This thesis is devoted to improve the application span of the 6LowPAN (IPv6 based Low Power Personal Area Network); a practical and commercially viable manifestation of IP-based ubiquitous sensor networks (IP-USNs). Ubiquitous Sensor Network (USN) that comprise low end devices (power, battery, cost, and life) are becoming increasingly important because they are poised to render a broad range of military and other commercial applications such as in Personal Area Networks (PANs). As many exciting applications emerge, that benefit from such IP connectivity, their burgeoning role necessitates provisioning of these applications beyond their local vicinity?entailing mobility. Sensor nodes usually have limited operating energy, processing power, memory and network efficiency. In order to keep network connectivity intact, especially while sensor nodes are moving, definition and provision of a mobility framework for these multi-constrained low end devices are necessary. In this thesis, we investigate existing state-of-the-art mobility support models, and propose a mobility support scheme for 6LoWPAN (LowMIPv6). We evaluate the improvement of LowMIPv6 over other existing models in terms of handover performance by simulating and comparing handover performance of LowMIPv6 scheme. Finally, we argue that the proposal can be used for the mobility for different scenario and application.