# Design, Simulation, and Comparison of Advanced Control Strategies for a 3-Degree-of-Freedom Robot
###### Abstract
In [8], researchers present a Learning-Based Nonlinear Model Predictive Control (LB-NMPC) algorithm designed to achieve high-performance path tracking in challenging terrains through learning. The system integrates a simple vehicle model with added perturbation, where perturbations are modeled as a Gaussian process based on system state, input, and other relevant variables. The system achieves mobile localization through an integrated vision-based navigation and mapping system, enabling operation in large-scale environments without a Global Positioning System (GPS). Experimental validation spans over 3 km of traversal across three distinct robotic platforms with masses ranging from 50 to 600 kg at speeds between 0.35 and 1.2 m/s. Results confirm that the controller can initialize from a generic vehicle model and progressively reduce vehicle-specific and trajectory-specific path-tracking errors through experience. In [9], researchers developed and simulated Fuzzy Logic Joint Controllers (FLJC) for a 6-DoF robot arm integrated with an artificial vision system for color discrimination. The system's performance was evaluated by comparing computational load, speed, and precision through displacement measurements in XYZ Cartesian axes across two and three dimensions. Results indicate an absolute error below 2 cm for gripper coordinates, while the artificial vision system maintains at least 95% accuracy in color discrimination for objects stacked in both the first and second levels. In [10], the research focuses on the design process, kinematic modeling, and parameterization of a 4-DoF SCARA-type robotic arm specifically engineered for agricultural environments. Current research continues on robotic arms and manipulation systems since commercially available solutions are not optimized for agriculture's dusty, dirty, and humid conditions. The project aims to develop a robotic arm capable of operating in adverse agricultural conditions, including rain, wind, dust, mud, and vibration, featuring an optimized number of DoF. This optimization enables adaptability to real agricultural conditions through specially designed joint components and lightweight links with a fast and simplified control unit. Initial results demonstrate workspace coverage of 11.4 m\({}^{2}\) for maximum frontal access and 2.9 m and 2.4 m for lateral access, confirming sufficient surface coverage for agricultural applications. Based on the aforementioned works, research predominantly employs simulations, implementing various control strategies that incorporate advanced control theory fundamentals, notably combining fuzzy logic and predictive control with emerging technologies like vision sensors. There exists a growing need to develop proprietary technologies aligned with the socio-economic requirements of each region, particularly in agriculture, medicine, and mining. In [11], it is indicated that the robotic manipulator has become an integral component of modern industrial automation. In their study, a model of a robotic arm with 6 DoF is presented in which two modern control strategies, Hoo and MPC, are applied. The designed control laws are subjected to various step and ramp inputs; their effectiveness is evaluated on transient parameters such as settling time, overshoot, and steady-state error. For the MPC controller, it is observed that the system response is related to the control window size; its performance improves when this size is increased. In their results, optimal values of np = 100 and nc = 20 were obtained. For the Hoo controller, the weighting functions have a significant effect on the performance of the designed control law, where these functions are used to trace the ramp, step, and sinusoidal responses of the system. From the graphs, all joints of the robotic arm showed similar behavior, with a delay in the controller response for the reference trajectories. The comparative analysis of the performance achieved by both controllers reveals that the MPC controller outperforms the Hoo.