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Whether the mobile robot has the ability to explore an entire environment influences the integrality of map built by mobile robot in unknown environment. However, this demand becomes challenging when mobile robot experiences positioning error and sensor noises in practical environment. In this paper, a novel exploration approach called FRT is proposed to solve the problem. The moment invariants widely used in image processing field and the DS evidence theory used for multi-sensors information fusion are both introduced into FRT algorithm to ensure the robustness of FRT algorithm. The FRT algorithm is validated by a simulation experiment and the experimental results demonstrate its performance.