### Simulation of optimal pursuit strategies with simple motion

#### Abstract

Strategies for pursuit of a target by one pursuer with simple movement are considered. The criterion is the time to capture the target. The proof of the optimality of the parallel approach strategy and the chas- ing strategy is presented. The strategy of parallel approach consists in the fact that the pursuer, knowing the velocity vector of the target at current moment, considers this vector to be constant and calculates a point on the target’s line of motion at which capture can occur if the pursuer moves at a constant maxi- mum speed. At each instant of time, the pursuer’s velocity vector is directed to the capture point, and the magnitude of the velocity is maximal. If the pursuer moves at maximum speed in the direction of the target, the pursuit strategy is called a chasing strategy. A number of examples of pursuit using the strate- gies of parallel approach and chasing strategy, calculated by the numerical method, are given. The main parameters of the movement of the agents affecting the time of capture are determined: the speed of the target and the pursuer, the coordinates of the target and the pursuer at the time of the beginning of the pursuit, the type and parameters of the target’s movement line; the pursuit task is determined by these para-meters. On the basis of numerical modeling, a sets of problems is outlined for which the parallel approach strategy is better then the chasing strategy or vice versa. The selected movement parameters roughly correspond to the movement parameters of modern combat aircraft and air defense equipment; in numerical experiments, the absolute value of the acceleration of the target does not exceed 10g, where g is the accele-ration of free fall. Since the pursuer’s motion is considered simple, any absolute value of its acceleration is allowed. In the case of applying the parallel approach strategy, this value slightly differs from the absolute value of the target’s acceleration; if a chasing strategy is used, the absolute magnitude of the pursuer’s acceleration can be much larger.

*Prom**ble**s in programming *

*2022; 3-4: 478-484*#### Keywords

#### Full Text:

PDF (Ukrainian)#### References

Isaacs R. (1999). Differential Games. New York: Dover Publications.

Chikrii A.A. (1992). Conflict-Controlled Processes. Kyiv: Nauk. Dumka. (In Russian).

Petrosyan L.A., Zenkevich N.A., Shevkoplyas E.V. (2012). Game theory. St. Petersburg: BHV-Petersburg. (In Russian).

Rikhsiev B.B. (1989). Simple Motion Differential Games. Tashkent: FAN. (In Russian).

Petrosyan L.A., Rykhsiev B.B. (1991) Pursuit on the plane. Moscow: Nauka. (In Russian).

Pashko S.V. Maximal time of pursuit for the strategy of parallel approach in case of equal speeds. Computer Mathematics. Kyiv: Institute of Cybernetics of the NAS of Ukraine. 2014. № 1. P. 140 – 149. (in Russian).

Pashko S.V., Yalovets A.L. Maximal Time of Pursuit for the Strategy of Parallel Approach. Problems in Programming. 2014. № 4. P. 78 – 93. (In Russian).

Pashko S.V. Construction of pursuit strategies using Lyapunov functions. Problems in Programming. 2017. № 4. P. 194 – 211. (In Ukrainian).

Pashko S.V. (2018). Mathematical methods of choosing optimal solutions in systems consisting of rational agents: dissertation for obtaining the scientific degree of Doctor of Sciences in Physics and Mathematics: 01.05.01. Kyiv. (In Ukrainian).

Parsons T.D. Pursuit-evasion in a graph. Theory and applications of graphs. 1978. P. 426–441.

Borie R.B., Craig A.T., Koenig S. Algorithms and Complexity Results for Pursuit-Evasion Problems. IJCAI-09. 2009. P. 59 – 66.

### Refbacks

- There are currently no refbacks.