The BPE formation concept, while advantageous for enabling decentralized localization and control in multi-vehicle systems, has several limitations. One significant drawback is its reliance on the assumption that some inter-agent bearings are persistently exciting (PE). If the formation topology changes or if the vehicles experience dynamic environments that affect their relative bearings, maintaining the BPE condition can become challenging. This can lead to difficulties in ensuring the uniqueness of the formation configuration and the stability of the observer-based controllers.
Furthermore, the BPE formation may not guarantee global observability in all scenarios, particularly in configurations where the number of PE bearings is insufficient. This limitation can restrict the applicability of the BPE concept in larger or more complex formations.
To generalize or relax the BPE formation concept, researchers could explore hybrid approaches that combine BPE with other localization techniques, such as integrating range measurements or using additional sensors that provide complementary information. Additionally, relaxing the conditions on the graph topology required for BPE could enhance its applicability, allowing for more flexible formations that can adapt to changing environments or communication constraints.