Prompt:
The given scene has a tray with three objects (a bottle, a wine_glass, and a martini_glass) on it. The radius of the tray is 1.8 and its center of gravity is 0.05 above the ground with a sliding friction of 0.1 and no spin or roll friction. The radius of bottle is 0.4 and its center of gravity is 1.1 above the ground. The center of gravity of the martini_glass is at a height of 0.5.The center of gravity of the wine_glass is 0.9 above the ground.The tray is impacted by a pusher and the tray with the objects on it moves. Python code in example_code_1.py creates the scene and runs the simulation. The trajectories in object_traj_example_1.txt show the motion of the center of gravity of the objects when running the simulation. Your task is to analyze the given example and then write similar code to produce the trajectories given in 'problem_trajectories.txt'. 

You must assume the scene is similar to the one given, however the physics between the tray and the objects are different, that is, the sliding-friction, damping, stiffness, and armature need to be adjusted for all the physical_parameters_for_object_id_* dictionaries in the example_code_1.py so as to reproduce the trajectories in 'problem_trajectories.txt'. You must assume that the physics of the tray with the ground remains the same and so is the external force applied on the tray by the pusher. The trajectories use a timestep of 0.2s. Do not attempt to change the physics parameters beyond their first significant digit. Your written code should strictly follow the same code structure as provided in example_code_1.py. You may further assume that multiple instances of the same object will have the same physical parameters.


You must not change the 'mass' of the objects in your generated code. Do not include the object trajectories in your generated code as that will fail our simulator.




Note that the simulation trajectory in problem_trajectories.txt may use instances of bottle, martini_glass, and wine_glass. The name of the objects is provided in the problem_trajectories.txt file. The mass for the objects are as follows: wine_glass is 4.0, martini_glass is 10.0 and bottle is 20.0.
\# nexample_code_1.py

sim = SIMULATOR_MODEL()
sim.create_pusher('3.0 3.0 0.05')
physical_parameters_for_object_id_tray = { 
             'sliding-friction': 0.1,
             'armature': 0.1,
             'stiffness': 0.0,
             'mass': 0.5,
             'damping': 20
         }
sim.create_tray(object_physics = physical_parameters_for_object_id_tray)
physical_parameters_for_object_id_1 = { 
             'sliding-friction': 0.1,
             'armature': 0.2,
             'stiffness': 0.3,
             'mass': 20.0, # 'mass' is 20.0 for bottle, 10.0 for martini_glass, and 5.0 for wine_glass
             'damping': 5.7
         }
sim.create_object(object_id=1, object_name='bottle', object_location=('row_1', 'column_3'), object_color='orange', object_physics=physical_parameters_for_object_id_1)

physical_parameters_for_object_id_2 = { 
             'sliding-friction': 0.5,
             'armature': 0.4,
             'stiffness': 1.0,
             'mass': 10.0, # 'mass' is 20.0 for bottle, 10.0 for martini_glass, and 5.0 for wine_glass
             'damping': 8.8
         }
sim.create_object(object_id=2, object_name='martini_glass', object_location=('row_1', 'column_2'), object_color='orange', object_physics=physical_parameters_for_object_id_2)

physical_parameters_for_object_id_3 = { 
             'sliding-friction': 0.6,
             'armature': 0.8,
             'stiffness': 0.6,
             'mass': 4.0, # 'mass' is 20.0 for bottle, 10.0 for martini_glass, and 5.0 for wine_glass
             'damping': 8.3
         }
sim.create_object(object_id=3, object_name='wine_glass', object_location=('row_1', 'column_1'), object_color='orange', object_physics=physical_parameters_for_object_id_3)


sim.create_scene()
sim_out=sim.run_simulation()
del sim


object_traj_example_1.txt

tray_motion_trajectory (x, y, z) = [(0.0, 0.0, 0.1), (-0.8, -0.8, 0.1), (-1.4, -1.4, 0.1), (-1.8, -1.8, 0.1), (-2.1, -2.1, 0.1), (-2.3, -2.3, 0.1), (-2.4, -2.5, 0.1), (-2.6, -2.6, 0.1), (-2.7, -2.7, 0.1)]

