This paper presents a novel proximity query (PQ) approach capable to detect the collision and calculate the minimal Euclidean distance between two non-convex objects in 3D, namely the robot and the environment. Such approaches are often considered as computationally demanding problems, but are of importance to many applications such as online simulation of haptic feedback and robot collision-free trajectory. Our approach enables to preserve the representation of unstructured environment in the form of triangular meshes. The proposed PQ algorithm is computationally parallel so that it can be effectively implemented on graphics processing units (GPUs). A GPU-based computation scheme is also developed and customized, which shows >200 times faster than an optimized CPU with single core. Comprehensive validation is also conducted on two simulated scenarios in order to demonstrate the practical values of its potential application in image-guided surgical robotics and humanoid robotic control.

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 reduced 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.