Flexible head-following motion planning for scalable and bendable continuum robots

Continuum robots, which are characterized by high length-to-diameter ratios and flexible structures, show great potential for various applications in confined and irregular environments. Due to the combination of motion modes, the existence of multiple solutions, and the presence of complex obstacle constraints, motion planning for these robots is highly challenging. To tackle the challenges of online and flexible operation for continuum robots, we propose a flexible head-following motion planning method that is suitable for scalable and bendable continuum robots. Firstly, we establish a piecewise constant curvature (PCC) kinematic model for scalable and bendable continuum robots. The article proposes an adaptive auxiliary points model and a method for updating key nodes in head-following motion to enhance the precise tracking capability for paths with different curvatures. Additionally, the article integrates the strategy for adjusting the posture of local joints of the robot into the head-following motion planning method, which is beneficial for achieving safe obstacle avoidance in local areas. The article concludes by presenting the results of multiple sets of motion simulation experiments and prototype experiments. The study demonstrates that the algorithm presented in this paper effectively navigates and adjusts posture to avoid obstacles, meeting the real-time demands of online operations. The average time for a single-step solution is $4.41\times 10^{-5}$ s, and the average tracking accuracy for circular paths is 7.8928 mm.