bottle_motion_trajectory (x, y, z) = [(-1.1, -1.1, 1.1), (-1.1, -1.1, 1.1), (-1.1, -1.1, 1.1), (-1.1, -1.1, 1.1), (-1.2, -1.2, 1.1), (-1.3, -1.3, 1.1), (-1.4, -1.5, 1.1), (-1.5, -1.6, 1.1), (-1.6, -1.7, 1.1)]

martini_glass_motion_trajectory (x, y, z) = [(-1.0, 0.0, 0.5), (-1.1, -0.0, 0.6), (-1.2, -0.1, 0.6), (-1.4, -0.4, 0.5), (-1.6, -0.6, 0.5), (-1.8, -0.8, 0.5), (-2.0, -0.9, 0.5), (-2.1, -1.0, 0.5), (-2.2, -1.1, 0.5)]

wine_glass_motion_trajectory (x, y, z) = [(-1.0, 1.0, 0.9), (-1.1, 0.9, 1.0), (-1.1, 0.9, 0.8), (-1.2, 0.9, 0.8), (-1.2, 0.9, 0.8), (-1.3, 0.8, 0.8), (-1.3, 0.8, 0.8), (-1.3, 0.8, 0.8), (-1.2, 0.8, 0.8)]



problem_trajectories.txt

tray_motion_trajectory (x, y, z) = [(0.0, 0.0, 0.1), (-0.7, -0.7, 0.1), (-1.2, -1.2, 0.1), (-1.5, -1.5, 0.1), (-1.8, -1.7, 0.1), (-2.0, -1.9, 0.1), (-2.1, -2.1, 0.1), (-2.3, -2.2, 0.1), (-2.4, -2.4, 0.1)]

bottle_motion_trajectory (x, y, z) = [(-1.1, -1.1, 1.1), (-1.1, -1.1, 1.2), (-1.2, -1.2, 1.1), (-1.3, -1.4, 1.1), (-1.5, -1.6, 1.1), (-1.6, -1.8, 1.1), (-1.7, -1.9, 1.1), (-1.9, -2.1, 1.1), (-1.9, -2.2, 1.1)]

martini_glass_motion_trajectory (x, y, z) = [(-1.0, 0.0, 0.5), (-1.1, -0.1, 0.6), (-1.3, -0.3, 0.5), (-1.5, -0.5, 0.4), (-1.7, -0.7, 0.4), (-1.9, -0.9, 0.4), (-2.1, -1.1, 0.4), (-2.3, -1.3, 0.4), (-2.4, -1.4, 0.4)]

wine_glass_motion_trajectory (x, y, z) = [(-1.0, 1.0, 0.9), (-1.2, 0.8, 1.0), (-1.3, 0.7, 0.9), (-1.5, 0.6, 0.8), (-1.7, 0.6, 0.8), (-1.8, 0.6, 0.8), (-1.9, 0.6, 0.8), (-1.9, 0.6, 0.8), (-2.0, 0.7, 0.8)]





We ran your code in our simulator using the physical parameters you provided below in physical_parameters_for_object_id_* dictionaries. The error in the prediction of the trajectories using these physical parameters is given below. Can you refine your code to make the trajectories look more similar to the ones in 'problem_trajectories.txt'? Your written code should strictly follow the same code structure as provided in example_code_1.py. 


