As the cost and demand for civil infrastructure operations rise, it is necessary to automatize some processes, such as detecting fissures in cement columns or inspecting pipelines, in order to lower costs and ensure the safety of workers. In this context, climbing robots have been proposed to perform as tools for inspection, maintenance and cleaning operations. This work presents the design and implementation of a robot inspired by geckos, which attaches to smooth surfaces by using suction cups with a hold/release mechanism. The control process of the robot involves an inverse differential kinematics solver based on a weighted quadratic optimization. This approach allows the robot to obtain full-body motion control in order to climb adequately. Simulation and testing were performed to evaluate the performance of the control algorithm, adjust the movements generated, and ensure the viability of the suction cups mechanism used in the robot. The results obtained for the computational implementations are shown and discussed in this work.