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Existing path planning schemes designed for wireless sensor networks generally account for abstract payload sensors, rendering them inapplicable to concrete sensor-array-based localization systems due to differences in measurement models. In this paper, we establish a general framework for path planning of a practical sensor array and factor in an oft-neglected degree of freedom regarding optimality, i.e., the array's orientation/attitude. The optimization problem is formulated based on the A-optimality criterion under constraints arising from the maximum distance between consecutive waypoints, maximal heading change, and forbidden regions. To facilitate semidefinite relaxation (SDR), we recast the optimization function into a fractional nonhomogeneous quadratic structure and transform the constraints into a bilinear form. By applying SDR and replacing the bilinear terms with a matrix variable, the problem is relaxed into a single-ratio fractional program. By leveraging the Charnes-Cooper variable transformation, we transform the single-ratio fractional program into a mixed semidefinite/second-order cone program (SD/SOCP) that can be solved in polynomial time. Finally, we apply the results to angle-of-arrival (AOA) and direct localization. Simulation results demonstrate that the proposed path planning scheme attains near-optimal performance.