GPT Attempt #1 produced : 

physical_parameters_for_object_id_1 = {  
    'sliding-friction': 0.18,  # slight increase
    'armature': 0.12,           # slight increase for more stable rotation
    'stiffness': 0.26,          # maintain slight decrease for some elasticity
    'mass': 20.0,               # fixed mass
    'damping': 7.8              # moderate decrease for controlled damping
}

physical_parameters_for_object_id_2 = {  
    'sliding-friction': 0.33,   # small increment for more consistent motion
    'armature': 0.32,           # subtle change for balanced responsiveness
    'stiffness': 0.72,          # slight reduction to maintain flexibility
    'mass': 10.0,               # fixed mass
    'damping': 6.2              # slight adjustment for better damping
}

physical_parameters_for_object_id_3 = {  
    'sliding-friction': 0.28,  # slight increase for better movement control
    'armature': 0.68,           # increment for more rotational resistance
    'stiffness': 0.49,          # maintain moderation in stiffness for balance
    'mass': 4.0,                # fixed mass
    'damping': 8.2              # subtle increase for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.94
Trajectory Error for martini_glass = 1.13
Trajectory Error for wine_glass = 1.64
Total Trajectory Error (including tray)= 4.95
Average Trajectory Error (including tray)= 1.24



GPT Attempt #2 produced : 

physical_parameters_for_object_id_1 = {  # bottle
    'sliding-friction': 0.18,  # fine-tuning for better response
    'armature': 0.11,          # keep slightly lowered for rotational inertia
    'stiffness': 0.22,         # maintain lower stiffness for motion
    'mass': 20.0,              # fixed mass
    'damping': 7.4             # moderate damping for better stability
}

physical_parameters_for_object_id_2 = {  # martini_glass
    'sliding-friction': 0.32,  # refined for slide and grip balance
    'armature': 0.32,          # balanced responsiveness
    'stiffness': 0.69,         # reduced for flexibility in motion
    'mass': 10.0,              # fixed mass
    'damping': 6.2             # tuned damping for smooth motion
}

physical_parameters_for_object_id_3 = {  # wine_glass
    'sliding-friction': 0.26,  # slightly increased for less sliding
    'armature': 0.65,          # balanced for rotational control
    'stiffness': 0.46,         # moderate stiffness for balance
    'mass': 4.0,               # fixed mass
    'damping': 8.3             # balanced damping for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.82
Trajectory Error for martini_glass = 1.44
Trajectory Error for wine_glass = 1.79
Total Trajectory Error (including tray)= 5.38
Average Trajectory Error (including tray)= 1.34



GPT Attempt #3 produced : 

physical_parameters_for_object_id_1 = {  # bottle
    'sliding-friction': 0.17,  # fine-tuning for better grip
    'armature': 0.12,          # slight increase for extra stability
    'stiffness': 0.23,         # maintains smoother movement
    'mass': 20.0,              # fixed mass
    'damping': 7.5             # moderate fine-tuning for stability
}

physical_parameters_for_object_id_2 = {  # martini_glass
    'sliding-friction': 0.32,  # balanced for consistent motion
    'armature': 0.33,          # balanced responsiveness
    'stiffness': 0.7,          # slight reduction for flexibility
    'mass': 10.0,              # fixed mass
    'damping': 6.3             # better damping for smoother motion
}

physical_parameters_for_object_id_3 = {  # wine_glass
    'sliding-friction': 0.27,  # balanced sliding and gripping
    'armature': 0.67,          # balanced for rotational control
    'stiffness': 0.46,         # moderate stiffness for balance
    'mass': 4.0,               # fixed mass
    'damping': 8.2             # moderate for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.94
Trajectory Error for martini_glass = 1.45
Trajectory Error for wine_glass = 1.67
Total Trajectory Error (including tray)= 5.43
Average Trajectory Error (including tray)= 1.36



