Cubic-spline trajectory planning of a constrained flexible manipulator

A cubic-splines trajectory planning of a constrained rigid-flexible manipulator to minimize the contact force is considered. Based on the general dynamic model of the chain of flexible links, equations of motion for the manipulator are derived using the extended Hamilton's principle. An analytical solution for the inverse dynamics problem using the assumed modes method is presented to compute the required joint torques for the tip mass to move along the constrained surface. Cubic-splines interpolation has been adjusted for the joint motion profiles to make sure that the end-effector will follow the prescribed trajectory without degradation. The knot points of the trajectories have been chosen on the constrained surface to achieve minimum contact force as possible.