This article presents the dynamic path planning for a mobile robot to track a randomly moving goal with avoidance of multiple randomly moving obstacles. The main feature of the developed scheme is its capability of dealing with the situation that the paths of both the goal and the obstacles are unknown a priori to the mobile robot. A new mathematical approach that is based on the concepts of 3-D geometry is proposed to generate the path of the mobile robot. The mobile robot decides its path in real time to avoid the randomly moving obstacles and to track the randomly moving goal. The developed scheme results in faster decision-making for successful goal tracking. 3-D simulations using MATLAB validate the developed scheme.

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