Infinite Shapes, Few Motors
Fast Models and Faithful Models
Friction and Mechanical Memory
Measuring a Body That Keeps Bending
When the Environment Pushes Back
A Family Without a Shared Controller
Learning From the Robot Itself
Conclusion
References and Further Reading
Factory robots move like a human arm, with rigid links connected by motorized joints. Continuum robots bend smoothly along their entire length, like an elephant trunk or an octopus tentacle. This flexibility allows them to navigate through blood vessels, airways, and tight machinery. The article discusses the challenges in controlling continuum robots, covering aspects from mechanics and models to friction, sensing, contact, design diversity, and emerging solutions.1
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Infinite Shapes, Few Motors
A conventional robot arm with 6 joints has 6 degrees of freedom, meaning 6 motor positions fully describe its posture. In comparison, a continuum robot has no discrete joints. Its backbone can curve differently at every point along its length, which gives it a theoretically infinite number of degrees of freedom. However, a typical prototype usually operates with just 4 tendons, each pulled by its own motor.1,2
This mismatch makes the robot underactuated. The controller commands only a handful of inputs, while the body settles into whatever shape the balance of tendon tension, material stiffness, and gravity allows. A control engineer must therefore predict how a small set of motor commands will spread through an elastic structure. That prediction depends heavily on the underlying mathematical model.1,2
Fast Models and Faithful Models
The most popular shortcut is the piecewise constant curvature model. It assumes that each segment of the robot bends into a perfect circular arc, reducing an endless variety of shapes to a few parameters. The resulting math runs fast enough for real-time control, so many controllers still use it. But real robots rarely form perfect arcs, especially when they carry a load or touch something.1
At the other extreme are models based on Cosserat rod theory, which treat the backbone as a continuous elastic rod and track how forces and moments change along it. These models capture bending, twisting, and loading far more faithfully. They also require solving demanding equations at every control step, which strains the computing budget of a robot that must respond within milliseconds.3
Friction and Mechanical Memory
Tendon-driven designs make things more complicated. Each tendon passes through small guide holes along the robot's backbone. Friction at these points dissipates some of the motor's tension before it reaches the tip. The amount of tension lost depends on how sharply the robot bends and how its tendons are arranged, so it changes constantly as the robot moves.3
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Friction also produces hysteresis, a form of mechanical memory. The same tendon positions can create different shapes based on whether the robot is bending or straightening. Researchers attribute this behavior to friction, actuator slack, and uneven tension. For a controller that assumes each command maps to one shape, hysteresis introduces errors that a fixed calibration cannot correct.4
Measuring a Body That Keeps Bending
Sensors could close the gap left by imperfect models by measuring the actual shape and correcting errors in real time. This method is called closed-loop control and works well for rigid robots, whose joints indicate their exact positions. However, a continuum robot lacks joints, so engineers must reconstruct a continuous curve from sensors embedded along its body or around it.5
Currently, options include using optical fibers, magnetic tracking, or the electrical properties of materials in the robot. Each sensor must fit inside a body that may be only a few millimeters wide without stiffening it or blocking the tools it carries. A recent review in MDPI Sensors highlights that making sensors smaller and developing new sensing methods are the biggest challenges. As a result, many robots still operate with only partial knowledge of their shape.5
When the Environment Pushes Back
Flexibility becomes a liability once the robot leaves the lab. A continuum robot inside a patient or an engine can brush against tissues, walls, and obstacles. This compliant structure can bend in unexpected ways, causing the robot’s tip to deviate from its intended target, even when the motors are not moving.6
These disturbances are hard to predict because they depend on unknown contact locations and forces. Engineers need controllers that maintain accuracy even when the robot is being pushed, a challenge known as robust control. The softness that keeps the robot safe around sensitive areas also makes it more susceptible to external forces, creating a trade-off between safety and precision.6
A Family Without a Shared Controller
Continuum robots are available in various configurations. Some utilize tendons for movement, while others rely on nested precurved tubes, pneumatic systems, or external magnetic fields. Each actuation method creates its own physics, error sources, and mathematical description. Therefore, a controller optimized for a cable-driven arm often does not translate well to a pneumatic system, prompting researchers to redesign control systems for each new robot configuration frequently.6
This diversity carries a practical cost. Developing a specialized controller requires considerable effort, and most methods need careful parameter tuning to perform well. Researchers have started testing adaptive controllers that adjust themselves during operation and work across several robot types. A recent study published in The International Journal of Robotics Research validated one such method on cable-driven, concentric-tube, pneumatic, and parallel continuum robots, as well as a flexible endoscope.6
Learning From the Robot Itself
Researchers are now allowing robots to create their own models. Machine learning methods track how a physical robot responds to different commands and learn from that data. This approach can account for factors like friction and material differences that are hard to quantify with exact equations, since the robot's recorded behavior already shows how these factors affect its movement.4
Mechanical memory can be learned as well. An IEEE Robotics and Automation Letters study trained a neural network to predict the 3D shape of a tendon-driven robot from its current and previous tendon positions. By accounting for history, the network outperformed a leading physics-based model and a learning model that ignored hysteresis. Such methods depend on extensive data for each specific robot, which limits how easily they can be transferred.4
Conclusion
Continuum robots are difficult to control because the qualities that make them valuable also undermine their precision. A body with countless possible shapes must be steered by a few motors and described by models that are either fast or faithful. Friction, hysteresis, limited sensing, contact forces, and design variety then stack additional errors on top of those modeling compromises.
Progress is arriving from several directions at once, including richer models, smaller sensors, adaptive controllers, and data-driven learning. The robots that eventually work reliably inside human bodies and complex machines may combine these tools. Precise control will come from treating flexibility as a permanent feature and building controllers that measure, predict, and correct it continuously as the robot moves.
References and Further Reading
- Russo, M. et al. (2023). Continuum Robots: An Overview. Advanced Intelligent Systems, 5(5), 2200367. DOI:10.1002/aisy.202200367. https://advanced.onlinelibrary.wiley.com/doi/10.1002/aisy.202200367
- Tendon-driven continuum robots. Stuttgart University. https://www.inm.uni-stuttgart.de/research_nonlinear_mechanics/project_dai/
- Wang, H., Du, J., & Mao, Y. (2025). Cosserat Rod-Based Tendon Friction Modeling, Simulation, and Experiments for Tendon-Driven Continuum Robots. Micromachines, 16(3), 346. DOI:10.3390/mi16030346. https://www.mdpi.com/2072-666X/16/3/346
- Cho, B. Y. et al. (2024). Accounting for Hysteresis in the Forward Kinematics of Nonlinearly-Routed Tendon-Driven Continuum Robots via a Learned Deep Decoder Network. IEEE Robotics and Automation Letters, 9(11). DOI:10.1109/LRA.2024.3455797. https://par.nsf.gov/servlets/purl/10547472
- Sincak, P. J. et al. (2024). Sensing of Continuum Robots: A Review. Sensors, 24(4), 1311. DOI:10.3390/s24041311. https://www.mdpi.com/1424-8220/24/4/1311
- Tan, N. et al. (2024). Behavior-predefined adaptive control for heterogeneous continuum robots. The International Journal of Robotics Research, 44(1). DOI:10.1177/02783649241259138. https://journals.sagepub.com/doi/epub/10.1177/02783649241259138
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