L_∞ parameter estimates for volumetric error in models of machine tools

Software error compensation is becoming an increasingly important aspect of numerically controlled machine tools. Currently, the error models are identified using the least-squares criterion. This criterion does not necessarily reflect the evaluation criteria of a machine's performance. In this paper, we develop a method for identifying the error model of a machine tool using a Chebyshev norm. The model parameter identification procedure becomes a linear program, and the resulting error models minimize the maximum error of the machine across its workspace thus affording strict bounds on the errors produced by the machine.