## 1 Introduction  
Industrial robots are an indispensable part of the manufacturing process in many industries, where their traits, i.e., precision, speed, and the ability to work basically nonstop, help increase productivity and decrease cost. It is therefore understandable, that there is a strong incentive to use industrial robots in other fields, like for example agriculture and medicine. The most common industrial robots are serial link 6R robots, 2R1T SCARA robots or parallel Delta robots driven by, most commonly, electric actuators, or in some cases hydraulic actuators [1]. These industrial robots were developed for many decades, their design is standardized, and their mathematical description and control design is fairly well researched. Unfortunately, these robots lack some key features needed in the aforementioned new fields of application. For example compliance, agility and complex modes of motion [2]. These requirements fulfil new emerging classes of robots i.e., redundant cascade and continuum robots [3]. Redundant robots are all those that have more degreesof freedom than is necessary to perform a certain task [4]. Development of these robots accelerated after the year 2000. Redundant robots in general, but especially cascade and continuum robots, have unique characteristics. For example, according to [5; 6], compliance, a good reach to weight ratio, modularity and other. These characteristics arise from their specific design. In general, continuum and cascade robots consist of several in-series-connected parallel modules which, if underactuated, form a continuum robot and if fully actuated form a cascade robot. To describe the motion of a redundant robot and design a control algorithm for it, it is first necessary to focus on its individual modules and their properties. The chosen actuator type influences the achievable properties of a module. Electrical linear servo motors as used by [7] within the structure of a module or outside it, as by [8], provide high amounts of force and stiffness. Moreover, they are usually equipped with position sensors that simplify control. Hydraulic actuators, as seen in [9], provide high forces and can be precisely positioned, but are slow. Nonstandard actuators such as SMA springs, as seen in the work of [10], or dielectric materials, as described in [11], can also be used in this application. Pneumatic actuators are a popular class of actuators in cascade robot design. They provide high power density, have relatively low weight, and can be easily manufactured to custom specifications, as described in [1; 12], or bought off the shelf in a variety of types and sizes [13; 14; 15]. In addition, the compressibility of air gives them a natural level of compliance. This property makes them the actuator of choice for medical applications, like for example in rehabilitation equipment [16] and flexible endoscopes [17; 18], in agriculture [19], as parts in mobile robots [20; 21], as the actuator for high-precision positioning systems [22] or as the stiffness regulating element in hybrid actuation schemes for continuum tendon driven robots as presented by [23]. There exist many well-known techniques that can be used to obtain robust controllers for complex systems, as described in [24]. Nevertheless, the control of a parallel platform module actuated by three or four pneumatic actuators remains a challenging task. One approach to controlling of these modules is to use a feed-forward controller alone or in combination with other types of controllers. The authors of [25] presented a modelling framework to design a model from which a feed-forward controller with satisfactory performance was developed. Ref. [26] developed a custom bellows-type actuator and applied it in a parallel platform with three degrees of freedom. Their control algorithm was a feed-forward controller based on an experimental mapping between pose, external forces and input pressure.