Ellipsoid-tree construction for solid objects
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Continuous collision detection for articulated models using Taylor models and temporal culling
ACM SIGGRAPH 2007 papers
Fast approach for computing roots of polynomials using cubic clipping
Computer Aided Geometric Design
C2A: controlled conservative advancement for continuous collision detection of polygonal models
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Continuous collision detection between two 2D curved-edge polygons under rational motions
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
An algebraic approach to continuous collision detection for ellipsoids
Computer Aided Geometric Design
Formation control of multiple elliptical agents with limited sensing ranges
Automatica (Journal of IFAC)
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Collision detection and avoidance are important in robotics. Compared with commonly used circular disks, elliptic disks provide a more compact shape representation for robots or other vehicles confined to move in the plane. Furthermore, elliptic disks allow a simpler analytic representation than rectangular boxes, which makes it easier to perform continuous collision detection (CCD). We shall present a fast and accurate method for CCD between two moving elliptic disks, which avoids any need to sample the time domain of the motion, thus avoiding the possibility of missing collisions between time samples. Based on some new algebraic conditions on the separation of two ellipses, we reduce collision detection for two moving ellipses to the problem of detecting real roots of a univariate equation, which is the discriminant of the characteristic polynomial of the two ellipses. Several techniques are investigated for robust and accurate processing of this univariate equation for two classes, of commonly used motions: planar cycloidal motions and planar rational motions. Experimental results demonstrate the efficiency, accuracy, and robustness of our method