Low-power Wireless Personal Area Networks (LoWPANs) are still in their early stage of development, but the range of conceivable usage scenarios and applications is tremendous. That range is extended by its inclusion in Internet with IPv6 Low-Power Personal Area Networks (6LoWPANs). This makes it obvious that multi-technology topologies, security and mobility support will be prevalent in 6LoWPAN. Mobility based communication increases the connectivity, and allows extending and adapting LoWPANs to changes in their location and environment infrastructure. However, the required mobility is heavily dependent on the individual service scenario and the LoWPAN architecture. In this context, an optimized solution is proposed for critical applications, such as military, fire rescue or healthcare, where people need to frequently change their position. Our scenario is health monitoring in an oil refinery where many obstacles have been found to the effective use of LoWPANs in these scenarios, mainly due to transmission medium features i.e. high losses, high latency and low reliability. Therefore, it is very difficult to provide continuous health monitoring with such stringent requirements on mobility. In this paper, a paradigm is proposed for mobility over 6LoWPAN for critical environments. On the one hand the intra-mobility is supported by GinMAC, which is an extension of IEEE 802.15.4 to support a topology control algorithm, 123 712 A. J. Jara et al.which offers intra-mobility transparently, and Movement Direction Determination (MDD) of the Mobile Node (MN). On the other hand, the inter-mobility is based on pre-set-up of the network parameters in the visited networks, such as Care of Address and channel, to reach a fast and smooth handoff. Pre-set-up is reached since MDD allows discovering the next 6LoWPAN network towards which MN is moving. The proposed approach has been simulated, prototyped, evaluated, and is being studied in a scenario of wearable physiological monitoring in hazardous industrial areas, specifically oil refineries, in the scope of the GinSeng European project.