To modify the given example_code_1.py in order to achieve the trajectories given in problem_trajectories.txt, we need to adjust the physical parameters of the objects (bottle, martini_glass, and wine_glass) while keeping the physics of the tray with the ground unchanged. We'll adjust the parameters: sliding-friction, armature, stiffness, and damping, as required. 

Below is the Python code that corresponds to your requirement:

```python
# Modified example_code_1.py to produce the trajectories given in problem_trajectories.txt

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)

# Adjusted physical parameters for bottle to match the trajectory in problem_trajectories.txt
physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.2,
    'armature': 0.3,
    'stiffness': 0.4,
    'mass': 20.0,
    'damping': 6.0
}
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 to match the trajectory in problem_trajectories.txt
physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.5,
    'armature': 0.3,
    'stiffness': 0.9,
    'mass': 10.0,
    'damping': 8.0
}
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 to match the trajectory in problem_trajectories.txt
physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.5,
    'armature': 0.7,
    'stiffness': 0.5,
    'mass': 4.0,
    'damping': 7.5
}
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 Changes
1. **Bottle**:
    - Sliding-friction changed to 0.2
    - Armature changed to 0.3
    - Stiffness changed to 0.4
    - Damping changed to 6.0

2. **Martini_glass**:
    - Retained sliding-friction as 0.5 (no significant change required)
    - Armature changed to 0.3
    - Stiffness changed to 0.9
    - Damping changed to 8.0

3. **Wine_glass**:
    - Sliding-friction changed to 0.5
    - Armature changed to 0.7
    - Stiffness changed to 0.5
    - Damping changed to 7.5

These adjustments are made to make sure that we adhere to the constraint that physical parameters should not change significantly. The values are kept close to their original first significant digit. 

Ensure you run this script in the same simulator environment to get the required object trajectories as specified in `problem_trajectories.txt`.

========

To refine the physical parameters and reduce the trajectory error, we need to carefully adjust the sliding-friction, armature, stiffness, and damping values for each object. Utilizing the previously provided errors and understanding the impact of each parameter on the motion, I will iteratively refine the values.

Let's update the parameters and provide the refined code version:

```python
# refined_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)

# Refining parameters for bottle
physical_parameters_for_object_id_1 = {
    'sliding-friction': 0.15,
    'armature': 0.25,
    'stiffness': 0.35,
    'mass': 20.0,
    'damping': 5.9
}
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)

# Refining parameters for martini_glass
physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.48,
    'armature': 0.32,
    'stiffness': 0.85,
    'mass': 10.0,
    'damping': 8.2
}
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)

# Refining parameters for wine_glass
physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.52,
    'armature': 0.72,
    'stiffness': 0.55,
    'mass': 4.0,
    'damping': 7.8
}
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:
1. **Bottle**: Slightly decreased sliding-friction and armature, reduced damping slightly.
2. **Martini_glass**: Slightly adjusted sliding-friction, reduced armature and stiffness, and modified damping.
3. **Wine_glass**: Tweaked sliding-friction and armature, adjusted stiffness, and slightly increased damping.

These iterative refinements should bring the simulated trajectories closer to the given problem trajectories. Please run this version through the simulator to observe the errors and further fine-tune if necessary.

========

To further refine the simulation parameters for the objects so that their trajectories more closely match the target trajectories in 'problem_trajectories.txt', let's iterate once more on the physical parameters. We will make small adjustments to sliding friction, armature, stiffness, and damping values while adhering to the constraints of maintaining their first significant digit.

### Refined Parameters Based on Previous Errors:
- The tray parameters should not be changed as per instructions.
- Starting from the last set of parameters, we will make slight adjustments:

#### **Physical Parameters Adjustments:**
- For the bottle, we need to reduce its sliding friction slightly and tweak armature and damping for finer tuning.
- For the martini_glass, we may slightly increase damping and adjust the stiffness.
- For the wine_glass, considering the highest error, we'll lower sliding friction slightly, adjust armature, and make fine adjustments to damping and stiffness.

