Estimating Forces Along Continuum Robots

Continuum robots can be slender and flexible to navigate through complex environments, such as passageways in the human body. In order to control the forces that continuum robots apply during navigation and manipulation, we would like to detect the location, direction, and magnitude of contact forces distributions as they arise. In this paper, we present a model-based framework for sensing distributed loads along continuum robots. Using sensed positions along the robot, we use a nonlinear optimization algorithm to estimate the loading which fits the model-predicted robot shape to the data. We propose that Gaussian load distributions provide a seamless way to account for a wide range of loadings, including approximate point loads and uniform distributed loads, while avoiding the ill-conditioning associated with highly resolved force distributions. In addition, we gain computational efficiency by re-framing the problem as unconstrained weighted least-squares minimization and by solving this problem with an Extended Kalman-filter framework. We validate the approach on two prototype tendon-driven continuum robots in multiple 3D loading scenarios, displaying a mean error of 0.58 N in load magnitude and 7% mean error in load location with respect to the length of the respective robot.