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Path planning of mobile robot in dynamic environment is one of the most challenging issues. To be more specific, path planning in multi-obstacle avoidance environment is defined as: given a vehicle A and a target G that are moving, planning a trajectory that will allow the vehicle to catch the target satisfy some specified constrains while avoiding obstacle O, and each of the obstacles can be either mobile or immobile in the environment. The corresponding problem is named target-pursuit and obstacles-avoidance (TPOA) and will be researched extensively in this chapter. The traditional method, such as probability road map, can achieve a successful path in 2D static environments. The planning process using this method generally consists of two phases: a construction and a query phase. In construction stage, the workspace of the robot is sampled randomly for generating candidate waypoints. In the query stage, the waypoints between the start and goal position are connected to be a graph, and the path is obtained by some searching algorithm, such as Dijkstra, A* algorithm and so on. Hraba researched the 3D application of probability road map where A* algorithm is used to find the near-optimal path (Hrabar, 2006). Although probability road map method is provably probabilistically complete (Ladd & Kavraki, 2004), it does not deal with the environment where the information is time-varying. The underlying reason is that this method only focuses on the certain environment. Once some uncertainty appears in the robot workspace, probability road map can not update with the changing environment and plan a valid trajectory for the mobile robot, never an optimal path. Artificial potential field is another traditional method which is generally used in both 2D and 3D environment. The mechanism that the robot is driven by attractive and repulsive force in a cooperative way is simple and often works efficiently even in dynamic environment. Kitamura et al. construct the path planning model based on the artificial potential field in threedimensional space which is described by octree (Kitamura et al, 1995). Traditionally, artificial potential field applies in two dimensions extensively. Also some other field concepts are invented. For example, there are harmonic potential functions (Kim & Khosla, 1992; Fahimi et al, 2009; Cocaud et al, 2008; Zhang & Valavanis, 1997), hydrodynamics (Liu et al, 2007),

Path Planning of Mobile Robot in Relative Velocity Coordinates