Fundamental Modelling and Control 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 inverse kinematics algorithms that calculate the actuation pressures required to achieve a desired robot position and orientation. The controller enables real-time trajectory tracking without relying on extensive empirical calibration or training data.

In complementary collaborative work with researchers at Inria, we developed a reduced finite element model for real-time inverse kinematics control. Combined with position feedback, the method achieved median trajectory-tracking errors below 2 mm for single- and two-segment soft continuum robots.

Sensor-free Contact Force Control

Building upon the stiffness and inverse kinematics models, I developed a compliance model-based approach for controlling the contact forces generated by soft continuum robots. The method uses the robot’s configuration-dependent compliance matrix to determine the deflection required to produce a desired Cartesian force. An inverse kinematics algorithm then calculates the corresponding actuation pressures.

The proposed approach enables:

  • contact force control along three Cartesian axes;
  • force regulation across different robot configurations;
  • control without dedicated force-sensing feedback;
  • operation without extensive training data.

The framework was experimentally validated using both single- and two-segment pneumatic soft continuum robots, achieving mean static force-control errors below 5% of the desired peak forces.

Learning-based Robot Control

In collaborative work led by Dr. Elijah Almanzor, I contributed to a vision-based learning framework for controlling the complete shape of soft continuum robots. The method combines deep visual inverse kinematics with camera feedback, enabling closed-loop shape control without embedded sensors.

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]

  5. J. Shi, S.-A. Abad, J. S. Dai and H. A. Wurdemann,
    Compliance Model-Based Contact Force Control for Soft Continuum Robots,
    Soft Robotics, 2026.
    [PDF]

  6. P. Chaillou, J. Shi, A. Kruszewski, I. Fournier, H. A. Wurdemann and C. Duriez,
    Reduced Finite Element Modelling and Closed-Loop Control of Pneumatic-Driven Soft Continuum Robots,
    IEEE International Conference on Soft Robotics (RoboSoft), 2023.
    *Equal contribution.
    [PDF]

  7. E. Almanzor, F. Ye, J. Shi, T. G. Thuruthel, H. A. Wurdemann and F. Iida,
    Static Shape Control of Soft Continuum Robots Using Deep Visual Inverse Kinematic Models,
    IEEE Transactions on Robotics, 2023.
    [PDF]