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This is the first part of a series papers on modeling and path planning of the city-climber robot, a novel wall-climbing robot which can climb walls, move on ceilings and transit between floor and walls. In order to provide the city-climber with 3D path planning capability to carry out tasks such as cleaning, painting, and building inspection in 3D environments, we use mixed integer linear programming (MILP) as a tool to incorporate logical constraints such as obstacle avoidance and waypoint selection with basic dynamic constraints. In this paper, we derive the dynamic model of the city-climber robot in different cases, i.e., on the floor, walls, and ceiling, respectively. Non-dimensional variables are introduced to simplify the models. Simulation results verified the correctness of the model since the trajectories match the expected practical motion of the robot. MILP-based 3D path planning will be presented in part 2 which account for the dynamic constraints and obstacle avoidance.