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

Maximillian Hachen, Chengnan Shentu, Sven Lilge, Jessica Burgner-Kahrs

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.

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

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.
Paper Structure (27 sections, 20 equations, 12 figures)

This paper contains 27 sections, 20 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model-Free Approaches
  4. Model-Based Approaches
  5. Contribution
  6. MPC Formulation
  7. Robot State and Output
  8. Time Dependent Modelling
  9. Model Predictive Controller
  10. MPC Cost Function
  11. The MPC Optimization Problem
  12. Initializing the MPC Predictions
  13. MPC Constraints
  14. Local Controller
  15. Complete Controller
  16. ...and 12 more sections

Figures (12)

  • Figure 1: Our proposed MPC controller enables TDCRs (left) to navigate between target end-effector positions while avoiding collision with a user-defined safe zone (right), which is crucial for safe teleoperation. Please see attachment for videos.
  • Figure 2: 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.
  • Figure 3: A three-segment TDCR. Blue coloured tendon-routing disks mark the end of each segment. The robot state $\boldsymbol{x}$ is composed of the actuator variables $q_i,m$ and $\gamma_m$. The output shape $\boldsymbol{y}$ is composed of the tendon-routing disk positions $\boldsymbol{p}_1$, …, $\boldsymbol{p}_{3n}$. The position $\boldsymbol{p}_d$ is the desired end-effector position.
  • Figure 4: The TDCR's joint spcae is used as its state, with a non-linear and disturbed output function based on the PCC model.
  • Figure 5: Step response of the reference DLS controller for reaching a target position 40mm away with disturbances.
  • ...and 7 more figures