3D Curvature-Based Tip Load Estimation for Continuum Robots

This letter presents a method intended for the estimation of external force and moment applied at the tip of thin rods using vision-based shape measurements, with a view to be applied on continuum robots. A versatile vision process is developed that does not require any additional markers nor sensors to provide an accurate tri-dimensional reconstruction of the deformable rod shape. Then, the tip loads (i.e., forces and moments) are directly deduced from the curvature along this curve formed by deformed rod thanks to the resolution of a linear system without requiring any iterative optimization. The curvature is determined with a robust method that allows filtering out measurement noise and artifacts. Simulations show that this approach gives fast and precise results in both 2D (planar forces estimation without torsion) and 3D (spatial forces estimation). Experimental results on cantilever rods demonstrate an accuracy of 2.2% and 2.7% of the applied forces and moments, respectively.