Type of robot
A continuum robot is a type of robot that is characterised by infinite degrees of freedom and number of joints. These characteristics allow continuum manipulators to adjust and modify their shape at any point along their length, granting them the possibility to work in confined spaces and complex environments where standard rigid-link robots cannot operate. In particular, we can define a continuum robot as an actuatable structure whose constitutive material forms curves with continuous tangent vectors. This is a fundamental definition that allows to distinguish between continuum robots and snake-arm robots or hyper-redundant manipulators: the presence of rigid links and joints allows them to only approximately perform curves with continuous tangent vectors.
The design of continuum robots is bioinspired, as the intent is to resemble biological trunks, snakes and tentacles. Several concepts of continuum robots have been commercialised and can be found in many different domains of application, ranging from the medical field to undersea exploration.
Classification.
Continuum robots can be categorised according to two main criteria: structure and actuation.
Structure.
The main characteristic of the design of continuum robots is the presence of a continuously curving core structure, named "backbone", whose shape can be actuated. The backbone must also be "compliant", meaning that the backbone yields smoothly to external loads.
According to the design principles chosen for the continuum manipulator, we can distinguish between:
Actuation.
The actuation strategy of continuum manipulators can be distinguished between "extrinsic" or "intrinsic" actuation, depending on where the actuation happens:
Advantages.
The particular design of continuum robots offers several advantages with respect to rigid-link robots. First of all, as already said, continuum robots can more easily operate in environments that require a high level of dexterity, adaptability and flexibility. Moreover, the simplicity of their structure makes continuum robots more prone to miniaturisation. The rise of continuum robots has also paved the way for the development of soft continuum manipulators. These continuum manipulators are made of highly compliant materials that are flexible and can adapt and deform according to the surrounding environment. The "softness" of their material grants higher safety in human-robot interactions.
Disadvantages.
The particular design of continuum robots also introduces many challenges. To properly and safely use continuum robots, it is crucial to have an accurate force and shape sensing system. Traditionally, this is done using cameras that are not suitable for some of the applications of continuum robots (e.g. minimally invasive surgery), or using electromagnetic sensors that are however disturbed by the presence of magnetic objects in the environment. To solve this issue, in the last years fiber-Bragg-grating sensors have been proposed as a possible alternative and have shown promising results. It is also necessary to notice that while the mechanical properties of rigid-link robots are fully understood, the comprehension of the behaviour and properties of continuum robots is still subject of study and debate. This poses new challenges in developing accurate models and control algorithms for this kind of robots.
Modelling.
Creating an accurate model that can predict the shape of a continuum robot allows to properly control the robot's shape. There are three main approaches to model continuum robots:
Sensing.
To develop accurate control algorithms, it is necessary to complement the presented modelling techniques with real time shape sensing. The following options are currently available:
Control strategies.
The control strategies can be distinguished in static and dynamic; the first one is based on the steady-state assumption, while the latter also considers the dynamic behaviour of the continuum robot. We can also differentiate between model-based controllers, that depend on a model of the robot, and model-free, that learn the robot's behaviour from data. 
Hybrid approaches, that combine model-free and model-based controllers, can also present a valid alternative.
Applications.
Continuum robots have been applied in many different fields.
Medical.
Continuum robots have been widely applied in the medical field, in particular for minimally invasive surgery. For example, Ion by Intuitive is a robotic-assisted endoluminal platform for minimally invasive peripheral lung biopsy, that allows to reach nodules located in peripheral areas of the lungs that cannot be reached by standard instrumentations; this allows to perform early-stage diagnoses of cancer.
Hazardous places.
Continuum robots offer the possibility of completing tasks in hazardous and hostile environments. For example, a quadruped robot with continuum limbs has been developed: it can walk, crawl, trot and propel to whole arm grasping to negotiate difficult obstacles.
Space.
NASA has developed a continuum manipulator, named Tendril, that can extend into crevasses and under thermal blankets to access areas that would be otherwise inaccessible with conventional means.
Subsea.
The AMADEUS project developed a dextrous underwater robot for grasping and manipulation tasks, while the FLAPS project created propulsion systems that replicate the mechanisms of fish swimming.