Impedance matching of boundary conditions in a one-link Flexible robot

The purpose of this study consisted of three main parts: first, to evaluate the characteristic impedance of a flexible one-link robotic arm, second, to develop a method of matching the beam's impedance at the controlled end of the manipulator so that transverse vibrational waves could be removed from the beam, and finally, to compare the beam's response to work done by other researchers.

A form of quasi-impedance was used to approximate the manipulator's characteristic impeance, since it was necessary to use boundary conditions which could be created by a typical robot manipulator. Using this method, it was determined that a negative spring constant would be necessary to create the desired boundary condition, and the system would therefore be unstable.

Therefore, using the concept of complex natural frequencies, boundary conditions were determined which would maximize the exponentially decaying part of the natural frequency, and therefore give the beam its largest damping. Again, it was determined that a negative spring was necessary to produce this condition.

Results from both methods were compared to a study by Cannon and Schmitz in which they created control algorithms for a similar beam. The impedance-matching method yielded the best results, with response time theoretically 35% faster than that of Cannon and Schmitz.

The difficulties of the inherintly unstable system are not thought to be great, since other control algorithms can be used to replace the unstable ones once the beam has attained its desired position.