GPT Attempt #4 produced : 

physical_parameters_for_object_id_1 = {  # for 'bottle'
    'sliding-friction': 0.2,  # adjusted
    'armature': 0.1,        # adjusted
    'stiffness': 0.2,       # adjusted
    'mass': 20.0,           # mass is 20.0 for bottle
    'damping': 8.0          # adjusted
}

physical_parameters_for_object_id_2 = {  # for 'martini_glass'
    'sliding-friction': 0.3,  # adjusted
    'armature': 0.3,        # adjusted
    'stiffness': 0.7,       # adjusted
    'mass': 10.0,           # mass is 10.0 for martini_glass
    'damping': 6.0          # adjusted
}

physical_parameters_for_object_id_3 = {  # for 'wine_glass'
    'sliding-friction': 0.1,  # adjusted
    'armature': 0.5,        # adjusted
    'stiffness': 0.4,       # adjusted
    'mass': 4.0,            # mass is 4.0 for wine_glass
    'damping': 7.0          # adjusted
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.74
Trajectory Error for martini_glass = 1.74
Trajectory Error for wine_glass = 1.95
Total Trajectory Error (including tray)= 5.87
Average Trajectory Error (including tray)= 1.47



GPT Attempt #5 produced : 

physical_parameters_for_object_id_1 = {  
    'sliding-friction': 0.18, # slight increase for better grip
    'armature': 0.12,         # keep slight increase for extra stability
    'stiffness': 0.22,        # maintain slight decrease for some elasticity
    'mass': 20.0,             # fixed mass
    'damping': 7.6            # moderate fine-tuning for stability
}

physical_parameters_for_object_id_2 = {  
    'sliding-friction': 0.31,  # balanced for consistent motion
    'armature': 0.34,          # balanced responsiveness
    'stiffness': 0.68,         # reduced for flexibility in motion
    'mass': 10.0,              # fixed mass
    'damping': 6.4             # tuned damping for smooth motion
}

physical_parameters_for_object_id_3 = {  
    'sliding-friction': 0.27,  # slightly increased for better movement control
    'armature': 0.66,          # balanced for rotational control
    'stiffness': 0.45,         # moderate stiffness for balance
    'mass': 4.0,               # fixed mass
    'damping': 8.2             # subtle increase for stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.9
Trajectory Error for martini_glass = 1.56
Trajectory Error for wine_glass = 2.01
Total Trajectory Error (including tray)= 5.99
Average Trajectory Error (including tray)= 1.5



GPT Attempt #6 produced : 

physical_parameters_for_object_id_1 = {  # bottle
    'sliding-friction': 0.17,  # slight increase for better grip
    'armature': 0.12,          # slight increase for better response
    'stiffness': 0.23,         # slight decrease for smoother movement
    'mass': 20.0,              # mass fixed
    'damping': 7.6             # moderate fine-tuned for stability
}

physical_parameters_for_object_id_2 = {  # martini_glass
    'sliding-friction': 0.32,  # balanced for consistent motion
    'armature': 0.34,          # keeps balanced responsiveness
    'stiffness': 0.68,         # slight reduction for flexibility
    'mass': 10.0,              # mass fixed
    'damping': 6.3             # better damping for smoother motion
}

physical_parameters_for_object_id_3 = {  # wine_glass
    'sliding-friction': 0.27,  # better sliding and gripping balance
    'armature': 0.67,          # balanced for rotational control
    'stiffness': 0.47,         # moderate stiffness for balance
    'mass': 4.0,               # mass fixed
    'damping': 8.2             # moderate for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.92
Trajectory Error for martini_glass = 2.21
Trajectory Error for wine_glass = 1.72
Total Trajectory Error (including tray)= 6.45
Average Trajectory Error (including tray)= 1.61



