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In this paper, we propose an autonomous tree climbing strategy for a novel tree climbing robot that is named Treebot. The proposed algorithm aims to guide Treebot in climbing along an optimal path by the use of minimal sensing resources. Inspired by inchworms, the algorithm reconstructs the shape of a tree simply by the use of tactile sensors. It reveals how the realization of an environment can be achieved with limited tactile information. An efficient nonholonomic motion planning strategy is also proposed to make Treebot climb on an optimal path. This is accomplished by the prediction of the future shape of the tree. The study that is presented in this paper also includes the formulation of Treebot kinematics and an analysis of the workspace of Treebot on different shapes of a tree. Numerous experiments have been conducted to evaluate the proposed autonomous climbing algorithm and to unveil the ability of Treebot.