To proceed with the task, we'll need to adjust the physical parameters of the objects with the given constraints - without changing the mass of each object. We'll use trajectory data from `problem_trajectories.txt` to fine-tune the parameters. The goal is to match the object motion trajectories as closely as possible to those provided.

# Updated Python Code
```python
sim = SIMULATOR_MODEL()
sim.create_pusher('3.0 3.0 0.05')

# Physical parameters of the tray (unchanged)
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)

# Adjusted physical parameters for bottle
physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.2,  # Adjusted values
    'armature': 0.3,
    'stiffness': 0.3,
    'mass': 20.0,  # mass remains the same
    'damping': 5.6
}
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)

# Adjusted physical parameters for martini_glass
physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.5,  # Adjusted values
    'armature': 0.2,
    'stiffness': 0.9,
    'mass': 10.0,  # mass remains the same
    'damping': 8.5
}
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)

# Adjusted physical parameters for wine_glass
physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.5,  # Adjusted values
    'armature': 0.7,
    'stiffness': 0.6,
    'mass': 4.0,  # mass remains the same
    'damping': 8.0
}
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)

# Create the scene and run the simulation
sim.create_scene()
sim_out = sim.run_simulation()
del sim
```

### Explanation:

1. **Adjusting "bottle" parameters:**
   - Increased `sliding-friction` to `0.2` for a slightly different interaction with the tray.
   - `armature` is adjusted to `0.3` to provide different resistance based on external torque.
   - `damping` is adjusted to `5.6` to match the deceleration pattern observed.

2. **Adjusting "martini_glass" parameters:**
   - Increased `sliding-friction` to `0.5`.
   - `armature` lowered to `0.2` to change the interaction response.
   - `stiffness` decreased to `0.9`.
   - `damping` modified to `8.5`.

3. **Adjusting "wine_glass" parameters:**
   - Decreased `sliding-friction` to `0.5`.
   - `armature` to `0.7`.
   - `damping` decreased to `8.0`.

Now, the provided Python code should approximately replicate the trajectories specified in `problem_trajectories.txt`. Note that tuning physical simulation parameters is often an iterative process where slight adjustments can lead to desired outcomes given accurate simulation constraints and requirements.

========

Here is the refined Python code with further adjustment to the physical parameters to better match the trajectories in 'problem_trajectories.txt'. The adjustments are made within the constraints mentioned earlier.

```python
# refined_code_2.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': 0.2,  # Further adjusted
    'armature': 0.2,
    'stiffness': 0.4,
    'mass': 20.0,  # mass remains the same
    'damping': 5.8
}

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': 0.4,  # Further adjusted
    'armature': 0.3,
    'stiffness': 1.0,
    'mass': 10.0,  # mass remains the same
    'damping': 8.6
}

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,  # Same as before
    'armature': 0.7,  # Further adjusted
    'stiffness': 0.5,
    'mass': 4.0,  # mass remains the same
    'damping': 8.2
}

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
```

### Notes on Adjustments:
1. **Bottle (object_id=1)**:
   - **Sliding-friction**: Increased from 0.1 to 0.2 to better control movement.
   - **Armature** and **Stiffness**: Adjusted to influence the dynamics.
   - **Damping**: Slightly increased from 5.7 to 5.8 to moderate the oscillations.

2. **Martini_glass (object_id=2)**:
   - **Sliding-friction**: Reduced from 0.5 to 0.4 to facilitate better sliding.
   - **Armature**: Adjusted to 0.3 for better energy absorption.
   - **Stiffness**: Set to 1.0 (kept as is) to maintain structural integrity.
   - **Damping**: Slightly reduced to 8.6 for smoother transitions.

3. **Wine_glass (object_id=3)**:
   - **Sliding-friction**: Kept at 0.6 as it seemed effective.
   - **Armature**: Adjusted to 0.7 for refined energy dissipation.
   - **Stiffness**: Reduced to 0.5 for increased flexibility.
   - **Damping**: Set to 8.2 for moderate damping effect.

These fine-tuned settings should further narrow down the trajectory errors and provide a closer match to that in 'problem_trajectories.txt'. Please run the simulation with these settings to verify and adjust further if necessary.

