Significance of spline curve in path planning of flexible manipulator

Two methods are presented to design the joint trajectory for a two-link flexible manipulator: 1) a combined Fourier series and polynomial function; and 2) a B-spline function. In both cases, the path satisfies the start and end kinematic constraints of motion. Using the energy approach for the above two cases, the final path is generated optimizing kinetic and strain energy at the goal point that reduces the residual vibration significantly. The present study is to compare the two methods and to predict that the B-spline curve has faster convergence property and at the same time, minimizes the performance index by six-fold and thus gives further reduction of residual vibration compared to the combined Fourier series and polynomial function. The dynamics of the manipulator arm, during its motion as well as free vibration after reaching the goal, are described by finite element analysis using Lagrange's equation of motion.