A Differential Geometry Modeling Method for Wheeled Climbing Robots Tracking Control on Variable Curvature Surfaces

Wheeled climbing robots equipped with tools can achieve high-coverage machining of large components with free-form surfaces. Trajectory tracking is the foundation for machining. However, there is a lack of a universal yet accurate model for robots while moving on variable curvature surfaces, making it difficult to guarantee tracking performance. Thus, this article proposes a universal contact frame based on differential geometry and establishes a kinematics model that uses surface parameters as state variables for robots moving on variable curvature surfaces. Based on this model, a tracking controller utilizing surface parameters error is then designed, enabling it to be applicable for tracking of climbing robots on free-form surfaces. Experiments with a wheeled climbing robot on a portion of a real wind turbine blade with a radius of more than 1.1 m demonstrate the effectiveness of the proposed method, with a root mean squared error (RMSE) of tracking accuracy of less than 1 mm.