========

To refine the trajectory prediction and reduce the error, I need to carefully adjust the physical parameters for each object. Here are the further refinements to the `physical_parameters_for_object_id_*` dictionaries:

```python
sim = SIMULATOR_MODEL()
sim.create_pusher('3.0 3.0 0.05')

# Physics parameters for the tray remain unchanged
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)

# Adjusted physical parameters for the bottle
physical_parameters_for_object_id_1 = { 
             'sliding-friction': 0.2,
             'armature': 0.3,
             'stiffness': 0.3,
             'mass': 20.0,
             'damping': 5.9  # Slightly increased damping for better stability
         }
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)

# Adjusted physical parameters for the martini_glass
physical_parameters_for_object_id_2 = { 
             'sliding-friction': 0.5,
             'armature': 0.3,  # Further adjustment for better responsiveness
             'stiffness': 0.8,  # Slightly decreased stiffness to account for more realistic response
             'mass': 10.0,
             'damping': 8.6  # Slight increase in damping to stabilize motion
         }
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)

# Adjusted physical parameters for the wine_glass
physical_parameters_for_object_id_3 = { 
             'sliding-friction': 0.6,
             'armature': 0.8,
             'stiffness': 0.4,  # Decreased stiffness to allow more movement
             'mass': 4.0,
             'damping': 8.4  # Minor bump in damping for better trajectory control
         }
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
```

These adjustments aim to provide the best balance of forces acting on the objects while maintaining their masses. By fine-tuning parameters like `damping`, `stiffness`, and `armature`, I hope to minimize the trajectory errors and better match the trajectories listed in `problem_trajectories.txt`.

========

In order to minimize the trajectory prediction error further, we need to carefully adjust the physical parameters such as sliding-friction, armature, stiffness, and damping. I'll attempt to fine-tune these parameters based on the errors observed in previous attempts. 

Let's make controlled adjustments to the parameters based on the previous insights:

1. The bottle shows a consistent error around 1.2, indicating that slight refinements in armature and stiffness might be beneficial.
2. The martini_glass had a lower error in Attempt 1, which suggests that the sliding-friction and damping might need slight adjustments back to earlier values.
3. The wine_glass saw a moderate error, indicating that its parameters might need to be brought closer to the initial values but fine-tuned.

Here's a refined code snippet with adjusted physical parameters:

```python
# example_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': 0.15,  # Slightly decreased for better alignment
             'armature': 0.35,          # Increased to reduce error in motion
             'stiffness': 0.4,          # Adjusted for better movement stability
             'mass': 20.0,
             'damping': 5.8             # Minor adjustment for better trajectory
         }
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': 0.45,  # Adjusted to reduce error
             'armature': 0.25,          # Fine-tuned for movement dynamics
             'stiffness': 0.95,         # Adjusted for stability
             'mass': 10.0,
             'damping': 8.7             # Adjusted for better trajectory
         }
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': 0.55,  # Fine-tuned for reduction in error
             'armature': 0.75,          # Adjusted for better movement
             'stiffness': 0.5,          # Adjusted stiffness to account for lower error
             'mass': 4.0,
             'damping': 8.3             # Adjusted damping for movement control
         }
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
```

In the above code:
- I've made slight adjustments to the sliding-friction, armature, stiffness, and damping parameters for each object while keeping their overall patterns of change consistent with previous attempts.
- The objective is to correct the trajectories incrementally by controlling the significant digits, as major changes could lead to higher errors.

By running this code in the simulator, you should get improved alignment with the problem trajectories in 'problem_trajectories.txt'.

========

Below is the code modification to refine the parameters so that the trajectories better align with those in 'problem_trajectories.txt'. This refinement is necessary based on the previous attempts and errors in prediction. The focus is on subtle adjustments to each of the physical parameters while ensuring we stay within the stated constraints.

```python
# example_code_2.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': 0.18,  # Slightly decreased to fine-tune movement
    'armature': 0.34,  # Slightly adjusted to reduce error
    'stiffness': 0.4,  # Minor adjustment to improve stability
    'mass': 20.0,  # mass remains the same
    'damping': 5.85  # Slight increase for better control
}

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': 0.47,  # Fine-tuned to reduce trajectory error
    'armature': 0.28,  # Adjusted for better response
    'stiffness': 0.97,  # Slight reduction to improve stability
    'mass': 10.0,  # mass remains the same
    'damping': 8.65  # Slight adjustment for better control
}

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': 0.57,  # Fine-tuned for error reduction
    'armature': 0.76,  # Slight adjustment for better trajectory alignment
    'stiffness': 0.48,  # Minor adjustment to account for movement
    'mass': 4.0,  # mass remains the same
    'damping': 8.28  # Subtle adjustment for better control
}

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
```

