arXiv subjects

Daigo Shishika

Publications and source records attributed to Daigo Shishika.

At least 37 records · Page 2Linked to original sources

arXiv2024

Guarding a Target Area from a Heterogeneous Group of Cooperative Attackers

In this paper, we investigate a multi-agent target guarding problem in which a single defender seeks to capture multiple attackers aiming to reach a high-value target area. In contrast to previous studies, the attackers herein are assumed to be heterogeneous in the sense that they have not only different speeds but also different weights representing their respective degrees of importance (e.g., the amount of allocated resources). The objective of the attacker team is to jointly minimize the weighted sum of their final levels of proximity to the target area, whereas the defender aims to maximize the same value. Using geometric arguments, we construct candidate equilibrium control policies that require the solution of a (possibly nonconvex) optimization problem. Subsequently, we validate the optimality of the candidate control policies using parametric optimization techniques. Lastly, we provide numerical examples to illustrate how cooperative behaviors emerge within the attacker team due to their heterogeneity.

eess.SY↗

arXiv2024

Deception in Differential Games: Information Limiting Strategy to Induce Dilemma

Can deception exist in differential games? We provide a case study for a Turret-Attacker differential game, where two Attackers seek to score points by reaching a target region while a Turret tries to minimize the score by aligning itself with the Attackers before they reach the target. In contrast to the original problem solved with complete information, we assume that the Turret only has partial information about the maximum speed of the Attackers. We investigate whether there is any incentive for the Attackers to move slower than their maximum speed in order to ``deceive'' the Turret into taking suboptimal actions. We first describe the existence of a dilemma that the Turret may face. Then we derive a set of initial conditions from which the Attackers can force the Turret into a situation where it must take a guess.

cs.GT↗

arXiv2024

Defending a Static Target Point with a Slow Defender

This paper studies a target-defense game played between a slow defender and a fast attacker. The attacker wins the game if it reaches the target while avoiding the defender's capture disk. The defender wins the game by preventing the attacker from reaching the target, which includes reaching the target and containing it in the capture disk. Depending on the initial condition, the attacker must circumnavigate the defender's capture disk, resulting in a constrained trajectory. This condition produces three phases of the game, which we analyze to solve for the game of kind. We provide the barrier surface that divides the state space into attacker-win and defender win regions, and present the corresponding strategies that guarantee win for each region. Numerical experiments demonstrate the theoretical results as well as the efficacy of the proposed strategies.

eess.SY↗

arXiv2024

Scaling Team Coordination on Graphs with Reinforcement Learning

This paper studies Reinforcement Learning (RL) techniques to enable team coordination behaviors in graph environments with support actions among teammates to reduce the costs of traversing certain risky edges in a centralized manner. While classical approaches can solve this non-standard multi-agent path planning problem by converting the original Environment Graph (EG) into a Joint State Graph (JSG) to implicitly incorporate the support actions, those methods do not scale well to large graphs and teams. To address this curse of dimensionality, we propose to use RL to enable agents to learn such graph traversal and teammate supporting behaviors in a data-driven manner. Specifically, through a new formulation of the team coordination on graphs with risky edges problem into Markov Decision Processes (MDPs) with a novel state and action space, we investigate how RL can solve it in two paradigms: First, we use RL for a team of agents to learn how to coordinate and reach the goal with minimal cost on a single EG. We show that RL efficiently solves problems with up to 20/4 or 25/3 nodes/agents, using a fraction of the time needed for JSG to solve such complex problems; Second, we learn a general RL policy for any $N$-node EGs to produce efficient supporting behaviors. We present extensive experiments and compare our RL approaches against their classical counterparts.

cs.RO↗

arXiv2024

Optimal Evasion from a Sensing-Limited Pursuer

This paper investigates a partial-information pursuit evasion game in which the Pursuer has a limited-range sensor to detect the Evader. Given a fixed final time, we derive the optimal evasion strategy for the Evader to maximize its distance from the pursuer at the end. Our analysis reveals that in certain parametric regimes, the optimal Evasion strategy involves a 'risky' maneuver, where the Evader's trajectory comes extremely close to the pursuer's sensing boundary before moving behind the Pursuer. Additionally, we explore a special case in which the Pursuer can choose the final time. In this scenario, we determine a (Nash) equilibrium pair for both the final time and the evasion strategy.

cs.GT↗

arXiv2023

Asymptotic Stability of Active Disturbance Rejection Control for Linear SISO Plants with Low Observer Gains

This paper theoretically investigates the closed-loop performance of active disturbance rejection control (ADRC) on a third-order linear plant with relative degree 3, subject to a class of exogenous disturbances. While PID control cannot be guaranteed to be capable of stabilizing such plants, ADRC offers a model-free alternative. However, many existing works on ADRC consider the observer gains to be taken arbitrarily large, in order to guarantee desired performance, such as works which consider parameterizing ADRC by bandwidth. This work finds that, for constant exogenous disturbances, arbitrary eigenvalue assignment is possible for the closed-loop system under linear ADRC, thus guaranteeing the existence of an ADRC controller for desired performance without taking any gains arbitrarily large. We also find that stabilization is possible when the exogenous disturbance is stable, and show how ADRC can recover the performance of model-based observers. We demonstrate aspects of the resulting closed-loop systems under ADRC in simulations.

