Soft Continuum Manipulator Research

Modal Kinematics

One of the most impressive examples in nature of dexterous behavior is the octopus. Its arms are flexible over their entire length, can bend in all directions, vary stiffness, grasp objects using whole-arm manipulation, and apply high forces with respect to its relatively light weight. Robotic arms inspired by the octopus have to undertake the challenge of emulating a virtually continuum structure to achieve prescribed objectives using current engineering technologies. The aim of this work is to develop an accurate model of a continuum robotic arm whose design incorporates key features of the octopus. The proposed arm will have high dexterity, compliant contact, and a soft prehensile grasp. It can be used in underwater exploration tasks in highly unstructured and narrow environments, and for grasping of irregularly shaped objects. Following figure shows a ultisection continuum arm prototype developed in the Italian Institute of Technology (IIT), Genova, Italy.


A novel kinematic model, based on a prototype continuum arm, that can be applied to any geometrically constrained variable length multisection continuum robot. This approach addresses previous model limitations and produces complete and correct results for forward and inverse kinematic problems. The proposed model is based on a novel MSF approach that facilitates intuitive derivation of MSFs, thus eliminating modal switching schemes and simplifying error models. It avoids kinematic singular configurations arising in previous models and introduces inverse kinematics for position and/or orientation. Also, inverse kinematic problems are solved directly in the joint space avoiding difficulties in inverse mapping stages due to nonlinear relationships. This physically motivated model produces correct results in all aspects of kinematic analysis and provides enhanced insight into the practical mechanics of the robotic arm.


Research Members: Isuru Godage, David Branson, Emanuele Guglielmino, Gustavo A Medrano-Cerda, and Darwin G Caldwell.

The following videos show the inverse position kinematic tracking through the modal kinematic model and the kinematic decoupling feature which was not reported in previous kinematic models.

Dual Quaterion Kinematics for Continuum Arms

DQ’s produce higher accuracy than homogeneous transformation matrices (HTM) when transformed to modal shape functions (MSF) of similar order and are numerically stable. Thus, the model is compact, more accurate and computationally efficient than the modal kinematics proposed by the author based on HTM’s. Also, DQ kinematics does not suffer from singularity related limitations of Euler angle based inverse orientation kinematics. Recursive schemes for deriving DQ’s and DQ Jacobians are also presented and can be extended arbitrarily. Both modal HTM and modal DQ kinematics are then applied to solve illustrative spatial inverse position and orientation tracking problems. Based on the results, this paper quantitatively compares both methods and highlights the advantages of modal DQ kinematics. The proposed DQ kinematics are easily extensible to variable length multisection continuum arm with general actuator configurations.

Modal Dynamics

Due to highly nonlinear and complex nature of resulting expressions, only a few dynamic models have been developed. Lumped or segmented approach to approximate a continuum section have been presented in literature. Composed of simple rigid-linked segments, they avoid complex expressions and singularities associated with the actual curve parametric models. However, many number of such segments are required to successfully approximate smooth bending and hence results in many joint space variables. This leads to complex system models that do not give an insight to actual mechanical structure thus making it difficult to control. A new general modal spatial dynamic model for multisection continuum arms is proposed based on the modal kinematics described above. It also produces efficient numerical simulation results and enables investigating effects of different control schemes on continuum arms. The proposed model can be utilized to dynamically simulate of numerous continuum arm application scenarios such as obstacle avoidance and whole arm grasping, which were not possible with previous models.

The videos above show a dynamic simulation of a 3-section continuum arm and the second video shows a demonstrates the effect of compliance (of the elastic materials used in construction) and gravity. This simulation uses the novel modal spatial dynamic models.

The results above compare the experimental and simulation dynamic response results side by side for a multisection continuum arm prototype. The damping parameters were computed to match the prototype. These videos clearly shows the model is capable of capturing the essential dynamics of the prototype arm’s compliant behavior.

A Center of Gravity Based Approach for Dynamics of Continuum Manipulators

To achieve their full potential, soft and compliant continuum robots must move faster and more accurately than they can today. To facilitate this, accurate and computationally efficient dynamic models are essential. While the integral Lagrangian approach can produce accurate models, it is complex and computationally intensive. In this article we propose a new dynamic model based on numerically stable modal kinematics that is both accurate and computationally efficient. The proposed model is a lumped parameter model, but one that is more accurate than prior lumped parameter models because mass locations and quantities are derived from a detailed description of the total energy in a continuum arm with continuously distributed mass. We experimentally validated the model using a pneumatic muscle-actuated continuum arm, and the proposed model successfully simulates the transient and steady-state dynamics of the prototype arm. Further, the model is also compared to the integral Lagrangian and a lumped parameter model to highlight its advantages in terms of computational efficiency and its accuracy