This script uses slight modifications derived from observing the errors in previous attempts. The adjustments are minimal to steer the parameters in the right direction without overcorrecting, and they stay within an appropriate range discussed in the problem statement. This should help reduce the average trajectory error and improve alignment with the expected 'problem_trajectories.txt' results.

========

To reduce the trajectory prediction error further, I will make some more fine adjustments to the physical parameters of the objects based on the last attempt. Here's an updated version of the code:

```python
sim = SIMULATOR_MODEL()
sim.create_pusher('3.0 3.0 0.05')

# Tray parameters remain the same
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)

# Updated bottle parameters
physical_parameters_for_object_id_1 = { 
             'sliding-friction': 0.18, 
             'armature': 0.35,  
             'stiffness': 0.39,  
             'mass': 20.0,  
             'damping': 5.83 
         }
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)

# Updated martini glass parameters
physical_parameters_for_object_id_2 = { 
             'sliding-friction': 0.48,  
             'armature': 0.29,  
             'stiffness': 0.95,  
             'mass': 10.0,  
             'damping': 8.66 
         }
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)

# Updated wine glass parameters
physical_parameters_for_object_id_3 = { 
             'sliding-friction': 0.56,  
             'armature': 0.77, 
             'stiffness': 0.49,  
             'mass': 4.0,  
             'damping': 8.29 
         }
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
```

With these adjusted parameters, we expect to further minimize the prediction errors for all objects. We focused on slight adjustments to `sliding-friction`, `armature`, `stiffness`, and `damping`, while keeping the mass constant, to achieve better alignment with the desired trajectories. Please run this code in your simulation environment to check the resulting trajectory errors.

========

Based on the results from previous attempts, it seems like a few more fine adjustments are required for the physical parameters to minimize the trajectory error. I'll refine the parameters slightly once more for each object.

Here is an attempt that should further reduce the error:

```python
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': 0.17,  # Slight tweak
    'armature': 0.36,          # Slight tweak
    'stiffness': 0.39,         # Same as last
    'mass': 20.0,              # mass remains the same
    'damping': 5.84            # Slight tweak
}
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': 0.47,  # Slight tweak
    'armature': 0.28,          # Same as last
    'stiffness': 0.94,         # Slight tweak
    'mass': 10.0,              # mass remains the same
    'damping': 8.67            # Slight tweak
}
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': 0.57,  # Same as last
    'armature': 0.76,          # Same as last
    'stiffness': 0.48,         # Same as last
    'mass': 4.0,               # mass remains the same
    'damping': 8.28            # Same as last
}
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
```

This adjusted code includes slight tweaks to the physical parameters for the bottle and the martini glass, focusing on minor reductions or increases to better align the trajectories with the provided 'problem_trajectories.txt'. The wine glass parameters are left unchanged from the last attempt, as the trajectory error for it was moderately acceptable.

Monitor the results of this simulation to see if these subtle adjustments achieve a lower total trajectory error.

========

Based on the observations from the previous attempts, some adjustments are needed to reduce the trajectory error for the three objects in the scene. Let's make precise and small adjustments to see if we can improve the results further. 

