Sub-optimal trajectory planning of flexible manipulator along specified path

Rapid end point positioning along a specified path is considered in this study. The structure between the actuator and the end point of the robot arm is assumed flexible and is the main cause of positioning error because of residual vibration. An algorithm, based on optimization of residual energy at the goal point and the fundamental property of time scaling of manipulator dynamics, is developed that iteratively determines the time optimal trajectory along the specified path under given start and end point conditions. It also considers the full nonlinear dynamics of the manipulator arm and its actuator saturation limit, The dynamics are described by finite element method using Lagrange´s equation and are expressed by the time scale factor. The performance index is optimized successfully through off-line computation for a two link flexible manipulator, one example of which is described in detail