Block-synchronous Harmonic Control for Scalable Trajectory Planning

Trajectory planning consists in finding a way to get from a starting position to a goal position while avoiding obstacles within a given environment or navigation space. Harmonic functions may be used as potential fields for trajectory planning. Such functions do not have local extrema, so that control algorithms may reduce to locally descend the potential field until reaching a minimum, when obstacles correspond to maxima of the potential and goals correspond to minima. This chapter presents a parallel hardware implementation of this navigation method on reconfigurable digital circuits. Trajectories are estimated after the iterated computation of the harmonic function, given the goal and obstacle positions of the navigation problem. The proposed massively distributed implementation locally computes the direction to choose to get to the goal position at any point of the environment. Changes in this environment may be immediately taken into account, for example when obstacles are discovered during an on-line exploration. To fit real-world applications, our implementation has been designed to deal with very large navigation environments while optimizing computation time.

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