### Refined Physical Parameters:
```python
# example_code_3.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': 0.28,  # Fine-tuned
    'stiffness': 0.36,
    'mass': 20.0,
    'damping': 5.8  # Reduced a bit
}
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': 0.49,  # Small increase
    'armature': 0.33,  # Slight adjustment
    'stiffness': 0.88,  # Fine-tuned
    'mass': 10.0,
    'damping': 8.4  # Slightly increased
}
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': 0.51,  # Reduced to match better
    'armature': 0.71,  # Slight adjustment
    'stiffness': 0.54,  # Adjusted minimally
    'mass': 4.0,
    'damping': 7.7  # Fine-tuned to reduce error
}
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 iteration aims to refine the parameters just enough to reduce the trajectory errors while staying within the constraint of not changing their first significant digits. Please run this code in your simulation environment and check the resulting trajectory errors.

========

Let's refine the physical parameters further based on the previous errors to try and reduce the overall trajectory prediction error. The adjustments will be small and aimed to better match the given trajectories.

```python
# Updated code based on previous attempts:

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 based on previous results
    'armature': 0.27,  # Fine-tuned
    'stiffness': 0.38,  # Slight change
    'mass': 20.0,
    'damping': 5.85  # Small adjustment
}
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,  # Slightly decreased for finer tuning
    'armature': 0.31,  # Adjusted minimally
    'stiffness': 0.87,  # Slight adjustment
    'mass': 10.0,
    'damping': 8.35  # Fine-tuned
}
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': 0.53,  # Small adjustment
    'armature': 0.75,  # Fine-tuning
    'stiffness': 0.56,  # Slightly adjusted
    'mass': 4.0,
    'damping': 7.85  # Fine-tuned
}
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 version, adjustments are made with very fine precision to better mimic the desired trajectories. Each change is subtle, focusing on tuning the values based on the previous results to try and optimize the error more effectively.

========

To further refine our parameters and reduce the trajectory error, I will make some additional small adjustments to the sliding-friction, armature, stiffness, and damping values. 

Here's the adjusted code with refined physical 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': 0.18,  # Small increase
    'armature': 0.26,  # Fine-tuning
    'stiffness': 0.40,  # Slightly increased
    'mass': 20.0,
    'damping': 5.65  # Slight reduction for better accuracy
}

physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.46,  # Decreased slightly
    'armature': 0.34,  # Slight increase
    'stiffness': 0.89,  # Minor adjustment
    'mass': 10.0,
    'damping': 8.25  # Slight decrease
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.54,  # Increased a little
    'armature': 0.74,  # Minor adjustment
    'stiffness': 0.57,  # Increased slightly
    'mass': 4.0,
    'damping': 7.80  # Maintained for testing
}

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
```

The refinements focus on small, incremental changes to the parameters, aiming to reduce the overall trajectory error. Each adjustment was chosen to optimize the balance among the sliding-friction, armature, stiffness, and damping properties for each unique object.

Let's test these updated parameters and evaluate the corresponding errors.

========

Given the iterative approach with smaller adjustments in the parameters, we are gradually reducing the mismatch between the given trajectory data and the predicted motion trajectories. Here is another round of fine-tuning:

```python
physical_parameters_for_object_id_1 = {
    'sliding-friction': 0.17,  # Further small adjustment from attempt 4
    'armature': 0.26,          # Slight reduction
    'stiffness': 0.38,         # Returning slightly
    'mass': 20.0,
    'damping': 5.7             # Intermediate between previous values
}

physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.45,  # Slight reduction from attempt 5
    'armature': 0.33,          # Fine-tuning
    'stiffness': 0.88,         # Slight reduction
    'mass': 10.0,
    'damping': 8.2             # Slight reduction for better accuracy
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.53,  # Reverting back to nearest better value
    'armature': 0.73,          # Slight reduction
    'stiffness': 0.55,         # Adjustment to previous potentially better value
    'mass': 4.0,
    'damping': 7.75            # Slight reduction for better alignment
}
```

The changes are very subtle from previous attempts, emphasizing minor tweaks based on observed errors. This code should be run to test the new adjustments, which may lead to lower trajectory prediction errors and therefore more accurate reproduction of the provided trajectories in 'problem_trajectories.txt'.

========

To improve the model's accuracy to match the trajectories provided in `problem_trajectories.txt`, we need to refine the physical parameters for each object (bottle, martini_glass, and wine_glass). We will make incremental adjustments, trying to reduce the trajectory error by comparing against the provided simulation results. Here's another attempt based on the given errors and strategies that have been observed to reduce trajectory errors.

