Simulating surfing with optimal control: sensor fusion for biomechanical analysis

Abstract Currently, no established biomechanical model exists for surfing. Musculoskeletal simulations provide valuable insights for athletes to enhance performance and prevent injuries using quantitative data such as joint angles, joint moments, and muscle forces. The dynamic nature of surfing makes biomechanics difficult to assess in a laboratory setting. Although inertial measurement units (IMUs) offer a potential solution, relying solely on IMU data in three-dimensional musculoskeletal models presents challenges, due to integration drift and noise. We present a multimodal approach combining IMU data with deep learning-based human pose estimation to simulate surfing movements. We collected data from seven experienced surfers on a river wave, providing a semicontrolled environment. Ten IMUs were placed on the participants, with cameras positioned around the wave. We defined an optimal control problem to drive three-dimensional biomechanical simulations and used an adapted contact model to represent the interaction between feet, surfboard, and water. To demonstrate the potential of our approach, we compared the kinematics and kinetics of the front and rear legs, and analyzed muscle forces. The study minimized tracking errors and established the first biomechanical model for surfing. Differences of up to 47% were found in rear and front leg joint moments and angles, with muscle forces being higher in the front leg. However, these differences were not statistically significant for our small sample. These results suggest weight distribution mainly relies on front leg muscles, while rear leg moments contribute to stabilization. Our findings showcase the high potential for biomechanical analysis in surfing performance using our approach.