Automated B-spline curve representation incorporating MDL and error-minimizing control point insertion strategies

1999 ◽  
Vol 21 (1) ◽  
pp. 49-53 ◽  
Author(s):  
T.-J. Cham ◽  
R. Cipolla
2019 ◽  
Vol 103 (1) ◽  
pp. 003685041988011
Author(s):  
Jiangping Mei ◽  
Fan Zhang ◽  
Jiawei Zang ◽  
Yanqin Zhao ◽  
Han Yan

According to the problem that the existing high-speed parallel robot cannot satisfy the operation requirements of non-planar industrial production line, a 6-degrees-of-freedom high-speed parallel robot is proposed to carry out the kinematic and dynamic analyses. Combining with the door-type trajectory commonly used by the parallel robot, it adopts 3-, 5-, and 7-time B-spline curve motion law to conduct the trajectory planning in operation space. Taking the average cumulative effect of joint jerky as the optimization target, a trajectory optimization method is proposed to improve the smoothness of robot end-effector motion with the selected motion law. Furthermore, to solve the deformation problem of the horizontal motion stage of the trajectory, a mapping model between the control point subset of B-spline and the motion point subset of trajectory is established. Based on the main diagonally dominant characteristic of the coefficient matrix, the trajectory deformation evaluation index is constructed to optimize the smoothness and minimum deformation of the robot motion trajectory. Finally, compared to without the optimization, the maximum robot joint jerk decreases by 69.4% and 72.3%, respectively, and the maximum torque decreases by 51.4% and 38.9%, respectively, under a suitable trajectory deformation.


2004 ◽  
Vol 36 (7) ◽  
pp. 639-652 ◽  
Author(s):  
Huaiping Yang ◽  
Wenping Wang ◽  
Jiaguang Sun

2010 ◽  
Vol 26 (6-8) ◽  
pp. 801-811 ◽  
Author(s):  
Mingxiao Hu ◽  
Jieqing Feng ◽  
Jianmin Zheng

1994 ◽  
Vol 18 (3) ◽  
pp. 327-334 ◽  
Author(s):  
Kuo-Liang Chung ◽  
Wen-Ming Yan

Author(s):  
Guicang Zhang ◽  
Kai Wang

Firstly, a new set of Quasi-Cubic Trigonometric Bernstein basis with two tension shape parameters is constructed, and we prove that it is an optimal normalized totally basis in the framework of Quasi Extended Chebyshev space. And the Quasi-Cubic Trigonometric Bézier curve is generated by the basis function and the cutting algorithm of the curve are given, the shape features (cusp, inflection point, loop and convexity) of the Quasi-Cubic Trigonometric Bézier curve are analyzed by using envelope theory and topological mapping; Next we construct the non-uniform Quasi-Cubic Trigonometric B-spline basis by assuming the linear combination of the optimal normalized totally positive basis have partition of unity and continuity, and its expression is obtained. And the non-uniform B-spline basis is proved to have totally positive and high-order continuity. Finally, the non-uniform Quasi Cubic Trigonometric B-spline curve and surface are defined, the shape features of the non-uniform Quasi-Cubic Trigonometric B-spline curve are discussed, and the curve and surface are proved to be continuous.


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