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Software Design to Solve Real Time Optimisation of Proportional Navigation Guidance using Genetic Algorithm Istas F. Nusyirwan The Sir Lawrence Wackett Centre for Aerospace Design Technology, RMIT University, GPO Box 2476V, Melbourne, Vic 3001, Australia
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Cees Bil1 The Sir Lawrence Wackett Centre for Aerospace Design Technology, RMIT University, GPO Box 2476V, Melbourne, Vic 3001, Australia
[email protected]
ABSTRACT Proportional navigation guidance (PNG) is widely implemented in missile guidance systems. In this paper, genetic algorithms is applied to find the optimal proportional navigation ratio, N, for a given pursuitevasion scenario. The genetic algorithms (GA) use a small population size, i.e. micro-GA, uniform crossover, mutation and employing elitism. Several scenarios were considered and it is found that for each scenario, the optimal value of the proportional naviga-tion guidance ratio, N, is dependent on the evader’s initial velocity and heading .
KEYWORDS Proportional Navigation Guidance, Genetic Algorithm
1. Introduction In this paper, a class of 2-D optimal pathplanning problems for a fighter aircraft with kinematics and tactical constraints during combat is considered. Most problems that involve two or more adversaries can be described in the form of games. The theory of games is used extensively by various field of knowledge such as economics, social studies, and military conflicts to assist in further understanding the nature of their respective disciplines. Even simple games theories have been developed [1], which can be applied to the real problem. Military pursuit-evasion game simulations using evolutionary algorithms were studied for various types of military operations, such as naval warfare simulation [2] and terrain-avoidance trajectory and missile avoidance [3, 4]. Basically, the key issues that need to be addressed in these simulations as outlined in [5], are: a. Minimising the risk of aircraft detection by radar; b. Minimising the risk of submarine detection by sensors; c. Minimising cumulative radiation damage in passing through a contaminated area; d. Finding optimal trajectories for multiple aircraft to avoid collision; e. Maximising the probability of target detecting by a searcher; f. Minimising the fuel consumption;
The optimal flight path trajectory problem for civil air traffic control was studied by [6] using non-linear programming with collocations on finite elements. The study of optimal trajectory for aircraft in a threat environment using calculus of variation was carried out by [5]. Other techniques, apart from evolutionary algorithms, are gradient-based algorithms, dynamic programming and network flow optimisation. The key concerns are whether the models can be implemented onboard aircraft as real time solvers, able to produce relatively accurate results in the presence of errors, and are stable throughout the operating regions. As said by [5], the efficiency of dis -creet optimisation issues depends on the type of objective function, technological constraints, and type of trajectory approximation scheme used. According to [5], many previous studies on trajectory generation for military air-craft applications are concentrated on feasible direction algorithms and dynamic pro-gramming. These methods tend to be computationally intensive and therefore are not well suited for onboard applications. In order to reduce the computation time, [7] uses a simple analytical risk function to further developed lateral and vertical algorithms to optimise flight trajectory with respect to time, fuel consumption, aircraft final posi-tion and exposed risks. In this research, the development of a methodology to determine the optimal path for aircraft is emphasised. The high non-linearity of the problems makes it almost impossible to solve in the classical way. ModSAF uses evolutionary algorithm in its simulation [8] to demonstrate the
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potential of artificial intelligence techniques in support of human-like behaviour simulation. Recently, the availability of high performance computer processors has opened the opportunity to use genetic algorithms such as micro-GA to their fullest extend to solve real time path planning problems.
