Fast convex minimization to detect collisions between polyhedra

Mirolo, Claudio; Pagello, Enrico

doi:10.1109/iros.2000.895202

Cited by 5 publications

(5 citation statements)

References 21 publications

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“…To solve the problem in this case, we derive another relative kinematic model which is equivalent to system (11). In this section, we consider the general case of moving objects.…”

Section: Moving Objects: Transformation Of Coordinatesmentioning

confidence: 99%

“…In this section, we consider the general case of moving objects. To solve the problem in this case, we derive another relative kinematic model which is equivalent to system (11). The relative velocity between R and M i can be written in terms of the relative velocity components in the Cartesian representation, that is, Finally, by the decomposition of v rel into components along and across the visibility line, we get the following system of kinematic equations:…”

Section: Moving Objects: Transformation Of Coordinatesmentioning

confidence: 99%

“…System (34) with v n and θ n as given by (35) is called the transformation model. This system is equivalent to system (11). If M i is a stationary object, then systems (11) and (34) are reduced to system (29).…”

Section: Moving Objects: Transformation Of Coordinatesmentioning

confidence: 99%

“…This system is equivalent to system (11). If M i is a stationary object, then systems (11) and (34) are reduced to system (29). Therefore, it is possible to reduce the collision course detection problem between a moving robot and a moving object M i to the collision course detection between a virtual moving robot R n and a stationary object M s i .…”

Section: Moving Objects: Transformation Of Coordinatesmentioning

confidence: 99%

“…The algorithmic complexity is the main drawback of this method. [10,11], and general polygonal models in ref. A safe swept volume method that uses convex approximation is suggested in ref.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Collision course by transformation of coordinates and plane decomposition

Bendjilali

Belkhouche

2009

Robotica

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This paper deals with the problem of collision course checking in a dynamic environment for mobile robotics applications. Our method is based on the relative kinematic equations between moving objects. These kinematic equations are written under polar form. A transformation of coordinates is derived. Under this transformation, collision between two moving objects is reduced to collision between a stationary object and a virtual moving object. In addition to the direct collision course, we define the indirect collision course, which is more critical and difficult to detect. Under this formulation, the collision course problem is simplified, and complex scenarios are reduced to simple scenarios. In three-dimensional (3D) settings, the working space is decomposed into two planes: the horizontal plane and the vertical plane. The collision course detection in 3D is studied in the vertical and horizontal planes using 2D techniques. This formulation brings important simplifications to the collision course detection problem even in the most critical and difficult scenarios. An extensive simulation is used to illustrate the method in 2D and 3D working spaces.

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“…To solve the problem in this case, we derive another relative kinematic model which is equivalent to system (11). In this section, we consider the general case of moving objects.…”

Section: Moving Objects: Transformation Of Coordinatesmentioning

confidence: 99%

Section: Moving Objects: Transformation Of Coordinatesmentioning

confidence: 99%