  1. Isuru S. Godage, Raul Wirz, Ian D. Walker, and Robert J. Webster, “Accurate and Efficient Dynamics for Variable Length Continuum Arms: A Center of Gravity Approach”, Soft Robotics (SoRo), 2015, pp. 96-106.
  2. Isuru S. Godage and Ian D. Walker, “Dual Quaternion Based Modal Kinematics for Multisection Continuum Arms“, in  IEEE International Conference on Robotics and Automation (ICRA) 2015, pp. 1416-1422.
  3. Isuru S. Godage, Gustavo A. Medrano-Cerda, David T. Branson, Emanuele Guglielmino, Darwin G. Caldwell, “Modal kinematics for multisection continuum arms“, in the Journal of Bioinspiration & Biomimetics (B&B), 2015,pp. 10 (2015) 03500201-20.
  4. Isuru S Godage, David T. Branson, Emanuele Guglielmino et al. (2011) Dynamics for Biomimetic Continuum Arms: A Modal Approach, 104-109. In IEEE International Conference on Robotics and Biomimetics (ROBIO).
  5. Isuru S Godage, Emanuele Guglielmino, David T Branson et al. (2011) Novel Modal Approach for Kinematics of Multisection Continuum Arms, 1093-1098. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).
  6. Isuru S Godage, David T Branson, Emanuele Guglielmino et al. (2011) Shape Function-Based Kinematics and Dynamics for Variable Length Continuum Robotic Arms, 452-457. In IEEE International Conference on Robotics and Automation (ICRA).
  7. Isuru S Godage, David T Branson, Emanuele Guglielmino et al. (2012) Path Planning for Multisection Continuum Arms, 1208-1213. In IEEE International Conference on Mechatronics and Automation (ICMA).
  8. Jessie L. C. Santiago, Isuru S. Godage, Phanideep Gonthina, Ian D. Walker, Soft Robots and Kangaroo Tails: Modulating Compliance in Continuum Structures via Mechanical Layer Jamming, in Soft Robotics (SoRo), 3(2), 2016.
  9. H. Habibi, C. Yang, R. Kang, I. D. Walker, Isuru S. Godage & D. T. Branson III, “Modeling an actuated large deformation soft continuum robot surface undergoing external forces using a lumped-mass approach”, in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018, (accepted).
  10. Rongjie Kang, Emanuele Guglielmino, Letizia Zullo, David T. Branson III, Isuru S. Godage, and Darwin G. Caldwell, Embodiment Design of Soft Continuum Robots, in Advances in Mechanical Engineering (AIM), 8(4), 2016, pp. 1687814016643302.
  11. Isuru S. Godage, Raul Wirz, Ian D. Walker, and Robert J. Webster III, “Efficient spatial dynamics for continuum arms“, in ASME Dynamic Systems and Control Conference (DSCC), 2015, pp. 1-8.
  12. Isuru S. Godage, Gustavo A. Medrano-Cerda, David T. Branson, Emanuele Guglielmino, and Darwin G. Caldwell, “Dynamics for Variable Length Multisection Continuum Arms“, in International Journal of Robotics Research (IJRR), 2015, pp. 1-28.
  13. Manas M. Tonapi, Isuru S. Godage, and Ian D. Walker, “A Novel Continuum Robotic Cable Aimed at Applications in Space“, in Continuum Manipulators Special Issue of Advanced Robotics (AR), 2015, pp. 861-875.
  14. Jessie Santhiago, Ian D. Walker, and Isuru S. Godage, “Continuum robots for space applications based on layer-jamming scales with stiffening capability“, in  IEEE Aerospace Conference (IAC), 2015, pp. 1-13.
  15. Manas M. Tonapi, Isuru S. Godage, and Ian D. Walker, “Spatial Kinematic Modeling of a Long and Thin Continuum Robotic Cable“, in  IEEE International Conference on Robotics and Automation (ICRA) 2015, pp. 3755-3761.
  16. Manas M. Tonapi, Isuru. S. Godage, and Ian D. Walker, “Design, Modeling and Performance Evaluation of a Long and Slim Continuum Robotic Cable”, in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2014, pp. 2852-2859.
  17. Manas Tanapi, Isuru S. Godage, Ian D. Walker (2014). Next Generation Rope-like Robot for In-Space Inspection, 2014, pp. 1-13. In IEEE Aerospace Conference (IAC).
  18. Emanuele Guglielmino, Isuru S. Godage, Letizia Zullo, Darwin G. Caldwell (2013). A Pragmatic Bio-inspired Approach to the Design of Octopus-inspired Arms, 4577-4582. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).
  19. Tianjiang Zheng, Isuru S Godage, David T Branson et al. (2013) Octopus inspired walking robot: Design, control and experimental validation, 816-821. In IEEE International Conference on Robotics and Automation (ICRA).
  20. Isuru S. Godage (2013). Modelling and Experimentation of Continuum Arms for Manipulation and Locomotion, PhD Thesis.