## 1 Introduction  
In contemporary robotics-research, the study of man-machine interactions is a very important area, especially in the context of robots that are released from their traditional, isolated protection cage to instead collaborate hand-in-hand with humans. For effective and efficient usage of such robots, three aspects are crucial: modeling, actuation, and sensing. Modeling plays a vital role in the development and commissioning process of such robots. Traditionally, although kinematic models for standard configurations of serial manipulators exist [1], when it comes to dynamical models these are usually derived using multibody systems (MBS) [2]. Efficient implementations for MBS already exist, providing the nonlinear equations of motion in a symbolical or numerical manner [3]. For industrial robots and modular manipulators, independent joint controllers are the most common control approach, for example, using PD or PID control schemes [4]. However, these decentralized linear control structures disregard the highly nonlinear behavior of such systems, usually do not exploit a possibly available model, fail to take information from other subsystems into account or require an elaborate tuning of the controller parameters. Another commonly used control technique, especially in trajectory tracking for rigid MBS, is the so-called computed torque method [5], which is a particular case of feedback linearization control that uses the method of inverse dynamics. Nevertheless, this model-based feed-forward control technique's performance depends strongly on the modeling quality of the robot dynamics. Model uncertainties, that is, unmodeled, unknown or varying friction properties or a change in payload, worsen the tracking accuracy immensely. A further advanced control technique for nonlinear systems is model predictive control (MPC), also known as predictive or receding horizon control, which is firmly established in research [6] and industrial application [7]. MPC uses the advantageous capability of a model to forecast the future dynamical behavior of the system. An optimal input sequence is obtained by solving online an open-loop optimal control problem (OCP) over a finite horizon subject to system dynamics and constraints at every sample time based on the latest measurements. In case of serial manipulators, MPC offers numerous advantages, for example, handling the multivariable control problem naturally, operating as a centralized control system, intuitive adjustment of controller parameters, trajectory tracking, or considering actuator and state limitations already in the control design [8]. Thanks to the vast increase of computational power and more efficient algorithms, MPC is getting applicable to systems with fast nonlinear dynamics like a robotic system. Numerous nonlinear MPC approaches exist to reduce the computational burden of online optimization and guarantee real-time feasibility. In Reference [9], for example, a laboratory crane is controlled by a gradient-based MPC scheme using suboptimal solutions to meet the real-time requirements. In Reference [10], the control of a KUKA LWR IV robot is considered and the so-called real-time iteration scheme [11; 12] solves the underlying OCP of the MPC problem, implemented in the ACADO toolkit [13]. A 6-DOF robotic arm is addressed in Reference [14], and herein the OCP is solved with the commercial interior-point-based nonlinear programming (NLP) solver FORCES PRO [15]. An approximate explicit MPC law is computed off-line beforehand for a robot manipulator in Reference [16] to bypass the online optimization, but this demands massive off-line computations and results in a static control law which loses the possibility of adapting the control law during operation to a greater extent. But all of the mentioned works use specialized and expensive hardware setups, which is in contrast to the presented and intended low-cost approach.