2. Efficient Trajectory Calculation During Combat A robust guidance law, which guarantees acceptable evasion or interception against an intelligent adversary is required. Extensive research has been done on making a missile more intelligent [3, 4], [9] [10]. However, very little work been done to de-velop guidance law to assist a fighter pilot to effectively engage an adversary or mis -siles, while acting as either the pursuer or the evader. Moore et al [11] has imple-mented a genetic programming system to optimise solutions to an extended twodimensional pursuer-evader problem that does not require knowledge of the pursuer’s current state. Moore has extended his research by incorporating aircraft limitations such as thrust, turning forces, drag and momentum. The evader moves by executing specific combinations of throttle setting and turning forces in specific sequences.This tech-nique requires a rigorous training program for both pursuer and evader under a sim-plified environment, e.g. a twodimensional case. This pre-calculation approach may have its drawbacks if it is applied to a realworld situation. Apart from that, the use of intelligent hybrid system as suggested by [15] is also promising. A combination of several intelligent systems such as fuzzy systems, expert systems and evolutionary algorithms may improve the response and accuracy of the results.
3. Proposed Methodology 3.1 Proportional Navigation Guidance (PNG) Proportional navigation guidance (PNG) is used in this study to guide the purser to-ward the evader. The earliest applications appeared at the end of the Second World War. It works by turning the pursuer at a rate proportional to the angular velocity of the line of sights (LOS) between the pursuer and the evader. LOS is defined as an imagi-nary line from the pursuer to the evader. The displacement vector of the evader center of mass (c.m.) with respect the pursuer c.m. is called the line-of-sight vector. Its ori-entation will remain constant in inertial space of the pursuer in on a interception course. For PNG, the pursuer is commanded to turn at a rate
proportional to the angu-lar velocity of the LOS. This ratio of the pursuer turning rate to the angular velocity of the LOS is called the proportional navigation ratio, N. If N=1, then the pursuer is turning at the same rate as the LOS, or homing on the target. Typical values for N are between 2-6 [14]. It means the pursuer is turning at faster rate than the LOS. This produces a lead angle for the pursuer. The generation of this lead angle can put the pursuer on a collision path with the evader. To analyse the aircraft flight trajectory, the required information is the aerody-namic data, structural data, engine’s performance, aircraft weight at various configu-rations, fuel weight, fuel consumption, flight envelope, weapon’s capability, and its initial position in Euclidean space. To simplify the simulation of aircraft motion, the velocity both aircrafts are as-sumed constant. The aircraft’s position and attitude are described within a fixed coor-dinate frame and then transformed to Earth or inertial coordinate system. The kine-matics transformation equations use quaternion formulation instead of Euler angle formulation, because it gives shorter computational time and are free from the “gimbal lock” problem.
3.2 Parameter Optimisation with Genetic Algorithm Representation The evader is assumed to fly in a predictable manner, i.e. flying in a straight line. In order to intercept the evader, the pursuer will use PNG to direct itself to the evader. The pursuer will employ GA to determine the optimal N in order to intercept the evader in the shortest time. The solution of the problem gives the optimal value of N i.e. the proportional navigation ratio. Thus, N is encoded in 30 bits chromosomes. Micro-GA is used because it requires smaller population size (typically 1/10 of nor-mal-GA) and also shows faster convergence than normal-GA. Faster computing time can be achieved by employing this approach. Implementation of the genetic search Fitness value. The fitness of a chromosome is the quality of the chromosome pro-duced. In this case, the fitness of a chromosome is the minimum time of capture. Reproduction. The selection is through tournament, i.e. survival of the fittest with a shuffling technique for choosing random pairs for mating. Recombination. In this study, classical one point cross over is used. The rate of cross over is set to 0.5.
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Mutation. Creep mutations are used in the simulation with 0.04 percent probabil-ity. Generation replacement. A pair of parents produces one child and they will com-pete in a tournament. The best solutions will be retained as the new generation. Table 1 : Simulation results for different air combat scenarios.
Fitness Function The fitness function is a number of subroutines written specifically to simulate air-craft kinematics in three dimensions. The effects due to atmospheric conditions, aero-dynamics forces and engine’s thrust are not considered in the simulation. This is to ensure that the results are purely from PNG. All aircrafts are modeled as a point-mass model. Each chromosome is decoded and fed into the subroutines and the result is in the form of time of capture. The less time of capture means a higher fitness value for the chromosome and guarantee its existence for the next generation.
and 5. The time taken to get the result is around 1 to 4 seconds.
