Proximity Query (PQ) is a process to calculate the relative placement of objects. It is a critical task for many applications such as robot motion planning, but it is often too computationally demanding for real-time applications, particularly those involving human-robot collaborative control. This paper derives a PQ formulation which can support non-convex objects represented by meshes or cloud points. We optimise the proposed PQ for reconfigurable hardware by function transformation and

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... d precision, resulting in a novel data structure and memory architecture for data streaming while maintaining the accuracy of results. Run-time reconfiguration is adopted for dynamic precision optimisation. Experimental results show that our optimised PQ implementation on a reconfigurable platform with four FPGAs is 58 times faster than an optimised CPU implementation with 12 cores, 9 times faster than a GPU, and 3 times faster than a double precision implementation with four FPGAs.