Optimization of a Test Trajectory for SCARA Systems

The synthesis of a smooth curve to implement the test trajectory used in SCARA systems is the subject of this paper. The test trajectory includes square corners between its vertical and horizontal segments, which are sources of velocity and acceleration discontinuities. Lame curves are used to smooth the corners to provide G(2)-continuity throughout the test trajectory. Moreover, to make the overall trajectory as smooth as possible, the parameters defining this curve should be selected so as to minimize a cost function. The trajectory is thus synthesized by minimizing the root-mean-square (rms) value of the kinetic energy time-derivative, subject to inequality constraints. using the Orthogonal Decomposition Algorithm, which is based on gradient evaluations.