5. Conclusion Proportional navigation guidance system is able to intercept an evader in the shortest possible time. The PNG ratio, N, is the important value that needs to be optimised to achieve this. Using micro genetic algorithm, the PNG ratio was optimised for a num-ber of air combat scenarios. The simulation time is reasonably fast using micro-GA, i.e. a small number of populations on a typical computer processor making it suitable for realtime application. It is also shown that the optimal values of the proportional navigation guidance ra-tio, N is highly dependent on the initial velocity and heading angle of the pursuer and the evader respectively in order to intercept the evader in the shortest time. Future works include further improving the fidelity of the aircraft dynamic model and to simulate different scenarios by varying speed, altitude, and heading to assess the effect of model errors on the optimal trajectory.
4. Discussion of Results The simulation considers five scenarios as per Table 1. Initially, the evader is 5000 m away from the pursuer heading to north easterly with speed 90 m/s at altitude of 5000 m and the pursuer is flying at the same altitude with speed of 100 m/s. The speed for the pursuer and evader for all scenarios remain constant. All scenarios are executed at a constant altitude of 5000 m. The azimuth of North is 00 and positive angle is in a counter-clockwise direction, i.e. west is 900 and east is –900. Both players’ positions are using flat-earth inertial axes system with an arbitrary point of origin. All scenarios are compared with N = 1, i.e. homing on target. The results show that the selection of N is dependent on the direction of the evader. The optimal value of N tends to be relatively higher if the evader’s initial heading is in perpendicular with the LOS as seen in scenario 1 and 4. A relatively small value for optimal N if the evader’s initial heading is almost in parallel with LOS such as seen in scenario 2,3
Figure 1 : Comparisons between optimised and unoptimised trajectory in Scenario 1
Figure 2 : Comparisons between optimised and unoptimised trajectory in Scenario 2
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Figure 4 : Comparisons between optimised and unoptimised trajectory in Scenario 4
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[5] Murphey R., U.S., Zabarankin M., Trajectory Optimizatio n in a Threat Environ-ment, in Research Report 2003-9, Dept. of Industrial & Systems Engineering. 2003, University of Florida: Florida. [6] Raghunatan A.U., G.V., Subramaniam D.,Biegler L.T.,Samad T., Dynamic Optimi-zation Strategies for 3D Conflict Resolution of Multiple Aircraft. AIAA, 2003. [7] Vian J.L., M.J.R., Trajectory Optimization with Risk Minimization for Military Aircraft. Journal of Guidance Control and Dynamics, 1989. 12(3): p. 311-317. [8] Fugère J., F.L., Y. Liang. An Approach to Design Autonomous Agents with Mod-SAF. in Systems, Man, and Cybernatics Inter. Conf. 1999. Hawaii: IEEE. [9] Bang, H.-L.C.H.R.M.-J.T.H., A co-evolutionary method for pursuit-evasion games with non-zero lethal radii. Engineering Optimization, 2004. 36(1): p. 19-36(18). [10] H.Lee, Y.I.L., E.J.Song, B.C.Sun, and M.J.Tahk, Missile Guidance using neural networks. Control Engineering Practice, 1997. 5(6). [11]Frank W. Moore, O.N.G. A New Methodology for Optimizing Evasive Maneuvers Under Uncertainty in the Extended Two -Dimensional Pursuer/Evader Problem. in IEEE Int. Conf. on Tools with Artificial Intelligence. 1997: IEEE. [12]Sweetman, B., Fighter Tactics, in Jane's Air Force, Jane's, Editor. 29 May 2001, Janes. [13]Carrol, D.L., Fortran Genetic Algorithm (GA) Driver : http://cuaerospace.com/carroll/ga.html, 2004 [14]Zipfel, P.H., Modeling and Simulation of Aerospace Vehicle Dynamics. AIAA Educational Series, ed. J.S. Przemieniecki. 2000, Reston: AIAA Inc. [15]Khosla, R.D., T., Engineering Intelligent Hybrid MultiAgent Systems. 1997, Boston: Kluwer Academic Publishers.
