Configuration Estimation of Continuum Robots Using Piecewise Constant Curvature Generalized Epi-Polar Constraint Model

In recent years, continuum robots have attracted more attention for they can work in more severe environments. However, at present, most of the research focuses on the mechanical structure innovation, and there are few pieces of research on the control of this kind of robot. Since continuum robots are deformable, their shape is a general curve in space. Therefore, they are not fully defined by actuator positions, which are different from the traditional rigid robots. To achieve more accurate control, a method of sensing robot configuration in real-time is necessary. However, the existing visual-based approaches all adopt external global cameras, which is difficult to adapt to the demand of unknown unstructured environments. This paper presents a system capable of estimating the configuration of continuum robots under piecewise constant curvature (PCC) assumption from cameras mounted on each constant curvature segment. Specifically, we first proposed the PCC 2R model, which is equivalent to each cc-segment of PCC continuum robots by two joints rigid bodies, thereby reducing the problem complexity and improving the numerical stability of the estimation. Then, based on the PCC 2R model, we proposed the PCC generalized epi-polar constraint to completely constrain the four degrees of freedom of each cc-segment in planar, it can be solved through one corresponds, to estimate the configuration of continuum robots under PCC. Finally, the above approach is verified by experiment.