GPT Attempt #7 produced : 

physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.1,  # reduced sliding friction to move more easily
    'armature': 0.2,          # slight increment for more resistance to motion
    'stiffness': 0.3,         # keeps similar elasticity
    'mass': 20.0,             # mass is fixed for bottle
    'damping': 6.0            # increased to reduce oscillation
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.4,  # increased for more grip
    'armature': 0.3,          # slightly adjusted
    'stiffness': 0.7,         # similar stiffness to maintain flexibility
    'mass': 10.0,             # mass is fixed for martini_glass
    'damping': 7.0            # increased damping for more stability
}

physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.3,  # adjusted for balance between grip and slide
    'armature': 0.7,          # increased armature for more rotational resistance
    'stiffness': 0.5,         # keeping stiffness in check for balance
    'mass': 4.0,              # mass is fixed for wine_glass
    'damping': 8.0            # fine-tuned damping for stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 1.44
Trajectory Error for martini_glass = 2.02
Trajectory Error for wine_glass = 1.65
Total Trajectory Error (including tray)= 7.02
Average Trajectory Error (including tray)= 1.75



GPT Attempt #8 produced : 

physical_parameters_for_object_id_1 = {  # bottle
    'sliding-friction': 0.15,  # slight increase for better grip
    'armature': 0.11,          # slight increase, close to 1st and 7th attempts
    'stiffness': 0.24,         # slight decrease for smoother movement
    'mass': 20.0,              # mass fixed
    'damping': 7.5             # moderate fine-tuned for stability
}

physical_parameters_for_object_id_2 = {  # martini_glass
    'sliding-friction': 0.34,  # balanced for consistent motion
    'armature': 0.33,          # keeps balanced responsiveness
    'stiffness': 0.71,         # slight reduction for flexibility
    'mass': 10.0,              # mass fixed
    'damping': 6.1             # better damping for smoother motion
}

physical_parameters_for_object_id_3 = {  # wine_glass
    'sliding-friction': 0.29,  # better sliding and gripping balance
    'armature': 0.69,          # balanced for rotational control
    'stiffness': 0.48,         # moderate stiffness for balance
    'mass': 4.0,               # mass fixed
    'damping': 8.1             # moderate for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.95
Trajectory Error for martini_glass = 2.62
Trajectory Error for wine_glass = 1.69
Total Trajectory Error (including tray)= 7.23
Average Trajectory Error (including tray)= 1.81



GPT Attempt #9 produced : 

physical_parameters_for_object_id_1 = {  # bottle
    'sliding-friction': 0.16,  # slight decrease for smoother response
    'armature': 0.11,          # keep slight increase for extra stability
    'stiffness': 0.24,         # slight increase for stability
    'mass': 20.0,              # fixed mass
    'damping': 7.5             # moderate damping for stability
}

physical_parameters_for_object_id_2 = {  # martini_glass
    'sliding-friction': 0.32,  # balanced for consistent motion
    'armature': 0.34,          # balanced responsiveness
    'stiffness': 0.68,         # reduce stiffness slightly
    'mass': 10.0,              # fixed mass
    'damping': 6.2             # tuned damping for smooth motion
}

physical_parameters_for_object_id_3 = {  # wine_glass
    'sliding-friction': 0.27,  # balanced for sliding and grip
    'armature': 0.66,          # balanced for rotational control
    'stiffness': 0.46,         # stick with slight reduction
    'mass': 4.0,               # fixed mass
    'damping': 8.2             # moderate for stable motion
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.99
Trajectory Error for martini_glass = 2.12
Trajectory Error for wine_glass = 1.72
Total Trajectory Error (including tray)= 6.48
Average Trajectory Error (including tray)= 1.62



GPT Attempt #10 produced : 

physical_parameters_for_object_id_1 = {  # bottle
    'sliding-friction': 0.18,  # adjusted for better grip
    'armature': 0.12,          # slightly increased for stability
    'stiffness': 0.23,         # slight decrease for smoother movement
    'mass': 20.0,              # fixed mass
    'damping': 7.7             # adjusted damping for stability
}

physical_parameters_for_object_id_2 = {  # martini_glass
    'sliding-friction': 0.32,  # balanced for consistent motion
    'armature': 0.34,          # balanced responsiveness
    'stiffness': 0.67,         # slight reduction for flexibility
    'mass': 10.0,              # fixed mass
    'damping': 6.3             # better damping for smoother motion
}

physical_parameters_for_object_id_3 = {  # wine_glass
    'sliding-friction': 0.28,  # slightly increased balancing sliding and gripping
    'armature': 0.67,          # balanced for rotational control
    'stiffness': 0.45,         # moderate stiffness for balance
    'mass': 4.0,               # fixed mass
    'damping': 8.3             # balanced damping for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.82
Trajectory Error for martini_glass = 1.48
Trajectory Error for wine_glass = 1.77
Total Trajectory Error (including tray)= 5.49
Average Trajectory Error (including tray)= 1.37



