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The measurements repeat 10 times, and the averages of the error measures are listed in Table III. As can be seen in Table III, the orientation errors of the planar features are all very small. The average absolute position error using the linear method is 82.62 m, and the average location error of planar features is 53.12 m. Using the proposed method, the average absolute position error is reduced to 28.07 m, and the location error is less than 11.0 m, which are comparable to those obtained using the nonlinear method. VI. CONCLUSION An automatic camera calibration scheme that utilizes a CMM and a novel camera calibration algorithm is presented for a multiple-sensor integrated coordinate measurement system. Distinct from other multiple-stage methods, the proposed camera calibration method requires neither particular initial guess procedure nor nonlinear minimization process. Synthetic and experimental tests have demonstrated that accurate camera calibration and precise coordinate measurements can be obtained using the proposed calibration scheme. With high-precision calibration targets generated automatically using CMM and the proposed camera calibration algorithm, a fully automated and accurate camera calibration process can be performed for a multiple-sensor integrated system.

This work makes two contributions to geometric motion planning for multiple robots:1) motion plans are computed that simultaneously optimize an independent performance measure for each robot; 2) a general spectrum is defined between decoupled and centralized planning, in which we introduce coordination along independent roadmaps. By considering independent performance measures, we introduce a form of optimality that is consistent with concepts from multiobjective optimization and game theory literature. Previous multiple-robot motion planning approaches that consider optimality combine individual performance measures into a scalar criterion. As a result, these methods can fail to find many potentially useful motion plans. We present implemented, multiplerobot motion planning algorithms that are derived from the principle of optimality, for three problem classes along the spectrum between centralized and decoupled planning:1) coordination along fixed, independent paths; 2) coordination along independent roadmaps; 3) general, unconstrained motion planning. Computed examples are presented for all three problem classes that illustrate the concepts and algorithms.