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

University of Toronto
Under review, 2024

We propose a MPC controller to enable tendon-driven continuum robots (TDCRs) to navigate between target end-effector positions while avoiding collision with a user-defined safe zone, which is crucial for safe teleoperation.

Abstract

Tendon-driven continuum robots (TDCRs) have the potential to be used in minimally invasive surgery and industrial inspection, where the robot must enter narrow and confined spaces. We propose a model predictive control (MPC) approach to leverage the non-linear kinematics and redundancy of TDCRs for whole-body collision avoidance, with real-time capabilities for handling inputs at 30Hz. 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 uncertainty 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 tasks.

Controller Overview

We integrate a nominal MPC for tip tracking and collision avoidance, with a local controller for disturbance rejection. The PCC model provides efficency for real-time performance, while the hierarchical architecture provides robustness against modeling uncertainty and disturbances.

Controller Overview

To the best of the authors' knowledge, this is the first controller capable of handling general shape constraints and joint velocity limits for a TDCR. Compared to a Jacobian-based controller, the MPC allows for straightforward imposition of hard limits on actuator speed and EE speed. Defining the feasible workspace can be easily accomplished using a 3D mesh, which is more challenging with a Jacobian-based approach. Overall, the MPC controller demonstrated distinct advantages in three key aspects:

  • Explicit collision avoidance constraints
  • Stability and convergence under disturbances
  • Straightforward formulation of control limits

BibTeX

@article{hachen2024nonlinearMPC,
        title={A Non-Linear Model Predictive Task-Space Controller Satisfying Shape Constraints for Tendon-Driven Continuum Robots}, 
        author={Maximillian Hachen and Chengnan Shentu and Sven Lilge and Jessica Burgner-Kahrs},
        journal={arXiv preprint arXiv:2409.09970},
        year={2024},
        }