To advance the field of lithium-ion battery (LIB) research, this paper unveils an accurate modelling of LIB that primarily relies on the equivalent circuit model, backed by the Osprey Optimization Algorithm (OOA). In the modelling stage, both single and double resistance-capacitance models are evaluated to depict the charge dynamics, incorporating the effects of fading, load, and temperature variations. The OOA approach is utilized to minimize integral squared errors between the actual measured and model-predicted battery voltages under constraints imposed by the model design variables. This approach is applied to a commercial 2.6 Ahr Panasonic LIB, with the performance of the OOA-based model being benchmarked against models developed by means of other optimization algorithms for further validation. Moreover, the robustness of the OOA method is assessed under battery uncertainty conditions or model parameter variation. A sensitivity analysis is performed on the battery model by employing a proposed approach that evaluates the impact of varying each parameter of the battery model by ±5 %, in a sequence that ascends and descends from 0 to 5 %. The single resistance-capacitance model is selected for in-depth validations. Notably, the OOA approach excels in estimating parameters for LIB modeling under both normal and abnormal operating conditions.