This work considers the problem of controlling transmit power within a wireless sensor network (WSN), where the practical constraints typically posed by an ambulatory healthcare setting are explicitly taken into account, as a constrained received signal strength indicator (RSSI) tracking control problem. The problem is formulated using an explicit generalised predictive control (GPC) strategy for dynamic transmission power control that ensures a balance between energy consumption and quality of service (QoS) through the creation of a stable floor on information throughput. Optimal power assignment is achieved by an explicit solution of the constrained GPC problem that is computed off-line using a multi-parametric quadratic program (mpQP). The solution is shown to be a piecewise-affine function. The new design is demonstrated to be practically feasible via a resource-constrained, fully IEEE 802.15.4 compliant, Moteiv's Tmote Sky sensor node platform. Design utility is benchmarked experimentally using a representative selection of scaled ambulatory scenarios.