This paper proposes an excitation trajectory optimization method for in-situ identification of dynamic parameters of industrial robots operating in constrained environments where human operators exist. Conventional parameter identification methods primarily focus on identification accuracy, requiring an ideal workspace without obstacles. These methods rarely consider scenarios where robots operate in complex, obstacle-rich environments, lacking the capability to actively adjust excitation trajectories to adapt to such constraints. To address this issue, we introduce a trajectory optimization strategy based on a boundary penalty function. By employing a Differential Evolution (DE) algorithm, the base parameters of the Fourier series-form excitation trajectory are optimized to satisfy both identification accuracy and environmental constraints simultaneously. The proposed method was validated by optimizing excitation trajectories and performing parameter identification in various obstacle environments. Comparisons were made with excitation trajectories that did not consider environmental constraints. Experiments are conducted with an Effort ER15 robot to demonstrate the effectiveness of the proposed approach. The robot successfully completed the excitation trajectory without collisions across multiple scenarios, with only a 1.66% reduction in parameter identification accuracy in constrained environments.