Algorithms for Continuum Robots

This research area is concerned with the development of efficient and real-time algorithms for model computation, motion generation as well as task- and situation adaptive control of continuum robots. The inherent flexibility and many to infinite degrees of freedom are the main challenges for algorithm development.


The theoretical foundation of traditional robots cannot be transferred directly to continuum robots. Thus far, there exist no general concepts for continuum robots, but methods for special cases and particular examples.

At CRL we aim at deriving fundamental methods, definitions, and characteristics for continuum robotics as they exist in conventional robotics. To achieve this, we investigate techniques leveraging elasticity theory, differential geometry, and optimization.

Motion Planning

Our lab is pioneering a novel approach in the motion planning of continuum robots, shifting the paradigm from traditional obstacle avoidance to embracing obstacles. By leveraging the underactuation and utilizing the interaction of a continuum robot with its environment, we aim to enhance reachability and steering capabilities, opening new avenues in robotic manipulation and navigation.

Trajectory generation and motion planning for continuum robots requires the development of scalable algorithms to consider the degrees of freedom and underactuation. While probabilistic methods led to sufficient first results, we are investigating motion planning algorithms which consider the morphology of continuum robots.

State Estimation

Our continuum robot state estimation work stems from a close collaboration with Dr. Tim Barfoot. Together, we found that the equations of motion commonly used in state estimation for a mobile robot trajectory which are parameterized by time, relate to those of quasi-static Cosserat rod model equations parameterized by arc length. This profound realization allowed us to repurpose a Gaussian process regression approach to state estimation, initially developed for continuous-time trajectory estimation in SE(3).

Our approach to state estimation for continuum robots is to fuse a prior distribution over robot states (i.e., shape and strain from a physical model) with sensed quantities (i.e., position/pose or strain) to generate a posterior distribution over robot states. In other words, we take a probabilistic approach to estimate the most likely robot state and its uncertainty. Philosophically, we do not require the most accurate prior model since the measurements will be tremendously helpful in our task. We therefore develop and employ a simple Cosserat rod model that essentially allows us to interpolate between discrete measurements.

Furthermore, we are exploring approaches from simultaneous localization and mapping in the bile robotics community and how they can be adapted and repurposed in continuum robotics. For instance, we are investigating how camera images obtained from the tip of a continuum robot can be used to gain information on the body posture of the robot within its environment. This is particularly challenging as typical industrial environments are ambiguous, with repetitive patterns and symmetries (e.g. the turbine blades within a jet engine), and as the robot's body may be temporarily and partially in contact with the environment.


  • Deans Strategic Fund (DSF): Connecting the Bot


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CIDGIKc Distance-Geometric Inverse Kinematics for Continuum Robots

Hanna Jiamei Zhang, Matthew Giamou, Filip Marić, Jonathan Kelly, Jessica Burgner-Kahrs

IEEE Robotics & Automation Letters, 8(11):7679 - 7686, 2023.

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Continuum Robot State Estimation Using Gaussian Process Regression in SE(3)

Sven Lilge, Timothy D. Barfoot, Jessica Burgner-Kahrs

The International Journal of Robotics Research, 41(13-14):1099-1120, 2022.

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Cooperative control of dual-arm concentric tube continuum robots

Hanna J. Zhang, Sven Lilge, M. Taha Chikhaoui, Jessica Burgner-Kahrs

International Conference on Manipulation, Automation and Robotics at Small Scales, 2022.

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Shape Representation and Modeling of Tendon-Driven Continuum Robots Using Euler Arc Splines

Priyanka Rao, Quentin Peyron, Jessica Burgner-Kahrs

IEEE Robotics and Automation Letters, 7 (3), pp. 8114 - 8121, 2022.

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Using Euler Curves to Model Continuum Robots

Priyanka Rao, Quentin Peyron, Jessica Burgner-Kahrs

IEEE International Conference on Robotics and Automation (ICRA), 2021.

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Shape Sensing Based on Longitudinal Strain Measurements Considering Elongation, Bending and Twisting

Vincent Modes, Tobias Ortmaier, Jessica Burgner-Kahrs

IEEE Sensors Journal, 21 (5), pp. 6712-6723, 2021.

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Tendon-driven Continuum Robots with Extensible Sections - A Model-based Evaluation of Path Following Motions

E Amanov, T -D Nguyen, J Burgner-Kahrs

International Journal of Robotics Research, 40 (1), pp. 7-23, 2021.

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Calibration of Concentric Tube Continuum Robots - Automatic Alignment of Precurved Elastic Tubes

Vincent Modes, Jessica Burgner-Kahrs

IEEE Robotics and Automation Letters, 5 (1), pp. 103–110, 2020.

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Quaternion-Based Smooth Trajectory Generator for Via Poses in SE(3) Considering Kinematic Limits in Cartesian Space

Reinhard Grassmann, Jessica Burgner-Kahrs

IEEE Robotics and Automation Letters, 4 (4), pp. 4192–4199, 2019.

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Controlling Concentric Tube Robots while Enforcing Shape Constraints

Sven Lilge, Jessica Burgner-Kahrs

Workshop on Open Challenges and State-of-the-Art in Control System Design and Technology Development for Surgical Robotic Systems, IEEE International Conference on Robotics and Automation, 2019.

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Control of Continuum Robots for Medical Applications - State of the Art

Mohamed Taha Chikhaoui, Jessica Burgner-Kahrs

International Conference and Exhibition on New Actuators and Drive Systems, pp. 154-164, VDE VERLAG GMBH, 2018.

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Towards Motion Coordination Control and Design Optimization for Dual-Arm Concentric Tube Continuum Robots

Mohamed Taha Chikhaoui, Josephine Granna, Julia Starke, Jessica Burgner-Kahrs

IEEE Robotics & Automation Letters, 3 (3), pp. 1793-1800, 2018.

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A 3-D Volume Coverage Path Planning Algorithm With Application to Intracerebral Hemorrhage Evacuation

Josephine Granna, Isuru S Godage, Raul Wirz, Kyle D Weaver, Robert J Webster III, Jessica Burgner-Kahrs

IEEE Robotics and Automation Letters, 1 (2), pp. 876–883, 2016.

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Implications of Trajectory Generation Strategies for Tubular Continuum Robots

Carolin Fellmann, Jessica Burgner-Kahrs

IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 202-208, 2015.

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Workspace Characterization for Concentric Tube Continuum Robots

Jessica Burgner, Hunter B Gilbert, Josephine Granna, Philip J Swaney, Robert J Webster III

IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1269–1275, 2014.

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On the Computational Design of Concentric Tube Robots -- Incorporating Volume-Based Objectives

Jessica Burgner, Hunter B Gilbert, Robert J Webster III

IEEE International Conference on Robotics and Automation, pp. 1193–1198, 2013.