eess.SY↗

arXiv2023

Lighter-Than-Air Autonomous Ball Capture and Scoring Robot -- Design, Development, and Deployment

This paper describes the full end-to-end design of our primary scoring agent in an aerial autonomous robotics competition from April 2023. As open-ended robotics competitions become more popular, we wish to begin documenting successful team designs and approaches. The intended audience of this paper is not only any future or potential participant in this particular national Defend The Republic (DTR) competition, but rather anyone thinking about designing their first robot or system to be entered in a competition with clear goals. Future DTR participants can and should either build on the ideas here, or find new alternate strategies that can defeat the most successful design last time. For non-DTR participants but students interested in robotics competitions, identifying the minimum viable system needed to be competitive is still important in helping manage time and prioritizing tasks that are crucial to competition success first.

cs.RO↗

arXiv2023

The Eater and the Mover Game

This paper studies the idea of ``deception by motion'' through a two-player dynamic game played between a Mover who must retrieve resources at a goal location, and an Eater who can consume resources at two candidate goals. The Mover seeks to minimize the resource consumption at the true goal, and the Eater tries to maximize it. While the Mover has the knowledge about the true goal, the Eater cannot differentiate between the two candidates. Unlike existing works on deceptive motion control that measures the deceptiveness through the quality of inference made by a distant observer (an estimator), we incorporate their actions to directly measure the efficacy of deception through the outcome of the game. An equilibrium concept is then proposed without the notion of an estimator. We further identify a pair of equilibrium strategies and demonstrate that if the Eater optimizes for the worst-case scenario, hiding the intention (deception by ambiguity) is still effective, whereas trying to fake the true goal (deception by exaggeration) is not.

eess.SY↗

arXiv2023

Path Defense in Dynamic Defender-Attacker Blotto Games (dDAB) with Limited Information

We consider a path guarding problem in dynamic Defender-Attacker Blotto games (dDAB), where a team of robots must defend a path in a graph against adversarial agents. Multi-robot systems are particularly well suited to this application, as recent work has shown the effectiveness of these systems in related areas such as perimeter defense and surveillance. When designing a defender policy that guarantees the defense of a path, information about the adversary and the environment can be helpful and may reduce the number of resources required by the defender to achieve a sufficient level of security. In this work, we characterize the necessary and sufficient number of assets needed to guarantee the defense of a shortest path between two nodes in dDAB games when the defender can only detect assets within $k$-hops of a shortest path. By characterizing the relationship between sensing horizon and required resources, we show that increasing the sensing capability of the defender greatly reduces the number of defender assets needed to defend the path.

cs.GT↗

arXiv2023

Team Coordination on Graphs with State-Dependent Edge Cost

This paper studies a team coordination problem in a graph environment. Specifically, we incorporate "support" action which an agent can take to reduce the cost for its teammate to traverse some edges that have higher costs otherwise. Due to this added feature, the graph traversal is no longer a standard multi-agent path planning problem. To solve this new problem, we propose a novel formulation by posing it as a planning problem in the joint state space: the joint state graph (JSG). Since the edges of JSG implicitly incorporate the support actions taken by the agents, we are able to now optimize the joint actions by solving a standard single-agent path planning problem in JSG. One main drawback of this approach is the curse of dimensionality in both the number of agents and the size of the graph. To improve scalability in graph size, we further propose a hierarchical decomposition method to perform path planning in two levels. We provide complexity analysis as well as a statistical analysis to demonstrate the efficiency of our algorithm.

cs.MA↗

arXiv2023

On the Adversarial Convex Body Chasing Problem

In this work, we extend the convex bodies chasing problem (CBC) to an adversarial setting, where an agent (the Player) is tasked with chasing a sequence of convex bodies generated adversarially by another agent (the Opponent). The Player aims to minimize the total cost associated with its own movements, while the Opponent tries to maximize the same cost. The set of feasible convex bodies is finite and known to both agents, which allows us to provide performance guarantees with max-min optimality. Under certain assumptions, we show the continuity of the optimal value function, and propose an algorithm to numerically approximate the optimal policies for both the Player and the Opponent within a guaranteed tolerance. Finally, the theoretical results are verified through numerical examples.

eess.SY↗

arXiv2022

Target Defense against Sequentially Arriving Intruders

We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. The intruders' objective is to breach the target boundary without being captured by the defender. As soon as the current intruder breaches the target or gets captured by the defender, the next intruder appears at a random location on a fixed circle surrounding the target. Therefore, the defender's final location at the end of the current game becomes its initial location for the next game. Thus, the players pick strategies that are advantageous for the current as well as for the future games. Depending on the information available to the players, each game is divided into two phases: partial information and full information phase. Under some assumptions on the sensing and speed capabilities, we analyze the agents' strategies in both phases. We derive equilibrium strategies for both the players to optimize the capture percentage using the notions of engagement surface and capture circle. We quantify the percentage of capture for both finite and infinite sequences of incoming intruders.

