Optimal Non-Bernoulli modeling method for experimental hydraulic robots

For hydraulic robots, modeling of the control flows is a key issue. The conventional modeling methods are based on the Bernoulli equation (i.e., the control flow is a function of the form equation which needs assumption of steady flow. In robotics, since the actual control flow is not always a steady flow, this paper provides a new practical modeling method without the Bernoulli equation. In a word, the proposed modeling method is a systematic version of the industrial modeling in which table representations are accepted and the assumption of steady flow is not needed. First, based on the input-state equation of hydraulic robots, we propose a new matrix representation of control flows via off-line input-output calculations. Second, based on the projection theorem in the matrix space, the optimal table representation is uniquely determined to be implementable. Finally, in comparison with the conventional modeling method with the Bernoulli equation, the effectiveness of the proposed modeling method is confirmed experimentally. The proposed modeling method is applicable to electric robots with complex friction and so on.