A Non-Linear Model Predictive Task-Space Controller Satisfying Shape Constraints for Tendon-Driven Continuum Robots

Tendon-driven continuum robots (TDCRs) have the potential to be used in minimally invasive surgery and industrial inspection, where the robot must navigate narrow and confined spaces. We propose a model predictive controller (MPC) to leverage the non-linear kinematics and redundancy of TDCRs for whole-body collision avoidance, with real-time capabilities for hanadling inputs at 30 Hz. Key to our method's effectiveness is the integration of a nominal piecewise constant curvature (PCC) model for efficient computation of feasible trajectories, with a local feedback controller to handle modeling uncertainties and disturbances. Our experiments in simulation show that our MPC outperforms conventional Jacobian-based controller in position tracking, particularly under disturbances and user-defined shape constraints, while also allowing the incorporation of control limits. We further validate our method on a hardware prototype, showcasing its potential for enhancing the safety of teleoperation.