Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating ob...Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiate almost everywhere w. r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.展开更多
The fast and accurate collision detection and distance calculation between geometric models is fundamen-tal in robotics, manufacturing and computer-simulated en-vironments. This paper surveys the state of the art in t...The fast and accurate collision detection and distance calculation between geometric models is fundamen-tal in robotics, manufacturing and computer-simulated en-vironments. This paper surveys the state of the art in the theory and algorithms of distance and pseudo distance func-tions between convex sets. An overview on the existing results, including fast algorithms for distance calculation, definitions and properties of various pseudo distance functions (the J-function, the growth distance, and the pseudo minimum translational distance), is presented. The distance and pseudo distance functions are versatile in a wide range of areas. Their applications in robot motion planning, grasp analy-sis/synthesis, form error evaluation, and engineering optimi-zation is demonstrated.展开更多
基金the National Natural Science Foundation of China (Grant Nos. 59805004, 59990470) the National Distinguished Youth Foundation (Grant No. 59725514).
文摘Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiate almost everywhere w. r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.
基金supported by the National Natural Science Foundation of China(Grant Nos.50175014,50390063 and 59990470).
文摘The fast and accurate collision detection and distance calculation between geometric models is fundamen-tal in robotics, manufacturing and computer-simulated en-vironments. This paper surveys the state of the art in the theory and algorithms of distance and pseudo distance func-tions between convex sets. An overview on the existing results, including fast algorithms for distance calculation, definitions and properties of various pseudo distance functions (the J-function, the growth distance, and the pseudo minimum translational distance), is presented. The distance and pseudo distance functions are versatile in a wide range of areas. Their applications in robot motion planning, grasp analy-sis/synthesis, form error evaluation, and engineering optimi-zation is demonstrated.
