## 1 Introduction
For example, the above studies do not consider natural terrains or soil Terramechanics, but consider aspects of velocity control, thermodynamics and trajectory curvature, which are not present in our problem. Hence, the involved control-theoretic and optimization-theoretic approaches cannot be readily applied to our problem. Finally, it is worth mentioning that the studies in [6; 21; 22; 23] are also closely related to this paper. In particular, the study in [21] proposes an improved ant colony algorithm for solving the problem of UGV path planning on uneven terrain with soil deformation and slope limitations. However, the study does not consider an explicit energy calculation model and considers only artificial/simulated terrain with a low number of traversal nodes. The study in [22] addresses the problem of finding UGV paths with minimum energy consumption using an \(A^{*}\)-like algorithm. However, this study does not take the soil Terramechanics into consideration. Moreover, it is based on directly minimizing the energy consumption as a single metric. The study in [6] addresses the problem of UGV shortest path planning on uneven natural terrains, subject to energy consumption constraints. This approach falls under the more general weight-constrained shortest path problem, which is well-known to be NP-hard to solve--see, e.g., [23]. The study in [23] is a preliminary exposition of some of the results presented in this paper. However, and in contrast to this paper, the study in [23] does not consider the soil Terramechanics. This paper adds the soil Terramechanics aspects, effectively resulting in soil trafficability limitations. This paper also adds the ant colony optimization (ACO) [24] implementation to the problem, as well as new results using new natural terrain graphs. We highlight the contributions of this paper as follows. * We propose a new greedy (Dijkstra-like) path planning algorithm for UGVs on irregular natural real-life terrains. The algorithm is based on a composite routing metric that combines the distance and energy consumption of the path. * We consider the vehicle-soil contact Terramechanics in our algorithm, which involves the vehicle structure information and soil composition data. The algorithm also takes realistic soil and slope limitations, UGV power limitations and air humidity into account. * Our numerical results indicate that the proposed composite metric performs better than the direct energy consumption metric in terms of reducing the overall constructed path distance, with a minimal increment in the energy consumption. Thus, our proposed approach strikes a better balance between the path distance and energy consumption. Additionally, it is verified that the proposed greedy algorithm strongly outperforms the ACO implementation in terms of both the path distance and consumed energy, and algorithm running time. * Our numerical running time results demonstrate that our algorithm is well-suited for sizable natural terrain graphs with thousands of nodes and tens of thousands of links. The remainder of paper is organized as follows. Section 2 presents the needed preliminary information, such as soil trafficking, and the employed energy model. In Section 3, we present the energy-efficient shortest path planning algorithm based on the composite metric routing approach. Section 4 lays out the simulations setup and illustrates the simulation results and discussion. Finally, Section 5 concludes the paper.