With the widespread application of industrial robots, the problem of absolute positioning accuracy becomes increasingly prominent. To ensure the working state of the robots, researchers commonly adopt calibration techniques to improve its accuracy. However, an industrial robot's working space is mostly restricted in real working environments, making the collected samples fail in covering the actual working space to result in the overall migration data. To address this vital issue, this work proposes a novel industrial robot calibrator that integrates a measurement configurations selection (MCS) method and an alternation-direction-method-of-multipliers with multiple planes constraints (AMPC) algorithm into its working process, whose ideas are three-fold: a) selecting a group of optimal measurement configurations based on the observability index to suppress the measurement noises, b) developing an AMPC algorithm that evidently enhances the calibration accuracy and suppresses the long-tail convergence, and c) proposing an industrial robot calibration algorithm that incorporates MCS and AMPC to optimize an industrial robot's kinematic parameters efficiently. For validating its performance, a public-available dataset (HRS-P) is established on an HRS-JR680 industrial robot. Extensive experimental results demonstrate that the proposed calibrator outperforms several state-of-the-art models in calibration accuracy.