# Model-Free Robotic Architecture with Task-Multiplexer and Discrete-Time Adaptive Control
## 1 Introduction  
Many commercial robotic systems are managed by closed architectures. To expand the performance of closed-architecture robots, macro-mini approaches have been utilized, such as in [1; 2]. The macro-robot is manipulated by the original closed architecture and a built-in controller. On the other hand, the mini-robot is handled by the open architecture and an advanced controller. Improvement of their performance is clearly significant, but the problem of dynamic decoupling effect has occurred [3]. The complexity of robotic systems has been continuously rising, and more advanced controllers are required, alongside the the engineering aspect [4; 5]. Furthermore, the robotic architecture itself is currently growing into more complicated systems, where the mathematic models are hardly determined; especially when the systems are considered as a class of discrete-time plants [6; 7]. Without any use of mathematical models for controlled plants, model-free adaptive controllers (MFAC) have been developed when the robots are considered as a class of unknown discrete-time systems [8; 9; 10]. By using only the input/output data, the design of MFAC based on the data-driven concept was established by linearization models that require the existence of a pseudo-partial derivative and a non-zero change of control effort [11; 12]. Without this constraint, the control scheme for the unknown mathematical model of robotic systems for the discrete-time domain has been proposed in [13; 14], by using direct IF-THEN rules and adaptive networks, but closed-loop analysis has been limited only the convergence of the tracking error. The convergence of internal signals, such as weight parameters, has been investigated for controllers designed by artificial neural networks (ANN) [15; 16] or fuzzy neural networks (FNN) [17; 18]. However, robotic systems with direct-drive schemes, such as variable-frequency drive (VFD), actually have high-order non-linear systems [19; 20]. The difficulty of acquiring analytic solutions for high-order systems has become an interesting issue. MFAC approaches in [10; 11; 12] have not determined the controlled plants as naturally high-order systems. Black-stepping controllers havebeen effectively utilized for solving high-order problems [21; 22]. Stability analysis has been conducted for both global and local states at each design-step. By decomposing the original system into several subsystems, all state variables are usually required for designing the visual control laws of the inner steps. Nevertheless, the full-state information is very difficult to obtain from robotic systems. In this work, a controller for an open-architecture robotic system with a task-multiplexer unit is developed. The robotic arm ABB model IRB-1400 is driven by six VFD units, operated by a digital computer. This robotic system is considered as a class of unknown discrete-time systems when the output is directly obtained by the task-multiplexer and the input is the command voltage for VFD units. By using only the input/output data, the equivalent model is established by the first Multi-input Fuzzy Rules Emulated Network (MiFREN). Next, the second MiFREN is utilized as an adaptive controller, where the online-learning algorithm is developed by the information obtained by the equivalent model. A closed-loop analysis is conducted to guarantee the convergence of the tracking error and internal signals. The main contributions of this work can be listed as the following:  
* Unlike the robotic control systems in [6; 7; 23], the proposed control scheme can be applied when the mathematical model of the robotic system is completely unknown. * The design of the controller requires only the relation between the input and output of robotic systems within the format of IF-THEN rules, according to basic human knowledge. Unlike the model-free approaches in [10; 24], the covariance matrix and the qualitative dynamic system are not required in this work.