Contribution to Inverse Kinematics of Flexible Robot Arms

An inverse kinematics problem of flexible manipulators is considered. The problem is of importance for compensation of tip deflections when the manipulators perform quasi-static operations. Basic equations based on both kinematic and static relationships are derived and explicit expressions of the mathematical model are presented. Based upon this model, a definition of the inverse kinematic task of flexible manipulators is formulated. Specific features of the task are considered, and a conventional approach applicable for resolving the task is analyzed. To avoid the disadvantages of the conventional approach, an implicit iterative scheme based upon step-by-step compensation for the relative elastic deflections is proposed. Corresponding convergence conditions of the scheme are derived, and applicability of the scheme is verified through simulation.