Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Applications of the dual Be´zier representation of rational curves and surfaces
Proceedings of the international conference on Curves and surfaces in geometric design
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Polynomial and Rational Pythagorean-Hodograph Curves Reconciled
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
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The aim of this paper is to demonstrate that the techniques of Computer Aided Geometric Design such as spatial rational curves and surfaces could be applied to Kinematics, Computer Animation and Robotics. For this purpose we represent a method which utilizes a special class of rational curves called Rational Frenet-Serret (RF) curves for robot trajectory planning. RF curves distinguished by the property that the motion of their Frenet-Serret frame is rational. We describe an algorithm for interpolation of positions by a rational Frenet-Serret motion. Further more we present an algorithm for tracking the constructed RF motion to achieve the desired velocity distribution profile of robot arm.