Application of the modified method simulating the behavior of a flock of Moths to solve the optimal open loop control problem of a mobile robot movement

The article proposes a modification of the metaheuristic optimization method simulating the behavior of a swarm of moths, which belongs to the group of bio-inspired methods. A step-by-step algorithm is formed and the efficiency of the modified method is studied on a generally accepted set of test functions of many variables with a complex structure of level surfaces, on the problem of optimal open loop control with a known exact solution, as well as on the problem of determining the parameters of the tension/compression spring with constraints such as inequalities. The advantage of the modified method over the original version is shown. It is demonstrated that the method allows finding solutions of sufficiently good quality in a time acceptable from a practical point of view. A solution to an applied problem of finding the optimal open loop control of a mobile robot on a plane in the presence of obstacles is given. The goal of the control is to achieve a given end point while minimizing the elapsed time and fulfilling the condition of enveloping forbidden areas. To find the control law as a function of time, a piecewise constant approximation was used, which allows reducing the problem to finding a finite number of unknown parameters. The solutions of the terminal problem of speed of response with different structure and parameters of the composite quality functional are considered using the sequential application of the developed modified method simulating the behavior of a swarm of moths, the random search method with sequential reduction of the study area and the path-relinking method. The results of comparison with known solutions are presented.

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