Two methods are developed for trajectory planning for a flexible-link manipulator in this thesis. One is for compensating for the tip deviation of the manipulator moving at low speed while carry heavy payloads. The other is for reducing the tip oscillation of the fast moving manipulator. Both methods are based on the kinematics of flexible-link manipulators developed in this thesis, using the algebra of rotations.

The algebra of rotations is a kinematic representation for describing manipulator motion. With the introduction of the Euler parameters, a new algebra of rotations-based method is developed in this thesis for computing a sequence of rotations. As a result of this development, the algebra of rotations becomes very efficient for manipulator kinematic analysis, superior to the homogeneous transformation and the screw theory based methods.

Owing to its superior computation efficiency, the algebra of rotations is used in this work to develop the kinematics of flexible-link manipulators. Based on this kinematics, the motion of a flexible link manipulator can be expressed in terms of three components:​ the motion of its rigid link counterpart:​ the motion due to link deflections and the variation of link deflections due to changes in manipulator configuration. Three Jacobians related to the three motion components are derived and used to facilitate the motion mapping between the task space and the generalized coordinate space.

In motion planning for slow-moving manipulators, the link deflections vary with the joint variables. A two-step algorithm is developed in this thesis to decouple the variation of link deflections from the change of joint variables. In the first step of the calculation, for a given manipulator movement, the joint displacements are determined without considering the variation of link defections. In the second step the additional joint displacements are determined to compensate for link deflection variations.

In motion planning for fast-moving manipulators, the link deflections and the joint motions are coupled. A sequential integration method is developed in this thesis to resolve this problem. Based on the proposed method, the joint motions can be determined in the course of integrating the dynamic equation for link deflections.

The simulation examples presented in the thesis show that the proposed motion-planning methods substantially improve the locating or tracking accuracy of flexible-link manipulators.