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Purpose This paper aims to propose an optimized overview of firefly algorithm (FA) over physical-natural impression of fireflies and its application in mobile robot navigation under the natural intelligence mechanism. Design/methodology/approach The brightness and luminosity are the decision variables in proposed study. The paper achieves the two major goals of robot navigation; first, the optimum path generation and, second, as an obstacle avoidance by co-in-centric sphere-based geometrical technique. This technique comprises the optimum path decision to objective function and constraints to paths and obstacles as the function of algebraic-geometry co-relation. Co-in-centric sphere is the proposed technique to correlate the constraints. Findings It is found that the present FA based on concentric sphere is suitable for efficient navigation of mobile robots at the level of optimum significance when compared with other approaches. Originality/value The paper introduces a novel approach to implement the FA for unknown and uncertain environment.

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