On inverting singular kinematics and geodesic trajectory generation for robot manipulators

1993 ◽  
Vol 8 (3) ◽  
pp. 325-359 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Ignacy Dulęba
Keyword(s):  
Robot Manipulators ◽  
Trajectory Generation

Motion Interpolation With G2 Composite Bézier Motions

1994 ◽  
Author(s):  
Q. J. Ge ◽  
Donglai Kang
Keyword(s):  
Robot Manipulators ◽  
Trajectory Generation ◽  
Second Order ◽  
Inverse Design ◽  
Geometric Continuity ◽  
Direct Construction ◽  
Cnc Machines ◽  
Smooth Motion ◽  
Computer Aided ◽  
Refined Version

Abstract This paper deals with smooth motion interpolation. Recently, a direct construction algorithm was developed for designing piecewise parametric motions with second order geometric continuity (G2). The present paper provides a refined version of the G2 spline algorithm and shows how the G2 spline motion can be used to fulfill the task of motion interpolation by solving the problem of inverse design for the G2 spline motion. The results are useful for computer aided motion animation, and Cartesian trajectory generation for CNC machines and robot manipulators.

The Application of Curvature Theory to the Trajectory Generation Problem of Robot Manipulators

1992 ◽  
Vol 114 (4) ◽  
pp. 677-680 ◽  
Author(s):  
M. M. Stanisˇic´ ◽  
K. Lodi ◽  
G. R. Pennock
Keyword(s):  
Robot Manipulators ◽  
Trajectory Generation ◽  
Rate Of Change ◽  
Speed Ratio ◽  
Coordination Problem ◽  
Geometric Problem ◽  
Curvature Theory ◽  
Instantaneous Speed ◽  
Generation Problem

This paper illustrates a new application of planar curvature theory to the geometric problem of trajectory generation by a two-link manipulator. The theory yields the instantaneous speed ratio, and the rate of change of the speed ratio, which correspond to the geometry of a desired point trajectory. Separate from the purely geometric speed ratio problem (i.e., the coordination problem) is the time based problem of controlling the joint rates in order to move with the specified path variables.

Motion Interpolation With G2 Composite Be´zier Motions

1995 ◽  
Vol 117 (4) ◽  
pp. 520-525 ◽  
Author(s):  
Q. J. Ge ◽  
Donglai Kang
Keyword(s):  
Robot Manipulators ◽  
Trajectory Generation ◽  
Geometric Algorithms ◽  
Inverse Design ◽  
Direct Algorithm ◽  
Geometric Continuity ◽  
Design Algorithm ◽  
Cnc Machines ◽  
Smooth Motion ◽  
Computer Aided

This paper deals with smooth motion interpolation. It presents two geometric algorithms for synthesizing composite Be´zier motions with second-order geometric continuity (G2). The first one is a direct algorithm for constructing a G2 spline motion that approximates a set of displacements; the second one is an inverse design algorithm for a G2 spline motion that interpolates through a set of displacements. The results are useful for computer aided motion animation, and Cartesian trajectory generation for CNC machines and robot manipulators.

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