Controlling velocity-limited systems to reduce residual vibration

To avoid vibration of robot arms when they are moved very rapidly, a set of shaped force profiles have been developed to minimize the excitation energy at the system´s first natural frequency during motion. The system is assumed to be velocity-limited. The force profiles are constructed from a versine (one-cosine) function and its harmonics, with coefficients chosen to minimize the spectral magnitude near the system natural frequency. The profiles can be tuned to the closed-loop natural frequency of a closed-loop system with motor position and velocity feedback. When integrated twice, the force profile becomes a reference trajectory which serves to bring the system to peak velocity with minimum excitation at the first natural frequency. Using a suitable dwell time between acceleration and deceleration, a specified position can be reached quickly with minimum residual vibration and within while never exceeding the velocity limit