Obstacle Avoidance Extremum Seeking Control based on Constrained Derivative-free Optimization

A new control scheme based on extremum seeking control (ESC) which employs a constrainedderivative-free optimization algorithm has been proposed in this paper. A theorem has been formulated to prove theconvergence result of ESC based on constrained derivative-free optimization. Generalized pattern search methodwith filter algorithm for constraint is used to generate a sequence of ESC control state. Since generalized patternsearch (GPS) method does not require continuously differentiable and Lipschitz conditions, noise cancellation algorithmis added to the proposed ESC algorithm which is then used for multi-agent robot system. The obstacles areexpressed as constraint functions instead of the traditional way of calculating the performance function of obstacles. Simulation results illustrate a multi-agent obstacle avoidance system which utilized the control algorithm to avoidobstacles that appear on the path of multi-agent robots. Based on the simulation results, it can be observed thatmulti-agents maintain their formation as per initial condition and follow the target without colliding into obstacleswhile navigating in a noisy environment. Performance comparison of the proposed algorithm with a referencealgorithm shows the efficiency of the proposed algorithm.