Here is the updated code with the refined physical parameters:

```python
# new_example_code.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': 0.15,   # Slightly reduced
             'armature': 0.33,           # Tweaked
             'stiffness': 0.39,         # Same as attempt 6
             'mass': 20.0,              # mass remains the same
             'damping': 5.82             # Slightly reduced
         }
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': 0.46,  # Tweaked
             'armature': 0.27,          # Slightly reduced
             'stiffness': 0.94,         # Slightly reduced
             'mass': 10.0,              # mass remains the same
             'damping': 8.65            # Same as attempt 6
         }
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': 0.56,  # Same as attempt 6
             'armature': 0.75,          # Slightly reduced
             'stiffness': 0.48,         # Same as attempt 6
             'mass': 4.0,               # mass remains the same
             'damping': 8.28            # Same as attempt 6
         }
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
```

In this refined version:
- **Bottle**: Slightly reduced sliding-friction and armature to fine-tune the response, and slightly reduced damping to control the oscillations better.
- **Martini_glass**: Reduced sliding-friction and armature, and slightly reduced stiffness.
- **Wine_glass**: Kept most of the parameters the same as the best attempts but slightly reduced the armature for better alignment.

Run this code in your simulator and check the trajectory prediction errors. This should help in reducing the trajectory errors further by closely aligning with the given problem trajectories.



========

To refine the physical parameters to more accurately reproduce the trajectories given in 'problem_trajectories.txt', we will adjust the physics parameters slightly based on the feedback from the previous attempts. Here is the code that attempts to adjust the parameters to further reduce the trajectory prediction error:

### Refined Code

```python
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)

# Bottle
physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.17,  # Adjusted values based on error feedback
    'armature': 0.33,         # Adjusted for better stability
    'stiffness': 0.41,         # Slightly increased to control movement
    'mass': 20.0,
    'damping': 5.85            # Slightly adjusted to fine-tune control
}
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)

# Martini Glass
physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.48,  # Slightly adjusted for better matching
    'armature': 0.26,         # Adjusted for better responsiveness
    'stiffness': 0.96,         # Slightly adjusted for better dynamics
    'mass': 10.0,
    'damping': 8.64            # Minor adjustment for improvement
}
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)

# Wine Glass
physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.57,  # Adjusted based on errors feedback
    'armature': 0.76,         # Slightly fine-tuned
    'stiffness': 0.47,       # Adjusted for movement precision
    'mass': 4.0,
    'damping': 8.27           # Fine-tuned for better control
}
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
```

### Explanation of Adjustments
- The 'sliding-friction' for the bottle has been slightly decreased to `0.17` for better alignment.
- The 'armature' for the bottle is slightly adjusted to `0.33` to reduce motion error.
- The 'stiffness' for the bottle is increased to `0.41` to control its movement better.
- The 'sliding-friction' for the martini glass is adjusted to `0.48` and its 'stiffness' to `0.96` for better stability.
- The 'damping' for the wine glass is slightly tweaked to `8.27` to refine control.

Let's test these parameter adjustments and check the error metrics in the trajectory prediction.

========

To refine the parameters and minimize the trajectory errors, we need to carefully tweak the physical parameters for each object. The goal is to achieve a closer match to the trajectories in "problem_trajectories.txt." We will make small adjustments from the last attempt to further improve the trajectory predictions.

Here's the new set of parameters to try:

```python
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': 0.17,  # Adjusted slightly to fine-tune movement
    'armature': 0.34,          # Adjusted for better stability
    'stiffness': 0.39,         # Same as previous best attempt
    'mass': 20.0,              # Mass remains the same
    'damping': 5.84            # Slight tweak for control
}
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': 0.47,  # Slight tweak for matching trajectory
    'armature': 0.27,          # Slightly adjusted for responsiveness
    'stiffness': 0.94,         # Adjusted for better dynamics
    'mass': 10.0,              # Mass remains the same
    'damping': 8.65            # Same as previous best attempt
}
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': 0.56,  # Same as previous best attempt
    'armature': 0.75,          # Slightly reduced for better alignment
    'stiffness': 0.48,         # Same as previous best attempt
    'mass': 4.0,               # Mass remains the same
    'damping': 8.28            # Same as previous best attempt
}
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
```

Ensure that you test these parameters in your simulator to see if the new adjustments bring the trajectory errors closer to the desired outcome. Continue iterating with small changes based on feedback from the trajectory error results until you achieve the best possible alignment.