cs.RO↗

arXiv2022

Guarding a Non-Maneuverable Translating Line with an Attached Defender

In this paper we consider a target-guarding differential game where the defender must protect a linearly translating line-segment by intercepting an attacker who tries to reach it. In contrast to common target-guarding problems, we assume that the defender is attached to the target and moves along with it. This assumption affects the defenders' maximum speed in inertial frame, which depends on the target's direction of motion. Zero-sum differential game of degree for both the attacker-win and defender-win scenarios are studied, where the payoff is defined to be the distance between the two agents at the time of game termination. We derive the equilibrium strategies and the Value function by leveraging the solution for the infinite-length target scenario. The zero-level set of this Value function provides the barrier surface that divides the state space into defender-win and attacker-win regions. We present simulation results to demonstrate the theoretical results.

eess.SY↗

arXiv2022

Guarding a Translating Line with an Attached Defender

In this paper we consider a Target-guarding differential game where the Defender must protect a linearly moving line segment by intercepting the Attacker who tries to reach it. In contrast to common Target-guarding problems, we assume that the Defender is attached to the Target and moves along with it. This assumption affects the Defender's maximum speed depending on its heading direction. A zero-sum differential game of degree for the Attacker-winning scenario is studied, where the payoff is defined to be the distance between the two agents at the time of reaching the Target. We derive the equilibrium strategies and the Value function by leveraging the solution for the infinite-length Target scenario. The zero-level set of this Value function provides the barrier surface that divides the state space into Defender-winning and Attacker-winning regions. We present simulation results at the end to demonstrate the theoretical results.

eess.SY↗

arXiv2022

One Apollonius Circle is Enough for Many Pursuit-Evasion Games

This paper investigates obstacle-free simple motion pursuit-evasion problems where the pursuer is faster and game termination is point capture. It is well known that the interior of the Apollonius Circle (AC) is the evader's dominance region, however, it was unclear whether the evader could reach outside the initial AC without being captured. We construct a pursuit strategy that guarantees the capture of an evader within an arbitrarily close neighborhood of the initial AC. The pursuer strategy is derived by reformulating the game into a nonlinear control problem, and the guarantee holds against any admissible evader strategy. Our result implies that the evader can freely select the capture location, but only inside the initial AC. Therefore, a class of problems, including those where the payoff is determined solely based on the location of capture, are now trivial.

math.OC↗

arXiv2021

Dynamic Defender-Attacker Blotto Game

This work studies a dynamic, adversarial resource allocation problem in environments modeled as graphs. A blue team of defender robots are deployed in the environment to protect the nodes from a red team of attacker robots. We formulate the engagement as a discrete-time dynamic game, where the robots can move at most one hop in each time step. The game terminates with the attacker's win if any location has more attacker robots than defender robots at any time. The goal is to identify dynamic resource allocation strategies, as well as the conditions that determines the winner: graph structure, available resources, and initial conditions. We analyze the problem using reachable sets and show how the outdegree of the underlying graph directly influences the difficulty of the defending task. Furthermore, we provide algorithms that identify sufficiency of attacker's victory.

eess.SY↗

arXiv2021

Defending a Perimeter from a Ground Intruder Using an Aerial Defender: Theory and Practice

The perimeter defense game has received interest in recent years as a variant of the pursuit-evasion game. A number of previous works have solved this game to obtain the optimal strategies for defender and intruder, but the derived theory considers the players as point particles with first-order assumptions. In this work, we aim to apply the theory derived from the perimeter defense problem to robots with realistic models of actuation and sensing and observe performance discrepancy in relaxing the first-order assumptions. In particular, we focus on the hemisphere perimeter defense problem where a ground intruder tries to reach the base of a hemisphere while an aerial defender constrained to move on the hemisphere aims to capture the intruder. The transition from theory to practice is detailed, and the designed system is simulated in Gazebo. Two metrics for parametric analysis and comparative study are proposed to evaluate the performance discrepancy.

cs.RO↗

arXiv2021

Perimeter-defense Game on Arbitrary Convex Shapes

This paper studies a variant of multi-player reach-avoid game played between intruders and defenders. The intruder team tries to score by sending as many intruders as possible to the target area, while the defender team tries to minimize this score by intercepting them. Specifically, we consider the case where the defenders are constrained to move on the perimeter of the target area. Since it is challenging to directly solve the multi-player game due to the high dimensionality of the joint state space, we leverage the solutions to smaller scale problems. First, we solve the one vs. one game, for which existing works either rely on numerical approaches or make simplifying assumptions (e.g., circular perimeter, or equal speed). This paper accommodates target areas with any arbitrary convex shapes and provides analytical solution which lends itself to a useful geometric interpretation. We also provide a detailed discussion on the optimality of the derived strategies. Secondly, we solve the two vs. one game to introduce a cooperative pincer maneuver, where a pair of defenders team up to capture an intruder that cannot be captured by either one of the defender individually. Finally, we introduce how the aforementioned building blocks are used in three different assignment-based defense strategies.

eess.SY↗