This paper introduces a novel distributive path planning method, the bending beam method, for mobile robots moving in environments monitored by wireless sensor networks. The proposed method is inspired by the deflection analysis of bending beams. The initial and goal positions of a mobile robot are connected by a virtual beam. The in-between obstacles are replaced with the effective loads acting on the beam. The resulting robot path is represented by the deflection curve of the beam under those loads. Following the principle of superposition, the beam deflection under all the loads is equal to the sum of the deflections caused by the individual loads acting on the beam separately. In an environment covered by a wireless sensor network, each sensor node monitors the obstacles (stationary and moving) in its neighborhood. By letting each sensor node compute the deflections of the virtual beam caused by only those neighboring obstacles, the computation load for the global robot path planning can be distributed among the sensor nodes. Thus, the path planning becomes a highly parallel computation procedure. The robot only needs to collect the results from the sensor nodes and sum them up to generate its path. Moreover, the robot path can be dynamically modified by the sensor nodes in the case of moving obstacles. As a result, the proposed method may substantially reduce the time complexity of the sensor-based motion planning for mobile robots in dynamic environments, with the assistance from sensor networks.

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