Magic-Formula-Based Feedforward Velocity Control of a Magnetically Coupled Wall-Climbing Robot

This study presents a model-based feedforward method for reducing velocity errors during the vertical travel of a magnetically coupled wall-climbing robot. Permanent magnets on opposite sides of the wall maintain magnetic coupling, while a spring-preloaded linkage adjusts the drive-wheel normal force. A dedicated test bench was used to measure the traction–slip characteristics of the urethane roller–acrylic contact at normal forces of 20 and 30 N. Magic Formula models were fitted to the measurements. Representative slip magnitudes were calculated from the models and the ascent force balance using a nominal equivalent resistance of the robot. These fixed magnitudes were applied to both ascent and descent through direction-dependent wheel-velocity commands. In experiments without longitudinal velocity feedback, the compensation reduced the absolute errors in mean velocity and travel distance, averaged over all tested conditions, by approximately 76% and 69%, respectively. The method was also integrated with proportional–integral velocity feedback and pure pursuit path tracking and assessed in repeated ascent–descent trials. The results demonstrate the error-reduction capability of the fixed feedforward compensation under the tested conditions.