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), (-1.1, -1.2, 0.1), (-1.5, -1.5, 0.1), (-1.8, -1.8, 0.1), (-2.0, -1.9, 0.1), (-2.2, -2.1, 0.1), (-2.3, -2.2, 0.1), (-2.4, -2.3, 0.1)]

bottle_motion_trajectory (x, y, z) = [(-1.1, -1.1, 1.1), (-1.2, -1.2, 1.1), (-1.4, -1.3, 1.1), (-1.5, -1.5, 1.0), (-1.6, -1.6, 0.8), (-1.7, -1.8, 0.6), (-1.7, -1.9, 0.5), (-1.8, -2.1, 0.5), (-2.0, -2.2, 0.5)]

martini_glass_motion_trajectory (x, y, z) = [(-1.0, 0.0, 0.5), (-1.1, -0.0, 0.6), (-1.2, -0.1, 0.5), (-1.3, -0.2, 0.5), (-1.5, -0.4, 0.5), (-1.7, -0.5, 0.5), (-1.9, -0.7, 0.5), (-2.0, -0.8, 0.5), (-2.1, -0.9, 0.5)]

wine_glass_motion_trajectory (x, y, z) = [(-1.0, 1.0, 0.9), (-1.1, 0.9, 1.0), (-1.1, 0.8, 0.9), (-1.2, 0.8, 0.8), (-1.3, 0.7, 0.8), (-1.4, 0.7, 0.8), (-1.4, 0.6, 0.8), (-1.4, 0.6, 0.8), (-1.4, 0.6, 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': 0.2,   # Adjusted
             'armature': 0.3,          # Adjusted
             'stiffness': 0.0,         # Adjusted
             'mass': 20.0,             # Kept the same
             'damping': 6.0            # Adjusted
         }

physical_parameters_for_object_id_2 = { 
             'sliding-friction': 0.3,   # Adjusted
             'armature': 0.3,          # Adjusted
             'stiffness': 0.7,         # Adjusted
             'mass': 10.0,             # Kept the same
             'damping': 4.5            # Adjusted
         }

physical_parameters_for_object_id_3 = { 
             'sliding-friction': 0.4,   # Adjusted
             'armature': 0.6,          # Adjusted
             'stiffness': 0.3,         # Adjusted
             'mass': 4.0,              # Kept the same
             'damping': 4.2            # Adjusted
         }
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 1.5
Trajectory Error for martini_glass = 1.33
Trajectory Error for wine_glass = 0.54
Total Trajectory Error (including tray)= 5.03
Average Trajectory Error (including tray)= 1.26



GPT Attempt #2 produced : 

physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.3,   # Adjusted to increase friction
    'armature': 0.3,           # Adjusted to moderate armature
    'stiffness': 0.0,          # Kept the same
    'mass': 20.0,              # Kept the same
    'damping': 6.3             # Slightly increased damping
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.4,   # Slightly increased sliding friction
    'armature': 0.4,           # Balanced armature
    'stiffness': 0.5,          # Further refined stiffness
    'mass': 10.0,              # Kept the same
    'damping': 5.0             # Adjusted damping for better results
}

physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.4,   # Adjusted slightly from previous
    'armature': 0.5,           # Reduced armature
    'stiffness': 0.4,          # Balanced stiffness
    'mass': 4.0,               # Kept the same
    'damping': 4.5             # Adjusted damping slightly
}
Trajectory Prediction Error using the above parameters is listed below: 
Trajectory Error for bottle = 1.32
Trajectory Error for martini_glass = 0.57
Trajectory Error for wine_glass = 0.44
Total Trajectory Error (including tray)= 2.9
Average Trajectory Error (including tray)= 0.72

End of Prompt
