A Two-Step Evading Strategy Against Three Cooperative Pursuers

This paper considers a pursuit-evasion game for non-holonomic systems where a group of pursuers attempts to capture an evader in a bounded connected domain. The problem is challenging because all vehicles have the same maneuvering capability in terms of speed and turn radius constraint. The paper initially discusses a simple approach for holonomic systems that is based on the minimization of the safe-reachable area (the area containing the set of points to where an evader can travel without being caught). This idea is then extended to develop a pursuit-evasion strategy for non-holonomic systems. However, solving such a problem is computationally intractable. Therefore, we propose a computationally efficient algorithm to obtain approximate solutions. This paper also proposes an alternative approach to obtain a simple yet effective solution to the cooperative pursuit problem that is based on missile guidance laws. As there is no analytical proof of capture, we empirically evaluate the performance of the algorithms and perform a comparative study using solutions obtained from umpteen simulations. A total of four different cooperative pursuit strategies and three different evader strategies are taken into account for the comparative study. In the process, an evader strategy which is superior to that based on the optimization of safe-reachable area is also identified.

Compliment responses are one of speech act types in pragmatic study. This study is aimed (1) to investigate the strategies used by the American and Makassarese people in responding to the complim ent, (2) to compare the response tendencies used by American and the Makassarese people based on Gender and age; and (3) to investigate the cultural influences on the American and Makassarese response.The research was a comparative study which and used a descriptive- qualitative approach. The data were collected from youtube.com and DCT questionnaire. The data were analyzed using a number of techniques, namely noting down the utterances, categorizing the responses identified based on Holmes’ semantic formula and explaining the cultural influences based on their responses. Firstly, the research result revealed that both the American and Makassarese people used 3 compliment strategies: accepting, evading and refusing. Americans would use the evading strategy when the speaker and his interlocutor were good friends; while a Makassarese would either use the evading strategy or the refusing strategy in his responses, when the speaker and his interlocutor were of a different kinship hierarchy, such as between the older and the younger brothers or sisters and between husband and wife. Secondly, The comparison of the compliment responses between the American and Makassarese males indicated that an American male had the tendency to evade a compliment in every topic except teenager had tendency to accept the compliment in any topic. While a Makassarese male tend to receive the compliment for all the topics, except for the comp liment for an achievement.on the other hand, an American woman had tendency to accept a compliment for all topics, but an older woman had a tendency to refuse a compliment. a Makassarese woman, had also a tendency to accept a compliment for all topics. Finally, Makassarese people, both men and women had the tendency to accept, evade or refuse compliments when they had kinship.

We investigate algorithms for playing multi-agent visibility-based pursuit-evasion games. A team of pursuers attempts to maintain visibility contact with an evader who actively avoids tracking. We aim for applicability of the algorithms in real-world scenarios; hence, we impose hard constraints on the run-time of the algorithms and we evaluate them in a simulation model based on a real-world urban area. We compare Monte-Carlo tree search (MCTS) and iterative deepening minimax algorithms running on the information-set tree of the imperfect-information game. The experimental results demonstrate that both methods create comparable good strategies for the pursuer, while the later performs better in creating the evader's strategy.

An approach is considered that allows generating a suboptimal strategy for the evader in a nonlinear feedback position control problem that can be implemented in real time. The evader does not know exactly what actions the pursuer will take up, and the evader's strategy is selected from the known functionality of both players and worse possible actions of the pursuer.

This paper is concerned with a class of pursuit‐evasion game problems amidst stationary and moving obstacles in a bounded environment. We concentrate on evader's strategy taking into account the following challenges: (i) pursuer and evader are nonholonomic wheeled mobile robots and the evader is slower than the pursuer; (ii) pursuer follows a proportional navigation law; and (iii) geometry of the environment is not known to the players,a priori. We propose an efficient evader‐centric anticipated velocity based guidance strategy. Pursuer's trajectory is anticipated at each step by the evader using quadratic polynomial interpolation. The aim of the evader is to escape interception with the pursuer for maximum possible time. To deal with static obstacles, a technique based on a well‐known tangent bug algorithm is presented. While dealing with dynamic obstacles, a recently introduced reciprocal orientation method is employed to avoid collision in situations when the dynamic obstacle also cooperates in the process. In case dynamic obstacles do not participate in the process of collision avoidance, a well‐known velocity obstacle method is employed for planning safe collision‐free paths. Efficiency of the proposed algorithms is analyzed with respect to the interception time and the distance traveled by the players. Copyright © 2014 John Wiley & Sons, Ltd.

The game of tag is frequently used in the study of pursuit and evasion strategies that are discovered through competitive coevolution. The aim of coevolution is to create an arms race where opposing populations cyclically evolve in incremental improvements, driving the system towards better strategies. A coevolutionary simulation of the game of tag involving two populations of agents; pursuers and evaders, is developed to investigate the effects of a boundary and two obstacles. The evolution of strategies through Chemical Genetic Programming optimizes the mapping of genotypic strings to phenotypic trees. Four experiments were conducted, distinguished by speed differentials and environmental conditions. Designing experiments to evaluate the efficacy of emergent strategies often reveal necessary steps needed for coevolutionary progress. The experiments that excluded obstacles and boundaries provided design pointers to ensure coevolutionary progress as well as a deeper understanding of strategies that emerged when obstacles and boundaries were added. In the latter, we found that an awareness of the environment and the pursuer was not critical in an evader's strategy to survive, instead heading to the edge of the boundary or behind an obstacle in a bid to `throw-off or hide from the pursuer' or simply turn in circles was often sufficient, thereby revealing possible suboptimal strategies that were environment specific. We also observed that a condition for coevolutionary progress was that the problem complexity must be surmountable by at least one population; that is, some pursuer must be able to tag an opponent. Due to the use of amino-acid building blocks in our Chemical Genetic Program, our simulations were able to achieve significant complexity in a short period of time.