```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,  # Slightly increased
    'armature': 0.26,          # Slight reduction
    'stiffness': 0.37,         # Slightly adjusted
    'mass': 20.0,
    'damping': 5.75            # Fine-tuned between previous attempts
}
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,  # Slight adjustment
    'armature': 0.32,          # Reduction for better accuracy
    'stiffness': 0.89,         # Slightly increased
    'mass': 10.0,
    'damping': 8.3             # Fine-tuning
}
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': 0.52,  # Slightly reduced for accuracy
    'armature': 0.72,          # Minor reduction
    'stiffness': 0.54,         # Adjusted minimally
    'mass': 4.0,
    'damping': 7.78            # Fine-tuned
}
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
```

### Adjustments Summary:
- **Bottle**: Adjusted `sliding-friction` to 0.16, `armature` to 0.26, `stiffness` to 0.37, and `damping` to 5.75.
- **Martini Glass**: Adjusted `sliding-friction` to 0.46, `armature` to 0.32, `stiffness` to 0.89, and `damping` to 8.3.
- **Wine Glass**: Adjusted `sliding-friction` to 0.52, `armature` to 0.72, `stiffness` to 0.54, and `damping` to 7.78.

These adjustments are intended to minimize the errors observed in previous attempts while making sure they follow the specified guidelines of changing parameters only slightly.

========

To further refine the physical parameters and reduce the trajectory prediction error, let's adjust the parameters incrementally based on the trends observed in the previous attempts. We'll attempt to make minimal changes to improve alignment with the expected trajectories.

Here's my new attempt:

```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': 0.14,  # Slightly reduced
    'armature': 0.26,  # No change
    'stiffness': 0.35,  # Slightly adjusted
    'mass': 20.0,
    'damping': 5.5  # Slight reduction
}

physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.42,  # Slight reduction
    'armature': 0.32,  # No change
    'stiffness': 0.85,  # Minor reduction
    'mass': 10.0,
    'damping': 8.1  # Slight reduction
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.50,  # Slight reduction
    'armature': 0.70,  # Minor reduction
    'stiffness': 0.53,  # Slight reduction
    'mass': 4.0,
    'damping': 7.6  # Slight reduction
}

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 use the above code and run it in the simulator to check the new prediction errors. The adjustments were made focusing on patterns observed with previous errors to fine-tune physical parameters gradually.

========

To refine the parameters further and minimize the trajectory prediction error, we should analyze the trends from the prior attempts and base our adjustments on that data. The goal is to have the total trajectory error closer to the ones observed in the 'problem_trajectories.txt'. Additionally, since significant digits beyond the first one cannot be changed, fine-tuning within those constraints is crucial. Let's make another refinement:

```python
# File: 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 adjusted
    'armature': 0.27,  # Fine-tuned
    'stiffness': 0.37,  # Slightly increased from last try
    'mass': 20.0,
    'damping': 5.7  # No change for stability
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.46,  # Adjusted based on trends
    'armature': 0.34,  # Slight increase
    'stiffness': 0.88,  # Fine-tuned
    'mass': 10.0,
    'damping': 8.3  # Fine-tuning for better results
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.52,  # Small adjustment
    'armature': 0.72,  # No change
    'stiffness': 0.54,  # Slightly reduced
    'mass': 4.0,
    'damping': 7.8  # Slight increase
}

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
```

Here's the reasoning behind these adjustments:
1. For the `bottle` (`object_id_1`):
   - `sliding-friction`: An average between previous values to find balance.
   - `armature`: Small tweak for balance.
   - `stiffness`: Slightly adjusted upwards as observed in trends.
   - `damping`: Maintaining for now to observe effects of other changes.

2. For the `martini_glass` (`object_id_2`):
   - `sliding-friction`: Adjusted based on previous experiments.
   - `armature`: Slightly increased for better fit.
   - `stiffness`: Fine-tuning given previous results.
   - `damping`: Slightly adjusted for better alignment.

3. For the `wine_glass` (`object_id_3`):
   - `sliding-friction`: Reduced slightly.
   - `armature`: Keeping stable as it produced better results.
   - `stiffness`: Balanced reduction for better fit.
   - `damping`: Slight increase to fine-tune.

