Time-Optimal Anti-Sloshing Trajectory Planning for Multiple Liquid-Filled Containers Subject to SCARA Motion

README------------------------------------------- MATLAB SCRIPT AND CSV FILES:------------The MATLAB script is used to load and visualize the trajectory data.It allows the user to compare optimized and non-optimized trajectories.The script generates plots for both Cartesian space and joint space,and includes sloshing simulation and experimental results.The data correspond to the paper entitled 'Time-Optimal Anti-Sloshing Trajectory Planning forMultiple Liquid-Filled Containers Subject to SCARA Motion'. HOW TO USE:-----------1. Open the file "generate_plots.m" in MATLAB. 2. At the top of the script, in the section marked "CONFIGURATION", set the four parameters: trajectory = "1A"; Choose between: "1A", "2A", "1B", "2B" motionLaw = "OPT"; Choose between: "OPT" (optimized), "NOPT" (non-optimized) h = 20; Static liquid height [mm]. Choose between: 20, 30, 40, "MULTI" ("MULTI" refers to the case where containers with different filling heights are transported simultaneously) etalim = 15; Sloshing-height limit [mm]. Choose between: 15, 25 Compatibility Notes: - The "NOPT" (non-optimized) motion law is available only for Trajectory "1A" or "2A" - etalim = 25 is avaiable only when the static liquid height is h = 40mm - h = "MULTI" is avaiable only with Trajectory "2A", etalim = 15 and motionLaw = "OPT" 3. Run the script. It will automatically: - Load the correct .csv files based on your selection - Plot the following: - Cartesian position, velocity, and acceleration of the point O' of the tray - Orientation angles, angular velocity, and angular acceleration of the tray about the x', y' and z' axes - Robot joint positions and velocities - Sloshing heights (both model and experimental) CSV FILES:----------The script reads the following CSV files (from the "CSV_files" folder): 1. <trajectory>_<suffix>_<h>_<etalim>_cartesian_trajectory.csv Note: "suffix" is a keyword automatically set by the script depending on the selected motion law (motionLaw). - If motionLaw = "OPT", then suffix = "optimized" - If motionLaw = "NOPT", then suffix = "nonoptimized" Example: 1A_optimized_h40_etalim15_cartesian_trajectory.csv Columns: [1] Time [s] [2] r_x tray position [m] [3] r_y tray position [m] [4] r_z tray position [m] [5] θx orientation [rad] [6] θy orientation [rad] [7] θz orientation [rad] [8] \dot{r}_x tray velocity [m/s] [9] \dot{r}_y tray velocity [m/s] [10] \dot{r}_z tray velocity [m/s] [11] ωx angular velocity [rad/s] [12] ωy angular velocity [rad/s] [13] ωz angular velocity [rad/s] [14] \ddot{r}_x tray acceleration [m/s²] [15] \ddot{r}_y tray acceleration [m/s²] [16] \ddot{r}_z tray acceleration [m/s²] [17] αx angular acceleration [rad/s²] [18] αy angular acceleration [rad/s²] [19] αz angular acceleration [rad/s²] 2. <trajectory>_<suffix>_<h>_<etalim>_joint_trajectory.csv Columns: [1] Time [s] [2–7] Robot joint positions q_i (i = 1,...,6) [rad] [8–13] Robot joint velocities \dot{q}_i (i = 1,...,6) [rad/s] 3. Sloshing data: - <trajectory>_<suffix>_<h>_<etalim>_SH_model_<cont>.csv - <trajectory>_<suffix>_<h>_<etalim>_SH_model_<cont>.csv - <trajectory>_<suffix>_<h>_<etalim>_SH_exp_<cont>.csv - <trajectory>_<suffix>_<h>_<etalim>_SH_exp_<cont>.csv where: cont = IC, 2, 3, 6, 7, EC Each file contains two columns: [1] Time [s] [2] Sloshing height η [mm] OUTPUT:-------The script generates 3 figures: Figure 1: Trajectory plots - 3D trajectory - Linear and angular velocities and accelerations along the three axes - Orientation angles, angular velocities and angular accelerations Figure 2: Joint space plots - Joint positions q_i (i = 1,...,6) - Joint velocities \dot{q}_i (i = 1,...,6) Figure 3: Sloshing heights - Model and experimental trends for IC and EC containers When h="MULTI", two additional plots are generated, showing the sloshing-heights trends of containers 2–6 and 3–7. CORRESPONDENCE WITH PAPER FIGURES (referred to the case with h = 40mm and etalim = 15mm):---------------------------------- 3D TRAJECTORY PLOTS (Figure 1 - subplot "3D Trajectory"):- 1A OPT/NOPT → Blue path in Figure 5a- 1B OPT → Red path in Figure 5a- 2A OPT/NOPT → Blue path in Figure 5b- 2B OPT → Red path in Figure 5b SLOSHING HEIGHT PLOTS (Figure 3):- 1A OPT → Figure 6a- 1A NOPT → Figure 6b- 1B OPT → Figure 6c- 2A OPT → Figure 7a- 2A NOPT → Figure 7b- 2B OPT → Figure 7c -------------------------------------------------------------------------------------------------------------------------------- ROBOT VIDEOS (referred to the case with h = 40mm and etalim = 15mm):------------In 'Videos' folder it is possible to visualize the videos recorded during the experiments,relative to Figs. 6 and 7 of the paper. The videos are named as follows: <trajectory>_<suffix>_<h>_<etalim>.mov