On closed-loop controls in pursuit-evasion

In this paper, we consider a pursuit-evasion game problem in a geometric setting, where a single pursuer and single evader are in motion with conflicting interests. The pursuer follows a recently introduced angular acceleration guidance law to catch the evader and the evader-centric strategy is supposed to keep the evader away from the pursuer for maximum possible time in an unknown environment having static obstacles. An evader-centric approach is proposed in the present paper that uses linear extrapolation to predict the future move of the evader and define its own strategy. The well-known tangent bug algorithm is employed to deal with static obstacles. Effectiveness of the proposed evader's strategy has been analyzed in terms of interception time and distance travelled by the players. Simulation results demonstrate effectiveness and efficiency of the proposed method.

ON CLOSED-LOOP CONTROLS IN PURSUIT–EVASION

A differential game of evasion with many participants (a game of kind in the terminology of Isaacs1) is considered. One controlled object (the evader) seeks to avoid contact with each of several pursuers. The motion of the evader is subject to a phase constraint. An efficient method (up to the explicit formulae) of constructing the evader's strategy is proposed. This strategy ensures evasion on the infinite time interval and the fulfilment of the phase constraint. The evader's control corresponding to this strategy is always a piecewise‐programme function of time, and the number of programme pieces is finite (there is an upper estimate for this number). There is a lower estimate for the minimal distance between the evader and the pursuers.

A pursuit-evasion game with partial information is studied. The evader observes the initial conditions only. The pursuer observes both the initial conditions and the relative evader-pursuer position in additive noise. The paper shows that the optimal strategies of a partial information game may differ qualitatively from its full information counterpart. In the particular case at hand the evader's strategy may be random, something that does not happen in the deterministic case.

In this paper, closed-loop Nash equilibrium strategies for an N-pursuer single-evader differential game over a finite time horizon with limited observations is considered. The game setting is such that each pursuer has limited sensing range and can observe the state vector of another player only if that player is within the pursuer's sensing range. The evader, on the other hand, has unlimited sensing range which allows it to observe the state of all pursuers at all times and implement a standard closed-loop Nash strategy. To derive strategies for the pursuers, a new concept of best achievable performance indices is proposed. These indices are derived in a way to be the closest to the original performance indices and such that the resulting pursuers' collective strategy satisfies a Nash equilibrium against the evader's strategy. The strategies obtained by such an approach are independent of the initial state vector. An illustrative example is solved and simulation results corresponding to different sensing ranges and performance indices of the game are presented.

The life history of Spanish pines and their relation to fire as the main disturbance factor in their ecosystems was analysed. The primary ecological attributes studied were the canopy seed bank (onset of cone production, percentage and persistence of serotinous cones), seed and cone morphology, sprouting and bark thickness. Four ecological groups were separated using multivariate cluster analysis and their life-history characteristics are discussed. Serotiny and early flowering in Pinus halepensis and P. pinaster reflect their evader strategy in relation to fire as this character is advantageous to survive frequent crown fires and to attain successful post-fire recruitment. Late flowering and absence of serotinous cones in P. nigra, P. sylvestris and P. uncinata indicate that their natural forest did not evolve under frequent crown fires. P. canariensis and P. pinea appeared in two single groups because of their sprouting capability and their seed size respectively. Intraspecific variation in P. pinaster was also analysed using the same criteria and high variability was found in its life history traits. A group of P. pinaster populations showed high levels of serotiny and thin bark as a possible adaptation to frequent stand-replacing crown fires. In contrast, a group of non- or weakly-serotinous populations seems to have evolved under a low-intensity fire regime where the best fitness corresponds to thick-barked individuals capable of surviving ground fires. Intermediate strategies were also evident in this species and were discussed in relation to the effect of different fire regimes caused by the understorey vegetation.

This paper proposes an evading strategy based on reinforcement learning for the pursuit-evasion problem considering hypersonic vehicle dynamics (evader) and multiple interceptors (pursuers). Analytical solutions are hard to obtain, so a reinforcement learning method is adopted for the vehicle’s guidance commands in evasion. To cast the problem to a Markov-Decision-Process (MDP), we first establish the motion model involves multiple pursuers and one evader. Moreover, we choose their positions, and velocities change in the three-dimensional space as the state transition, considering a proportional navigation interception guidance. Furthermore, the weighted sum of the zero-effort-miss perpendicular to line-of-sight and the magnitude of maneuver is chosen to be a reward function. After training using a PPO-Clip algorithm, a policy for evasion is obtained. Numerical experiments validate that the method we put forward can be used in the sequential evasion decision against multiple pursuers for a hypersonic vehicle.

A Cooperative Pursuit-Evasion Game for Non-holonomic Systems