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Continuous collision detection for two moving elliptic disks
 IEEE Trans. Robotics
, 2006
"... Abstract—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 ..."
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Cited by 11 (1 self)
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Abstract—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. Index Terms—Collision detection, ellipses, elliptic disks, interference analysis, rational motion. I.
Continuous collision detection for elliptic disks
 IEEE Transactions on Robotics
, 2006
"... Collision detection and avoidance is important for various tasks in robotics. Compared with commonly used circular disks, elliptic disks provide compact shape representation for robots or other vehicles confined to move in the 2D plane. Furthermore, elliptic disks allow simpler analytic representati ..."
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Cited by 6 (1 self)
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Collision detection and avoidance is important for various tasks in robotics. Compared with commonly used circular disks, elliptic disks provide compact shape representation for robots or other vehicles confined to move in the 2D plane. Furthermore, elliptic disks allow simpler analytic representation than rectangular boxes do; this makes it easier to perform continuous collision detection. We shall present a fast and accurate method for continuous collision detection between two moving elliptic disks; continuous collision detection does not need to sample the time domain of motion, thus avoiding missing possible collision 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. Various techniques are investigated in detail for robust and accurate processing of this univariate equation for two classes of commonly used motions: (1) planar screw motions; and (2) planar rational motions, i.e. motions that can be represented as rational functions of the time parameter t. Experimental results are presented to demonstrate the efficiency, accuracy and robustness of our method.
Continuous Collision Detection for Ellipsoids
"... We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids under rational Euclidean or affine motion. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition describ ..."
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Cited by 4 (0 self)
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We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids under rational Euclidean or affine motion. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then we derive a timedependent characteristic equation for two moving ellipsoids, which enables us to develop an efficient algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with practical examples.
Oriented Bounding Surfaces with at most Six Common Normals
"... Abstract — We present a new type of oriented bounding surfaces, which is particularly well suited for shortest distance computations. The bounding surfaces are obtained by considering surfaces whose support functions are restrictions of quadratic polynomials to the unit sphere. We show that the comm ..."
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Abstract — We present a new type of oriented bounding surfaces, which is particularly well suited for shortest distance computations. The bounding surfaces are obtained by considering surfaces whose support functions are restrictions of quadratic polynomials to the unit sphere. We show that the common normals of two surfaces of this type – and hence their shortest distance – can be computed by solving a polynomial of degree six. This compares favorably with other existing bounding surfaces, such as quadric surfaces, where the computation of the common normals is known to lead to a polynomial of degree 24. I.
Contact Prediction Between Moving Objects Bounded by
"... This paper presents an algorithm for exact contact prediction between moving objects bounded by curved surfaces. The algorithm uses hierarchies of oriented bounding boxes (HOBBs) and local numerical methods for finding contact. Objects need not be convex and are described using the Brep scheme. The ..."
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This paper presents an algorithm for exact contact prediction between moving objects bounded by curved surfaces. The algorithm uses hierarchies of oriented bounding boxes (HOBBs) and local numerical methods for finding contact. Objects need not be convex and are described using the Brep scheme. The bounding faces are represented by nonuniform rational Bsplines (NURBS). The collision time is sought in short time intervals during the motion, during which time is one of the problem variables. HOBBs are based on curvature regions of the surfaces. This criterion ensures that local numerical methods will converge to the contact points if they exist. The patches enclosed in overlapping leaf nodes are tested for contact by solving a system of nonlinear equations, based on the type of collision expected. The types of collision studied are cusp–cusp, cusp–ridge, cusp– face, ridge–ridge, ridge–face, and face–face collisions. The current algorithm is implemented and compared to an efficient polyhedral collision package, and results appear promising. [DOI: 10.1115/1.4005453] 1
RealTime Continuous Collision Detection for Moving Ellipsoids under Affine Deformation
"... We present an exact algebraic algorithm for realtime continuous collision detection (CCD) for moving ellipsoids under affine deformations. An efficient collision test is first developed for two static ellipsoids, which takes less than 1 microsecond. Using this practical result and the properties of ..."
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We present an exact algebraic algorithm for realtime continuous collision detection (CCD) for moving ellipsoids under affine deformations. An efficient collision test is first developed for two static ellipsoids, which takes less than 1 microsecond. Using this practical result and the properties of our algebraic condition, we produce a realtime solution to the CCD problem that computes the exact collision time intervals.
Efficient Continuous Collision Detection for Bounding Boxes under Rational Motion
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