# 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.

## Modeling

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 mobile 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.

## Funding

- NSERC Discovery Grant (April 1, 2019 – March 31, 2025)
- Deans Strategic Fund (DSF): Connecting the Bot

## Publications

**Computationally Efficient Lookahead Search for Contact-aided Navigation for Tendon-driven Continuum Robots**

IEEE International Conference on Soft Robotics, Late Breaking Results, 2024.

**On the Disentanglement of Tube Inequalities in Concentric Tube Continuum Robots**

IEEE International Conference on Robotics and Automation, 2024.

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

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

**Cooperative control of dual-arm concentric tube continuum robots**

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

**Using Euler Curves to Model Continuum Robots**

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

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

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

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

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

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

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

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

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

**Controlling Concentric Tube Robots while Enforcing Shape Constraints**

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.

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

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

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

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

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

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

**Implications of Trajectory Generation Strategies for Tubular Continuum Robots**

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

**Workspace Characterization for Concentric Tube Continuum Robots**

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

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

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