To increase the productivity by fast motion and to complete a motion by small energy consumption, robot manipulators are required to have light and flexible structures. If fast motions are performed by light and flexible robot arms, however, the compliance which inherently exists in the transmission and structural elements will cause considerable vibration of the robot endpoint at the end of a move. Several different approaches have been suggested to reduce residual vibration, which can be loosely categorized as either open-loop or closed-loop strategies. The open-loop strategies consist of specifying force or torque profiles to drive the dynamical system. Closed-loop strategies utilizing constant or variable feedback gains have also been designed for reducing residual vibration of flexible systems. In recent years, there has been a considerable body of research on input shaping for rapid end-point positioning of a structure with minimum residual vibration.
There have been, however, few attempts to reduce residual vibration by designing path itself. Residual vibration sustained after a positioning move freely oscillates with the initial conditions which are the position and velocity errors at the end of a move. This vibration results not only from the dynamic characteristics of system but also from the manipulator path between its two endpoints. This paper focuses upon establishing the manipulator path that reduces this residual vibration, given that a required motion must be accomplished within a certain time. First of all, a simple and effective dynamic model to ease the computation complexities both in motion and path analysis is established. All flexibilities of links and joints are taken into account in this model. The distributed model is used to represent the link flexibility. Relative coordinates are adopted as the coordinate system. Special moving coordinates, called virtual link coordinate system, is used to represent the link flexibilities.
Then, based upon this model, we optimize the path to reduce residual vibration. Characteristics of residual vibration are identified from linearized equations of motion. From these results, the performance index is selected to reduce residual vibration effectively. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables, i.e. Fourier coefficients, the only ones which have a considerable effect on the reduction of residual vibration. A two-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate manipulator path.
Finally, a closed-loop control theory is applied to track the planned path in the case of load variation. Specifically, it is desired that the optimally designed path has a better trajectory tracking capabilities during the residual vibration over the cycloid path, in various cases of load. Perturbation adaptive control is used as closed-loop control scheme. The paths to be tracked are selected as the unlimited optimal path and torque-limited optimal path.