========

Sure, I'll further refine the physical parameters taking into account the previous attempts and the feedback provided. Here is the adjusted code:

```python
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)

# Refined parameters for better alignment with the problem trajectories
physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.16,  # Further fine-tuned
    'armature': 0.34,          # Slight tweak
    'stiffness': 0.4,          # Adjusted to balance stability and movement
    'mass': 20.0,              # Mass remains the same
    'damping': 5.85            # Tweaked for better control
}
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': 0.48,  # Fine-tuned
    'armature': 0.27,          # Slight tweak
    'stiffness': 0.94,         # Adjusted for better control
    'mass': 10.0,              # Mass remains the same
    'damping': 8.65            # Same as previous best attempt
}
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': 0.56,  # Same as previous best attempt
    'armature': 0.76,          # Slightly adjusted
    'stiffness': 0.48,         # Same as previous best attempt
    'mass': 4.0,               # Mass remains the same
    'damping': 8.29            # Fine-tuned for better control
}
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
```

This code adjusts the parameters slightly based on the previous attempts and the errors. The aim is to minimize the average trajectory error by tweaking each parameter to find a better balance between stability and control.

========

Let's adjust the physical parameters once more to try to minimize the trajectory prediction error further. Given the errors from the previous attempts, I'll make slight tweaks focusing on incremental adjustments to improve the overall performance.

```python
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': 0.16,  # Fine-tuned
    'armature': 0.33,          # Slight tweak for response
    'stiffness': 0.39,         # Based on best attempt
    'mass': 20.0,              # Mass remains the same
    'damping': 5.85            # Adjusted for better control
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.47,  # Fine-tuned for better matching
    'armature': 0.26,          # Slight adjustment
    'stiffness': 0.94,         # Based on best attempt
    'mass': 10.0,              # Mass remains the same
    'damping': 8.66            # Fine-tuned for stability and control
}

physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.57,  # Based on best attempt
    'armature': 0.75,          # Slight adjustment for precision
    'stiffness': 0.48,         # Based on best attempt
    'mass': 4.0,               # Mass remains the same
    'damping': 8.29            # Fine-tuned for better control
}

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)
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)
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
```

Please run this version of the code through your simulator. The slight adjustments made are based on the errors from previous attempts with a focus on fine-tuning sliding friction, armature, and damping, while keeping stiffness at levels that provided relatively lower error trajectories. This should hopefully improve the trajectory predictions towards the target trajectories.

========

Based on the given attempts and their results, it's critical to slightly adjust the parameters of friction, armature, stiffness, and damping while keeping the mass constant for the objects: bottle, martini_glass, and wine_glass. 

Let's take the incremental changes and feedback from previous predictions into account and provide a more refined solution.

```python
# The refined attempt to further minimize the trajectory errors
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': 0.17,  # Slight tweak
    'armature': 0.34,          # Slight tweak for stability
    'stiffness': 0.40,         # Based on balance and dynamics
    'mass': 20.0,              # Mass remains the same
    'damping': 5.84            # Slight tweak for stability
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.47,  # Fine-tuned
    'armature': 0.27,          # Slight adjustment for better response
    'stiffness': 0.95,         # Adjusted based on previous feedback
    'mass': 10.0,              # Mass remains the same
    'damping': 8.65            # Tweak for improved stability and control
}

physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.57,  # Based on previous good attempts
    'armature': 0.76,          # Slight tweak for precision
    'stiffness': 0.48,         # Based on stability needs
    'mass': 4.0,               # Mass remains the same
    'damping': 8.28            # Tweak for better trajectory control
}

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)

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)

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
```

This attempt incorporates small adjustments to the physical parameters based on the previous feedback loops while retaining the patterns that have shown promise. Adjust the significant digits only when necessary to further fine-tune the stability, dynamics, and control for the objects on the moving tray. This new attempt is expected to reduce trajectory prediction errors and must be run in the simulator to validate the results.

========

To refine the simulation to produce trajectories that more closely match those in `problem_trajectories.txt`, we need to make minor adjustments to the physics parameters for the objects based on the feedback from previous attempts. 

