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The goal of rescue robotics is to extend the capabilities and to increase the safety of human rescue teams. During a rescue mission a mobile robot is deployed on a rescue site and is operated from a safe place by a human operator. The operator can not see the robot and the environment and a decision on the path selection is very complicated. Our goal is to provide a kind of automatic “pilot system” to propose an operator a good direction or several options to traverse the environment, taking into an account the robot's static and dynamic properties. To find a good path we need a special path search algorithm on debris and a proper definition of a search tree, which can ensure smooth exploration. While the main goal of the algorithm is to keep the robot maximally stable at every step of its path, in some cases we need the robot to lose its balance and to change a 3D orientation discontinuously. Losing balance on purpose is an important feature for safe climbing up and going down the debris and it is the central issue of this paper. Exhaustive simulations were used to structure and analyze data and experiments were used to verify our approach to removing unsuitable directions of the search from the search tree.