GPT Attempt #11 produced : 

physical_parameters_for_object_id_1 = {  # bottle
    'sliding-friction': 0.19,  # adjusted for better grip
    'armature': 0.12,          # maintain stability
    'stiffness': 0.22,         # slight decrease for smoother movement
    'mass': 20.0,              # fixed mass
    'damping': 7.8             # adjusted damping for stability
}

physical_parameters_for_object_id_2 = {  # martini_glass
    'sliding-friction': 0.31,  # balanced for consistent motion
    'armature': 0.35,          # minor adjustment for responsiveness
    'stiffness': 0.66,         # slight reduction for flexibility
    'mass': 10.0,              # fixed mass
    'damping': 6.4             # tuned damping for smooth motion
}

physical_parameters_for_object_id_3 = {  # wine_glass
    'sliding-friction': 0.29,  # fine-tuned to balance sliding and gripping
    'armature': 0.68,          # balanced for rotational control
    'stiffness': 0.46,         # maintain elasticity control
    'mass': 4.0,               # fixed mass
    'damping': 8.3             # fine-tuned for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.79
Trajectory Error for martini_glass = 1.47
Trajectory Error for wine_glass = 1.66
Total Trajectory Error (including tray)= 5.18
Average Trajectory Error (including tray)= 1.29



GPT Attempt #12 produced : 

physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.19,  # fine-tuned for adequate grip
    'armature': 0.12,          # slight increase for stability
    'stiffness': 0.22,         # slight decrease for smoother motion
    'mass': 20.0,              # fixed mass
    'damping': 7.8             # adjusted for improved damping
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.31,  # balanced for consistent motion
    'armature': 0.35,          # minor adjustment for responsiveness
    'stiffness': 0.66,         # slight reduction for flexibility
    'mass': 10.0,              # fixed mass
    'damping': 6.4             # tuned damping for smooth motion
}

physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.29,  # fine-tuned to balance sliding and gripping
    'armature': 0.68,          # balanced for rotational control
    'stiffness': 0.46,         # maintain elasticity control
    'mass': 4.0,               # fixed mass
    'damping': 8.3             # fine-tuned for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.79
Trajectory Error for martini_glass = 1.47
Trajectory Error for wine_glass = 1.66
Total Trajectory Error (including tray)= 5.18
Average Trajectory Error (including tray)= 1.29



GPT Attempt #13 produced : 

physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.17,  # slightly reduced for balance
    'armature': 0.12,         # slight increase for stability
    'stiffness': 0.23,        # maintain elasticity
    'mass': 20.0,             # fixed mass
    'damping': 7.7            # adjusted for better damping response
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.32,  # balanced friction
    'armature': 0.34,          # slight adjustment
    'stiffness': 0.67,         # slight flexibility maintenance
    'mass': 10.0,              # fixed mass
    'damping': 6.3             # adjusted for smoother damping
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.28,  # balanced friction
    'armature': 0.68,          # maintains rotational control
    'stiffness': 0.46,         # stiffness for balance
    'mass': 4.0,               # fixed mass
    'damping': 8.2             # fine-tuned for stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.9
Trajectory Error for martini_glass = 2.53
Trajectory Error for wine_glass = 1.79
Total Trajectory Error (including tray)= 6.96
Average Trajectory Error (including tray)= 1.74



