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This paper proposed a novel path planning method which is called the line-generating obstacle detecting and avoidance method (LGODAM) for mobile robot supported by a certainty grids map which can be upbuilt by SLAM. The LGODAM can be applied to obstacles with any shape of its outline. By this means, the local optimum problem is well resolved, also the mission of global path planning is decomposed into a series of phasic sub mission in real-time way during the running of mobile robot. In our research, uni-vector field tracking controller is applied to robot. The effectiveness and elegance of the LGODAM is demonstrated by simulation studies. A number of test cases are presented, each shows a stable, smooth, reasonable and no oscillating path to the destination of mobile robot.