Gradient-descent based trajectory planning for regulation of a two-link flexible robotic arm

In the control of flexible manipulators, most work in the literature concentrates on the suppression of link deformations. In this study, the aim is not to suppress the deflections, but to calculate joint angles to minimize the tip position error. A gradient descent method is utilized off-line for the trajectory planning of a two-link flexible manipulator under gravity. Fuzzy logic control with gravity compensation is applied for the position control of the manipulator where the reference inputs are the values of the joint angles as determined by the trajectory planning procedure. Simulations have been carried out to show the performance of both the trajectory planning method and of the fuzzy controller in a regulation problem. Results are illustrated both in the joint space and in the operational space