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 available only when the static liquid height is h = 40mm - h = "MULTI" is available only with Trajectory "2A" or "2B", 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, 4, 5, 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-height 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 'Robot_videos' folder it is possible to visualize the videos of the robot recorded during the experiments,relative to Figs. 6 and 7 of the paper. The videos are named as follows: <trajectory>_<suffix>_<h>_<etalim>.mov -------------------------------------------------------------------------------------------------------------------------------- LIQUID VIDEOS:------------In 'Liquid_videos_left/right' folders it is possible to visualize the videos recorded on the single containers during the experiments, relative to all the trajectories presented in the paper; "left" and "right" refer to the two GoPro attached to the tray. The videos are named as follows: <trajectory>_<suffix>_<h>_<etalim>_<cont>.MP4 MARKER VIDEOS:------------In 'Liquid_videos_left/right' folders it is possible to also visualize the marker videos, which were used to extract the sloshing-height tends from the liquid recordings.Due to the nature of the experimental setup and the various recording sessions, multiple camera localization runs were necessary.For this reason twelve videos for the marker identification are present for each folder. Specifically: - marker_1.mp4 This file corresponds to localization for videos: - 1A_optimized_h40_etalim15_IC.mp4; 1A_nonoptimized_h40_etalim15_IC.mp4; 2A_optimized_h40_etalim15_IC.mp4 - 1A_optimized_h40_etalim25_IC.mp4; 1A_nonoptimized_h40_etalim25_IC.mp4 - marker_2.mp4 This file corresponds to localization for videos: - 1A_optimized_h40_etalim15_EC.mp4; 1A_nonoptimized_h40_etalim15_EC.mp4; 2A_optimized_h40_etalim15_EC.mp4 - 1A_optimized_h40_etalim25_EC.mp4; 1A_nonoptimized_h40_etalim25_EC.mp4 - marker_3.mp4 This file corresponds to localization for videos: - 2A_optimized_h40_etalim15_IC.mp4; 2A_optimized_h40_etalim15_EC.mp4 - 2B_optimized_h40_etalim15_IC.mp4; 2B_optimized_h40_etalim15_EC.mp4 - marker_4.mp4 This file corresponds to localization for videos: - 1B_optimized_h40_etalim15_IC.mp4; 1B_optimized_h40_etalim15_EC.mp4 - 1B_optimized_h40_etalim25_IC.mp4; 1B_optimized_h40_etalim25_EC.mp4 - marker_5.mp4 This file corresponds to localization for videos: - 2A_optimized_h40_etalim25_IC.mp4; 2B_optimized_h40_etalim25_IC.mp4 - 1A_optimized_h30_etalim15_IC.mp4; 1A_nonoptimized_h30_etalim15_IC.mp4; 2A_optimized_h30_etalim15_IC.mp4 - 1B_optimized_h30_etalim15_IC.mp4; 2B_optimized_h30_etalim15_IC.mp4 - 1A_optimized_h20_etalim15_IC.mp4; 1A_nonoptimized_h20_etalim15_IC.mp4; 2A_optimized_h20_etalim15_IC.mp4 - 1B_optimized_h20_etalim15_IC.mp4; 2B_optimized_h20_etalim15_IC.mp4 - 2A_optimized_hMULTI_etalim15_IC.mp4 - marker_6.mp4 This file corresponds to localization for videos: - 2A_optimized_h40_etalim25_EC.mp4; 2B_optimized_h40_etalim25_EC.mp4 - 1A_optimized_h30_etalim15_EC.mp4; 1A_nonoptimized_h30_etalim15_EC.mp4; 2A_optimized_h30_etalim15_EC.mp4 - 1B_optimized_h30_etalim15_EC.mp4; 2B_optimized_h30_etalim15_SH_exp_EC.mp4 - 1A_optimized_h20_etalim15_EC.mp4; 1A_nonoptimized_h20_etalim15_EC.mp4; 2A_optimized_h20_etalim15_EC.mp4 - 1B_optimized_h20_etalim15_EC.mp4; 2B_optimized_h20_etalim15_EC.mp4 - 2A_optimized_hMULTI_etalim15_EC.mp4 - marker_7.mp4 This file corresponds to localization for videos: - 2A_nonoptimized_h30_etalim15_EC.mp4; 2A_nonoptimized_h30_etalim15_IC.mp4 - 2A_nonoptimized_h20_etalim15_EC.mp4; 2A_nonoptimized_h20_etalim15_IC.mp4 - 2B_optimized_hMULTI_etalim15_IC.mp4; 2B_optimized_hMULTI_etalim15_IC.mp4 - marker_8.mp4 This file corresponds to localization for videos: - 2A_optimized_hMULTI_etalim15_2.mp4; 2A_optimized_hMULTI_etalim15_7.mp4 - marker_9.mp4 This file corresponds to localization for videos: - 2B_optimized_hMULTI_etalim15_2.mp4; 2B_optimized_hMULTI_etalim15_7.mp4 - marker_10.mp4 This file corresponds to localization for videos: - 2A_optimized_hMULTI_etalim15_3.mp4; 2A_optimized_hMULTI_etalim15_6.mp4 - marker_11.mp4 This file corresponds to localization for videos: - 2B_optimized_hMULTI_etalim15_3.mp4; 2B_optimized_hMULTI_etalim15_6.mp4 - marker_12.mp4 This file corresponds to localization for videos: - 2A_optimized_hMULTI_etalim15_4.mp4; 2A_optimized_hMULTI_etalim15_5.mp4 - 2B_optimized_hMULTI_etalim15_4.mp4; 2B_optimized_hMULTI_etalim15_5.mp4