ln this article we will look to some methods for computing a trajectory in multidimensional space which describes the desired motion of a manipulator. A trajectory refers to a time history of position, velocity, and acceleration for each degree of freedom.
This problem includes the human interface problem of how we wish to specify a trajectory or path through space. ln order to make the description of manipulator motion easy for a human user of a robot system, the user should not be required to writedown complicated functions of space and time to specify the task. Rather, we must allow the capability of specifying trajectories with simple descriptions of the desired motion, and let the system figure out the details. For example, the user may just specify the desired goal position and orientation of the end-effector, and leave it to the system to decide on the exact shape of the path to get there, the duration, the velocity profile, and other details.
We will consider motions of a manipulator as motions of the tool frame, {T}, relative to the station frame, {S}. This is the same manner in which an eventual user of the system would think, and designing a path description and generation system in these terms will result in a few important advantages.
When we specify paths as motions of the tool frame relative to the station frame, we decouple the motion description from any particular robot, end-effector, or workpieces. This results in a certain modularity, and would alIow the same path description to be used with a different manipulator, or with the same manipulator with a different tool size. Further, we can specify and plan motions relative to a moving workstation (perhaps a conveyor belt) by planning motions relative to the
station frame as always, and at run time causing the definition of {S} to be changing with time.
The basic problem is to move the manipulator from an initial position to some desired final position. That is, we wish to move the tool frame from its current value, {Tinitial} to a desired final value, {Tfinad}. Note that this motion in general involves a change in orientation as welI as a change in position of the tool relative to the station.
Sometimes it is necessary to specify the motion in much more detail than simply stating the desired fina,l configuration. Qne way to include more detail in a path description is to give a sequence of desired via points or intermediate points between the initial and final positions. Thus, in completing the motion, the tool frame must pass through a set of intermediate positions and orientations as described by the via points. Each of these via points is actualIy a frame which specifies both the position and orientation of the tool relative to the station. The name path points includes alI the via points plus the initial and final points. Remember that although we generalIy use the term "points,"
Author: David Alejandro Trejo Pizzo. IEEE Member and researcher @ AIGROUP, working in the FIC Project. Student @ Universidad de Palermo.