GPT Attempt #14 produced : 

physical_parameters_for_object_id_1 = {  # bottle
    'sliding-friction': 0.19,  # fine-tuned for better grip
    'armature': 0.12,          # slight increase for stability
    'stiffness': 0.22,         # slight decrease for smoother movement
    'mass': 20.0,              # fixed mass
    'damping': 7.7             # adjusted damping for stability
}

physical_parameters_for_object_id_2 = {  # martini_glass
    'sliding-friction': 0.32,  # balanced for consistent motion
    'armature': 0.35,          # minor adjustment for responsiveness
    'stiffness': 0.67,         # slight reduction for flexibility
    'mass': 10.0,              # fixed mass
    'damping': 6.4             # tuned damping for smooth motion
}

physical_parameters_for_object_id_3 = {  # wine_glass
    'sliding-friction': 0.29,  # fine-tuned to balance sliding and gripping
    'armature': 0.68,          # balanced for rotational control
    'stiffness': 0.46,         # maintain elasticity control
    'mass': 4.0,               # fixed mass
    'damping': 8.3             # fine-tuned for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.8
Trajectory Error for martini_glass = 1.29
Trajectory Error for wine_glass = 1.35
Total Trajectory Error (including tray)= 4.58
Average Trajectory Error (including tray)= 1.15



GPT Attempt #15 produced : 

physical_parameters_for_object_id_1 = {  # for 'bottle'
    'sliding-friction': 0.19,  # adjusted for better grip
    'armature': 0.12,          # maintain stability
    'stiffness': 0.22,         # slight decrease for smoother movement
    'mass': 20.0,              # fixed mass
    'damping': 7.8             # adjusted damping for stability
}

physical_parameters_for_object_id_2 = {  # for 'martini_glass'
    'sliding-friction': 0.31,  # balanced for consistent motion
    'armature': 0.35,          # minor adjustment for responsiveness
    'stiffness': 0.67,         # slight reduction for flexibility
    'mass': 10.0,              # fixed mass
    'damping': 6.3             # better damping for smoother motion
}

physical_parameters_for_object_id_3 = {  # for 'wine_glass'
    'sliding-friction': 0.29,  # fine-tuned to balance sliding and gripping
    'armature': 0.68,          # balanced for rotational control
    'stiffness': 0.46,         # maintain elasticity control
    'mass': 4.0,               # fixed mass
    'damping': 8.3             # fine-tuned for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.79
Trajectory Error for martini_glass = 1.68
Trajectory Error for wine_glass = 1.84
Total Trajectory Error (including tray)= 5.7
Average Trajectory Error (including tray)= 1.43



GPT Attempt #16 produced : 

physical_parameters_for_object_id_1 = {  
    'sliding-friction': 0.19,  # fine-tuned for better grip
    'armature': 0.12,          # slight increase for stability
    'stiffness': 0.22,         # slight decrease for smoother movement
    'mass': 20.0,              # fixed mass
    'damping': 7.7             # adjusted damping for stability
}

physical_parameters_for_object_id_2 = {  
    'sliding-friction': 0.31,  # balanced for consistent motion
    'armature': 0.34,          # minor adjustment for responsiveness
    'stiffness': 0.66,         # slight reduction for flexibility
    'mass': 10.0,              # fixed mass
    'damping': 6.4             # tuned damping for smooth motion
}

physical_parameters_for_object_id_3 = {  
    'sliding-friction': 0.28,  # slightly increased balancing sliding and gripping
    'armature': 0.68,          # balanced for rotational control
    'stiffness': 0.46,         # maintain elasticity control
    'mass': 4.0,               # fixed mass
    'damping': 8.3             # fine-tuned for better stability
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 0.79
Trajectory Error for martini_glass = 1.68
Trajectory Error for wine_glass = 1.84
Total Trajectory Error (including tray)= 5.7
Average Trajectory Error (including tray)= 1.43

End of Prompt
