Evaluation of the Analytical Modeling of a Stewart-Gough Actuated Ball-and-Plate System using Experimental Data.

Resumo

Stewart-Gough Platforms (SGPs) are parallel manipulators with various applications, such as wave stabilization of off-shore structures in the oil and gas industry, due to it’s precise position and orientation control across all six degrees of freedom. Associating an SGP with a ball-and-plate system (BPS), where a ball is allowed to freely roll over an actuated plate, can provide a test bed for nonlinear trajectory control strategies. This study aimed to develop an analytical simulation model of the behavior of a physical SGP-BPS system, and to validate it using empirical data. The model was based on principles of analytical geometry and kinematics, with the objective of accurately replicating the behavior of a physical platform, available at the Laboratory of Monitoring and Control from the Federal University of Paraná (UFPR). This platform was actuated by six servomotors, whose angular positions determined the attitude of a plate equipped with a resistive touchscreen sensor. A free-rolling steel sphere was placed on top of the plate and had its coordinates continuously read by a micro-controller that determined and fed the necessary servo angles to the system to adjust the sphere position and/or trajectory as intended. The sphere position was recorded over time, as well as timestamps and individual angles for each actuator, during several experiments covering a wide range of operating scenarios. The analytical model was assessed using the data collected during the operation of the physical platform. The model was provided with the initial position and velocity of the sphere, as well as the angular positions of each actuator during the operation of the platform. This stream of angular inputs and timestamps allowed the model to predict the plate orientation and the sphere position and velocity over time. The model accuracy was evaluated by comparing the sphere’s simulated position and velocity with the experimental data, for the same set of input angle values. The main parameters for this evaluation were the euclidean norm error and absolute maximum error between the simulated position and the actual position of the ball over time. Results showed a good correlation between model predictions and experimental data. The analytical model is expected to be applied on future works in the creation of a digital twin of the platform for real-time control applications, and the development of a data-driven controller for off-shore wave stabilization systems.