Fundamentals of Soft Continuum Robots

Kinematics, stiffness modelling and model-based control of soft continuum robots

Soft continuum robots exhibit highly compliant and nonlinear behaviour, making conventional rigid-body kinematics and control methods unsuitable. My research establishes analytical frameworks for modelling and controlling pneumatically actuated soft continuum robots, with a particular focus on kinematics, configuration-dependent stiffness and model-based inverse kinematics. These developments provide the theoretical foundations for accurate robot prediction, interaction analysis and closed-loop control, and underpin many of my subsequent research activities in soft medical robotics.

Kinematics and Stiffness Modelling

Analytical models are essential for understanding the nonlinear mechanics of soft continuum robots and enabling model-based robot design and control. I developed analytical frameworks based on Cosserat rod theory to describe both the kinematic behaviour and the configuration-dependent stiffness of fibre-reinforced soft continuum robots.

The proposed models capture several important nonlinear phenomena, including:

  • large deformation of compliant structures;
  • material hyperelasticity;
  • cross-sectional deformation during elongation;
  • interaction between robot configuration and mechanical stiffness.

The resulting framework enables accurate prediction of robot shape, tip position and force-generation capability while remaining computationally efficient for real-time applications.

Illustration of robot compliance for (a) rigid-linked and (b) soft continuum robots, under two different robot configurations.
Configuration-dependent kinematics and stiffness modelling of soft continuum robots.

Model-Based Inverse Kinematics Control

Building upon the analytical modelling framework, I developed model-based inverse kinematics algorithms for pneumatically actuated soft continuum robots. Instead of relying on empirical calibration or learning-based approaches, the controller directly exploits the analytical robot model to determine the actuation pressures required to achieve a desired robot configuration.

The proposed framework enables:

  • model-based inverse kinematics;
  • real-time trajectory tracking;
  • improved positioning accuracy;
  • seamless integration with higher-level control algorithms.

This work establishes a complete mechanics-based control framework for soft continuum robots and provides the theoretical basis for later developments in interaction control and autonomous robotic manipulation.

More details are available in the IEEE/ASME Transactions on Mechatronics paper.

The modelling and control methods presented on this page are described in the following publications:

  1. J. Shi, W. Gaozhang, S.-A. Abad and H. Wurdemann,
    Stiffness Modelling and Control for Soft Material Continuum Robotic Manipulators,
    In Soft Material Robotic Systems: Recent Advances and Future Developments,
    Springer, 2026.
    [Chapter]

  2. J. Shi, Understanding Compliance Properties of Soft Continuum Robots: From Analytical Model to Model-based Control,
    RSS Pioneers, 2024.
    [PDF]

  3. J. Shi, S.-A. Abad, J. S. Dai and H. A. Wurdemann,
    Position and Orientation Control for Hyperelastic Multisegment Continuum Robots,
    IEEE/ASME Transactions on Mechatronics, 2024.
    [PDF]

  4. J. Shi, A. Shariati, S.-A. Abad, Y. Liu, J. S. Dai and H. A. Wurdemann,
    Stiffness Modelling and Analysis of Soft Fluidic-Driven Robots Using Lie Theory,
    The International Journal of Robotics Research, 2024.
    [PDF]