Interventions in emergency situations require to be fast, accurate and safe, in order to bring a quick assistance. As it may often be risky for people to bring a direct assistance, the use of automatic devices, such as mobile robots, in a first step can offers a safe solution. Nevertheless, it implies the motion control on low structured environment moreover at important speed. This may generate important perturbations with respect to classical motion control law, which cannot be considered in such applications. In this paper, a new control approach, taking into account natural ground characteristics is proposed, in order to preserve the accuracy and stability of the robot. An adaptive and predictive control algorithm is firstly designed, based on both an extended kinematic and a dynamic representation. It permits to address path tracking in harsh conditions and preserve a high level of accuracy without considering the robot stability in a first step. In addition, an active velocity and trajectory management algorithm is developped from control point of view to avoid the rollover risk and obstacle collision thanks to the notion of traversability. Since the adaptive control law estimates the dynamic parameters of the robot (grip conditions, centre of gravity position), a 3D model is available and a stability metric is evaluated in real time. Beyond this evaluation, a predictive control principle is deduced to compute the maximal admissible control variables to preserve the robot stability (i.e. robot maximal velmocity). Such maximal robot action is then merge to a 3D digital map obtained via Lidar sensor, in order to evaluate stability along its expected trajectories, and select the best way with the highest reachable speed. Capabilities of such approach is investigated through full scale experiments.