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.
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