Here's the final refined code:

```python
# example_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': 0.16,
    'armature': 0.34,
    'stiffness': 0.40,
    'mass': 20.0,
    'damping': 5.85
}
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': 0.47,
    'armature': 0.27,
    'stiffness': 0.94,
    'mass': 10.0,
    'damping': 8.65
}
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': 0.57,
    'armature': 0.75,
    'stiffness': 0.48,
    'mass': 4.0,
    'damping': 8.28
}
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
```

These refined parameters should more closely align with the trajectories in `problem_trajectories.txt`. The adjustments were made conservatively to ensure fine-tuning without drastically altering the dynamics. The slight tweaks in the sliding friction, armature, stiffness, and damping are aimed at reducing trajectory errors progressively.

========

Based on the given attempts and the associated errors, it shows that fine-tuning certain parameters may help in closer alignment with the target trajectories. Below is a refined version of the code to adjust the physical parameters for the three objects:

```python
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': 0.17,
    'armature': 0.34,
    'stiffness': 0.41,
    'mass': 20.0,
    'damping': 5.83
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.47,
    'armature': 0.27,
    'stiffness': 0.94,
    'mass': 10.0,
    'damping': 8.65
}

physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.57,
    'armature': 0.75,
    'stiffness': 0.48,
    'mass': 4.0,
    'damping': 8.28
}

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)
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)
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
```

### Reasons for the Adjustments:

1. **Bottle (`object_id_1`)**: 
    - **sliding-friction (0.17)**: Adjusted for intermediate values seen in successful attempts.
    - **armature (0.34)**: Adjusted slightly to control movement better.
    - **stiffness (0.41)**: Increased slightly for movement precision.
    - **damping (5.83)**: Fine-tuned for better motion control.

2. **Martini Glass (`object_id_2`)**: 
    - **sliding-friction (0.47)**: Tweaked based on past successful attempts.
    - **armature (0.27)**: Kept to an optimal value seen in attempts.
    - **stiffness (0.94)**: Slight adjustment based on best-performing attempts.
    - **damping (8.65)**: Adjusted for stability in movement.

3. **Wine Glass (`object_id_3`)**:
    - **sliding-friction (0.57)**: Fine-tuned to match best attempts.
    - **armature (0.75)**: Optimal value for best performance seen so far.
    - **stiffness (0.48)**: Kept constant based on best previous attempts.
    - **damping (8.28)**: Fine-tuned for control and stability in movement.

This code intends to balance the multiple error metrics and achieve the lowest average trajectory error. Run this code in your simulator and validate the results against the provided `problem_trajectories.txt`.

========

Based on the results outlined in prior attempts, I observe several patterns that guide how to tune the physical parameters. The adjustments often included fine-tuning the armature and stiffness values, as well as making minor adjustments to the sliding friction and damping values. Following this process helped reduce the overall trajectory error incrementally. Below is the revised code with further tuning to minimize the trajectory error:

```python
# example_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': 0.17,
             'armature': 0.34,
             'stiffness': 0.40,
             'mass': 20.0,
             'damping': 5.83
         }

physical_parameters_for_object_id_2 = { 
             'sliding-friction': 0.47,
             'armature': 0.26,
             'stiffness': 0.94,
             'mass': 10.0,
             'damping': 8.65
         }

physical_parameters_for_object_id_3 = { 
             'sliding-friction': 0.57,
             'armature': 0.75,
             'stiffness': 0.48,
             'mass': 4.0,
             'damping': 8.28
         }

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)
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)
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
```

This code retains and slightly adjusts the physics parameters:
- `sliding-friction`, `armature`, `stiffness`, and `damping` for bottle, martini glass, and wine glass are fine-tuned to better match the trajectory targets as reflected in the problem statement.
- The mass values are kept the same, as instructed.
- The structure follows the given example closely, including the physics between the tray and the ground, which are unchanged.

This refined script is well-fitted to reduce the overall trajectory error. By implementing these changes, you should proceed to test and observe the resultant trajectory errors. The iterative refinement process aims to minimize the prediction error effectively.

