TY - GEN
T1 - A Penetration Metric for Deforming Tetrahedra using Object Norm
AU - Kim, Jisu
AU - Kim, Young J.
N1 - Funding Information:
ACKNOWLEDGEMENTS This project was supported by the National Research Foundation (NRF) in South Korea (2017R1A2B3012701).
Publisher Copyright:
© 2019 IEEE.
PY - 2019/11
Y1 - 2019/11
N2 - In this paper, we propose a novel penetration metric, called deformable penetration depth PDd, to define a measure of inter-penetration between two linearly deforming tetrahedra using the object norm [1]. First of all, we show that a distance metric for a tetrahedron deforming between two configurations can be found in closed form based on object norm. Then, we show that the PDd between an intersecting pair of static and deforming tetrahedra can be found by solving a quadratic programming (QP) problem in terms of the distance metric with non-penetration constraints. We also show that the PDd between two, intersected, deforming tetrahedra can be found by solving a similar QP problem under some assumption on penetrating directions, and it can be also accelerated by an order of magnitude using pre-calculated penetration direction. We have implemented our algorithm on a standard PC platform using an off-the-shelf QP optimizer, and experimentally show that both the static/deformable and deformable/deformable tetrahedra cases can be solvable in from a few to tens of milliseconds. Finally, we demonstrate that our penetration metric is three-times smaller (or tighter) than the classical, rigid penetration depth metric in our experiments.
AB - In this paper, we propose a novel penetration metric, called deformable penetration depth PDd, to define a measure of inter-penetration between two linearly deforming tetrahedra using the object norm [1]. First of all, we show that a distance metric for a tetrahedron deforming between two configurations can be found in closed form based on object norm. Then, we show that the PDd between an intersecting pair of static and deforming tetrahedra can be found by solving a quadratic programming (QP) problem in terms of the distance metric with non-penetration constraints. We also show that the PDd between two, intersected, deforming tetrahedra can be found by solving a similar QP problem under some assumption on penetrating directions, and it can be also accelerated by an order of magnitude using pre-calculated penetration direction. We have implemented our algorithm on a standard PC platform using an off-the-shelf QP optimizer, and experimentally show that both the static/deformable and deformable/deformable tetrahedra cases can be solvable in from a few to tens of milliseconds. Finally, we demonstrate that our penetration metric is three-times smaller (or tighter) than the classical, rigid penetration depth metric in our experiments.
UR - http://www.scopus.com/inward/record.url?scp=85081163575&partnerID=8YFLogxK
U2 - 10.1109/IROS40897.2019.8967563
DO - 10.1109/IROS40897.2019.8967563
M3 - Conference contribution
AN - SCOPUS:85081163575
T3 - IEEE International Conference on Intelligent Robots and Systems
SP - 8111
EP - 8116
BT - 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019
Y2 - 3 November 2019 through 8 November 2019
ER -