This special issue is devoted to robot motion planning. The main scope of this issue covers research work on mobile robotics. Motion planning is necessary when the robot determines its own actions. For the last decade, the paradigm of motion planning in mobile robotics has shifted from off-line motion planning to on-line motion planning and from planning in a static environment to planning in a time-varying environment. Recent progress of computational power has enabled this paradigm shift, since on-line motion planning and planning in time-varying environments require repeated computation based on sensory information which is always renewed. The guest editors organized this special issue in order to highlight those two new paradigms. We present two survey papers: One is a survey of on-line motion planning for a sensor-based navigation of a mobile robot, and the other is a survey of motion planning for mobile robots in a time-varying environment. Along with the survey papers, distinguished technical papers are provided in this special issue. Concerning path planning, a paper describing a case study on motion planning with teaching is included (Ogata et al). Motion planning based on Fuzzy logic is one approach, and three papers from Maeda, Ishikawa et al. and Nagata et al. also belong to this category. To offer a case study on reactive motion decision making, one paper by Ando et al. is included. A recently emerging subject is related to motion planning for cooperation of multiple mobile robots or a single robot among multiple moving obstacles. Three papers from Yoshioka et al., Ota et al., and Fujimura discuss problems on motion planning for cooperation of multiple mobile robots. One paper from Tsubouchi et al. discussed the motion planning of a single robot among multiple moving obstacles. Motion planning to select an appropriate corner cube as a landmark is addressed in the paper from Hashimoto et al. The guest editors hope that this special issue will provide the readers with a lock at some current issues and new perspectives on robot motion planning.