About the Use of the Floating Frame in the Optimal Control of the Flexible Robot Arm

摘要

The mathematical model of a single-link flexible manipulator is obtained by measuring transverse deflections in a rotating reference frame which is floating with respect to the link. The use of this particular frame, the rigidbody mode frame, enables one to obtain weakly coupled equations of motion. The size of the inertia coupling terms can be easily evaluated: these terms can be shown to be negligible thus leading to an essentially linear model. An example of optimal control of manipulator's tip position is numerically reproduced. The same controller is first applied to the mechanical model of the arm accounting for non-linear coupling and then to the linear model: the two responses are found to be very close to each other.