Command Shaping for Minimizing Residual Vibration in a Flexible-Joint Robot

The performance of mechanical systems is limited by residual oscillations caused by joint fl exibility. Command shaping reduces the residual oscillations at resonance frequencies of the system while achieving fast motions by carefully constructing torque commands to the motors. Two different cost functions are utilized to fi nd the optimal input that minimizes residual oscillations at natural frequencies. One can be solved analytically with a closedform solution, while the other requires a numerical solution. Two different input profi les are tested for both methods on a two-link fl exible-joint robot. One profi le uses a versine basis function and the other uses a ramped sinusoid basis function.