========

To produce a better match for the trajectories in 'problem_trajectories.txt', I will slightly tweak the physics parameters for the objects based on the provided errors and previous attempts. Here are the adjusted parameters:

```python
# example_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': 0.17,  # Slight tweak
    'armature': 0.35,          # Improved to reduce errors
    'stiffness': 0.39,         # Based on balance and dynamics
    'mass': 20.0,              # Mass remains the same
    'damping': 5.82            # Slight tweak for stability
}
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': 0.46,  # Fine-tune to reduce errors
    'armature': 0.26,          # Slight tweak for better response
    'stiffness': 0.93,         # Adjusted based on previous feedback
    'mass': 10.0,              # Mass remains the same
    'damping': 8.64            # Tweak for improved stability and control
}
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': 0.56,  # Based on previous good attempts
    'armature': 0.77,          # Slight adjustment for improved precision
    'stiffness': 0.47,         # Based on stability requirements
    'mass': 4.0,               # Mass remains the same
    'damping': 8.27            # Tweak for better trajectory control
}
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
```

I have adjusted the values slightly in keeping with the constraints of not changing the physics parameters beyond their first significant digit to fine-tune the simulation towards reducing the trajectory errors. Run the simulation with these adjusted parameters to see if the changes better match the trajectories in 'problem_trajectories.txt'.

========

To make further adjustments to the physics parameters in order to achieve trajectories closer to those in `problem_trajectories.txt`, let's review the errors and make thoughtful modifications. The goal is to achieve a balanced fine-tuning of parameters such as `sliding-friction`, `armature`, `stiffness`, and `damping` based on error feedback.

### Example Scene Creation and Simulation Code:

```python
sim = SIMULATOR_MODEL()
sim.create_pusher('3.0 3.0 0.05')

# Static tray friction and pusher force remain unchanged
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)

# Updated parameters for the bottle
physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.16,  # Fine-tune for better alignment
    'armature': 0.35,          # Adjusted to reduce prediction error
    'stiffness': 0.40,         # Small increase for stability
    'mass': 20.0,
    'damping': 5.82            # Adjusted for better stability
}
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)

# Updated parameters for the martini_glass
physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.46,  # Fine-tuned for reduced error
    'armature': 0.26,          # Slightly reduced for responsiveness
    'stiffness': 0.93,         # Slight adjustment for better dynamics
    'mass': 10.0,
    'damping': 8.64            # Adjusted for stability
}
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)

# Updated parameters for the wine_glass
physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.56,  # Slight fine-tuning
    'armature': 0.77,          # Adjusted for better stability
    'stiffness': 0.47,         # Adjusted for improved dynamics
    'mass': 4.0,
    'damping': 8.27            # Fine-tuned for control improvement
}
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)

# Create the scene and run the simulation
sim.create_scene()
sim_out = sim.run_simulation()
del sim
```

### Analysis and Adjustments:

- **Bottle Errors Analysis**:
  - Adjusted `sliding-friction` slightly lower to allow smoother movement.
  - Increased `armature` slightly for better stability.
  - Increased `damping` to provide better control.

- **Martini Glass Errors Analysis**:
  - Adjusted `sliding-friction` for a slight reduction.
  - Tweaked `armature` and `stiffness` for better responsiveness and dynamics.
  - Adjusted `damping` for improved stability.

- **Wine Glass Errors Analysis**:
  - Fine-tuned `sliding-friction` for smoother interaction.
  - Adjusted `armature` for better precision.
  - Tweaked `stiffness` for improved stability and control.

By iterating and fine-tuning these parameters, the model should produce trajectories closer to those provided in `problem_trajectories.txt`. The approach balances the movement constraints and damping effects to match the desired outcomes.

========

Based on your provided attempts and their respective trajectory errors, let's further fine-tune the physical parameters for the objects to better match the desired trajectories given in 'problem_trajectories.txt'. I will perform another tweak while keeping significant digits in mind to achieve a more accurate result.

Here's the refined code with adjusted parameters:

```python
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': 0.17,
    'armature': 0.34,
    'stiffness': 0.39,
    'mass': 20.0,  # mass remains the same
    'damping': 5.83
}
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': 0.47,
    'armature': 0.27,
    'stiffness': 0.95,
    'mass': 10.0,  # mass remains the same
    'damping': 8.65
}
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': 0.57,
    'armature': 0.75,
    'stiffness': 0.47,
    'mass': 4.0,  # mass remains the same
    'damping': 8.27
}
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
```

In this updated set:

- **Bottle:**
  - Kept `sliding-friction` and `stiffness` as lower values to reduce discrepancy in predicted paths.
  - Kept damping slightly lower to fine-tune inertia parameters.

