Blending Velocities in Task Space in Computing Robot Motions

The computational burden is less than that of blending positions and orientations.

Blending of linear and angular velocities between sequential specified points in task space constitutes the theoretical basis of an improved method of computing trajectories to be followed by robotic manipulators. Task space denotes the coordinate transformation describing the end-effector position and orientation, as well as other parameters (e.g., arm angle, base position) which completely and conveniently describe the arm pose without explicit specification of the joint angles. A related prior method of generating trajectories involves blending of positions and orientations between sequential points in task space. The present improved method achieves the same results as does the prior method, but with much less computation.

In the improved method, a generalized velocity-vector-blending technique provides a relatively simple, common conceptual framework for blending linear, angular, and other parametric velocities. The velocity vectors originate from straight-line segments that connect the specified task-space points, which are called "via frames" and which represent specified robot poses (see figure). Linear-velocity-blending functions can be chosen from among firstorder, third-orderpolynomial, and cycloidal options (see figure). Angular velocities are blended by use of a firstorder approximation of a previous orientation-matrix-blending formulation. The angular-velocity approximation yields a small residual error, which is quantified and corrected.

The method was tested, both by computer simulation and by experimentation on a computer-controlled seven-degree-of-freedom robot arm on a one-degree-of-freedom platform, as shown in simplified form in the figure. Linear blending was arbitrarily chosen for these tests. The results of both the simulation and experiments showed that the method offers both the relative simplicity and the speed needed for generation of robot manipulator trajectories in real time.

Point of Contact:
Richard A. Volpe
Mail Stop 198-219
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena, CA 91109
818-354-6328
Richard.A.Volpe@jpl.nasa.gov

Telerobotics Program page

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Last updated: May 10, 1996