motion and trajectories.
We study the fundamental limits of matching pursuit, or the pure greedy algorithm, for approximating a target function $ f $ by a linear combination $f_n$ of $n$ elements from a dictionary. When the target function is contained in the variation space corresponding to the dictionary, many impressive works over the past few decades have obtained upper and lower bounds on the error $\|f-f_n\|$ of matching pursuit, but they do not match. The main contribution of this paper is to close this gap and obtain a sharp characterization of the decay rate, $n^{-α}$, of matching pursuit. Specifically, we construct a worst case dictionary which shows that the existing best upper bound cannot be significantly improved. It turns out that, unlike other greedy algorithm variants which converge at the optimal rate $ n^{-1/2}$, the convergence rate $n^{-α}$ is suboptimal. Here, $α\approx 0.182$ is determined by the solution to a certain non-linear equation.