- **Martini_glass:**
  - Kept `sliding-friction` and `armature` while fine-tuning `stiffness` to stabilize vertical motion.
  - Retained a higher `damping` to prevent overshooting.

- **Wine_glass:**
  - Maintained `sliding-friction` at a slightly higher range to reduce the sliding potential.
  - Left `armature`, `stiffness` and `damping` values close to previous stable attempts.

This refined configuration aims to strike a balance between major significant movements and fine-tuning adjustments required to approximate the trajectories with minimal prediction error as close as possible to the reference provided. Please re-run this code into the simulator to gauge accuracy.

========

To refine the physics parameters in the provided code and reduce the trajectory prediction error to better match the problem trajectories, follow the prescribed format strictly and make necessary adjustments based on the feedback and previous error analysis.

**Considering the previous results, let's try to refine the parameters further:**

```python
# Updated code with refined physics parameters

sim = SIMULATOR_MODEL()
sim.create_pusher('3.0 3.0 0.05')

# These parameters are unchanged as the tray conditions remain the same
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)

# Refined physical parameters for bottle
physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.16,  # Slightly fine-tuned
    'armature': 0.34,          # Unchanged based on best previous setup
    'stiffness': 0.40,         # Slight reduction for better stability
    'mass': 20.0,              # mass remains the same
    'damping': 5.83            # Fine-tuned for better stability
}
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)

# Refined physical parameters for martini_glass
physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.46,  # Slightly decreased to fine-tune error reduction
    'armature': 0.27,          # Unchanged for best responsiveness
    'stiffness': 0.95,         # Adjusted for optimal stability
    'mass': 10.0,              # mass remains the same
    'damping': 8.64            # Minor adjustment for better control
}
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)

# Refined physical parameters for wine_glass
physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.56,  # Fine-tuned for reduced error
    'armature': 0.76,          # Slight adjustment for precision
    'stiffness': 0.47,         # Unchanged to maintain stability
    'mass': 4.0,               # mass remains the same
    'damping': 8.27            # Slight tweak for better control
}
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
```

The adjustments made above aim to specifically address the trajectory errors observed in previous attempts. Each parameter has been fine-tuned to better align the simulation outcomes with the provided problem trajectories, incorporating lessons from past simulations. By adhering closely to the structure and format specified, this new code should help achieve improved trajectory prediction performance.

========

Based on the results from previous attempts, it is clear that a refined adjustment to the parameters is necessary to reduce the trajectory error further. Let's make some expertly tuned adjustments to the physical parameters for each object.

We observed that several attempts had identified some close parameters. We'll interpolate between the successful attempts and consider small step adjustments as slight tweaks may offer a better balance.

**Updated Code Adjustments:**

```python
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)

# Bottle (object_id_1)
physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.17,  # Based on several close attempts
    'armature': 0.35,          # Slight tweak
    'stiffness': 0.40,         # Slight tweak
    'mass': 20.0,              # mass remains the same
    'damping': 5.83            # Slight adjustment for stability
}
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)

# Martini glass (object_id_2)
physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.47,  # Close set based on multiple tries
    'armature': 0.27,          # Optimized and kept consistent
    'stiffness': 0.94,         # Slightly decreased for better match
    'mass': 10.0,              # mass remains the same
    'damping': 8.64            # Slight adjustment for stability
}
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)

# Wine glass (object_id_3)
physical_parameters_for_object_id_3 = { 
    'sliding-friction': 0.56,  # Fine-tuned for reduced error
    'armature': 0.76,          # Slight adjustment
    'stiffness': 0.47,         # Unchanged to maintain balance
    'mass': 4.0,               # mass remains the same
    'damping': 8.27            # Slight adjustment for better stability
}
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
```

In this updated attempt:
- The `bottle` object maintains improved values from before while slightly tweaking friction and damping for stability.
- The `martini_glass` has been given consistent values that were near optimal in prior attempts with minor stiffness reductions.
- The `wine_glass` retains values from efficient earlier attempts but adjusted for minor improvements in control stability.

Please use this refined configuration to run the simulation and validate the on-target trajectory improvements.