Continuum Parallel Robots

Continuous robots (CR) are a new class of manipulators developed to improve the reduced interaction capabilities of rigid-body robots. RCs are generally made by assembling thin flexible bodies (rods, also called "continuous bodies" in reference to continuum mechanics), and their motion is obtained by controlling the deformations of the robot's constituent flexible elements. The intrinsic flexibility of RCs means they can be used in many fields where human-robot interaction is fundamental, such as minimally invasive surgery and collaborative manipulation tasks. In other fields, such as inspection tasks, which also benefit from the robots' ability to reach complex shapes and work in confined environments, their great flexibility is attractive.

Continuous robotics is booming, and the increasing use of RCs in different fields of technology has motivated researchers to come up with a variety of designs. Naturally, as in rigid robotics, serial designs were the first to appear. These include a wide range of robots, of which the most representative examples are concentric-tube RCs (RCTCs) and tendon-actuated RCs (RCATs). These robots are generally small in size, and are ideal for insertion tasks in confined environments such as the human body. Their size is limited by their serial architecture: they are subject to gravity, and the larger they are, the more they must be able to support their own weight. Generally speaking, they are limited to dimensions of the order of ten or twenty centimetres, and to handling loads of a few grams.

To counterbalance these disadvantages while retaining the flexibility of RCs, another class of robots has been proposed: continuous parallel robots (CPRs). They are obtained by assembling several flexible bodies in parallel, often linked together at their ends, but also at intermediate positions, by rigid platforms, thus increasing their intrinsic stiffness. As a result, they can be used to handle heavier loads (a few tens or even hundreds of grams), but their intrinsic stiffness also enables high precision to be achieved on a small scale (in the nanometer range).

The first work on RPCs dates back to 2013. The majority of existing work focuses on proposing proofs of concept, modeling and analyzing the behavior of these robots. Several RPC architectures have been proposed, using different actuation strategies (varying flexible leg lengths, leg actuation at the end, tendon actuation, etc.).

The models used to predict the behavior of RPCs are very different from those used in rigid robotics. Indeed, these robots consist of a flexible structure with an infinite number of passive degrees of freedom (ddl), since they deform continuously. This requires the use of suitable tools to model the infinite...