Input robustification for motion control of systems without rigid-body mode

Robust proximate-time-optimal inputs can be obtained by carrying out the optimization scheme on an augmented system where the vibrational modes are purposely repeated. This method has been successfully implemented on systems with rigid-body mode in many researchers´ work. However, the input robustification for systems without rigid-body mode poses a unique problem because of the time-unboundedness of the input. In this paper, a robustification scheme based on the command shaping technique of constrained least-square optimization is proposed to address this problem and an example is used to illustrate the process. To smooth out in-maneuver oscillation due to the fast maneuver, an energy optimization formulation is presented. The incorporation of the ET (extended insensitivity) technique is also explored to extend the robustness while maintaining a reasonable response speed.