Re-run the simulation with this updated configuration to check the errors and adjust accordingly further if needed.

========

Let's attempt to refine the physical parameters further to reduce the trajectory prediction error. Here is the proposed code with adjusted parameters:

```python
# problem_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': 0.16,  # Slightly increased for stability
    'armature': 0.25,          # No change
    'stiffness': 0.36,         # Slightly reduced for better matching
    'mass': 20.0,
    'damping': 5.8             # Fine-tuned for better results
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.44,  # Slight adjustment
    'armature': 0.31,          # Slight reduction
    'stiffness': 0.87,         # Maintained from a better result
    'mass': 10.0,
    'damping': 8.2             # Fine-tuning for better accuracy
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.51,  # Slight adjustment
    'armature': 0.71,          # Fine-tuning for better results
    'stiffness': 0.56,         # Slightly increased for better matching
    'mass': 4.0,
    'damping': 7.72            # Slight increase for better matching 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)
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
```

By iteratively adjusting the parameters and maintaining the code structure strictly in line with the original example, we aim to reduce the trajectory prediction error further. The adjustments ensure that changes remain in the range of their first significant digit for better accuracy. This should help align the simulated trajectories more closely with the `problem_trajectories.txt` file.

========

To refine the physical parameters and minimize the trajectory error for each object, I'll make careful, incremental adjustments based on the previous attempts and errors provided. The goal is to steadily converge towards a smaller error by fine-tuning each parameter without drastic changes.

Let's refine our adjustments and rerun with the new 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': 0.16,  # Slight incremental adjustment
    'armature': 0.27,          # Fine-tuned slightly
    'stiffness': 0.36,         # Small adjustment
    'mass': 20.0,
    'damping': 5.72            # Fine tuning damping
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.45,  # Slight incremental adjustment
    'armature': 0.32,          # Fine-tuning armature
    'stiffness': 0.88,         # Small incremental adjustment
    'mass': 10.0,
    'damping': 8.22            # Small damping adjustment
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.522, # Fine-tuning friction to reduce error
    'armature': 0.715,         # Small incremental adjustment
    'stiffness': 0.557,        # Slightly fine-tuned stiffness
    'mass': 4.0,
    'damping': 7.75            # Fine tuning damping
}

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 code in your simulator and verify if the errors decrease. The strategy here is to make very slight, careful adjustments keeping in mind the previous error trends, aiming to fine-tune the parameters towards achieving a lower overall trajectory error.

========

Given the previous attempts and the provided feedback, it looks like some parameters for the objects need further fine-tuning to reduce the trajectory prediction error. Here's an updated attempt considering all previous errors and adjustments:

**Updated Attempt:**

```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': 0.15,  # Adjusted
    'armature': 0.27,          # Slightly increased
    'stiffness': 0.36,         # Fine-tuned
    'mass': 20.0,
    'damping': 5.70            # Slightly reduced for better matching
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.44,  # Adjusted
    'armature': 0.33,          # Slightly increased
    'stiffness': 0.87,         # Slightly decreased
    'mass': 10.0,
    'damping': 8.25            # Slightly increased
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.52,  # Adjusted
    'armature': 0.71,          # Slightly decreased
    'stiffness': 0.56,         # Slightly increased
    'mass': 4.0,
    'damping': 7.75            # Slightly increased for better damping 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 further refines the parameters based on the trajectory errors seen in previous attempts:

- The bottle's `sliding-friction` and `damping` have been adjusted to target the trajectory errors more accurately.
- The martini glass parameters, including `armature`, were slightly increased while `sliding-friction` and `stiffness` were decreased for better control over damping.
- The wine glass parameters were adjusted to balance sliding friction and armature while ensuring damping values control drift and alignment.

Please execute this attempt in the simulator to verify the results and refine further if necessary.

========

Sure, using the existing information and trends from past attempts, I will provide a refinement to the physical parameters for an optimal trajectory alignment:

```python
# new_code.py

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

# Physical parameters for the tray remain untouched
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)

# Optimized physical parameters for the bottle
physical_parameters_for_object_id_1 = {
    'sliding-friction': 0.16,  # Slight incremental adjustment
    'armature': 0.27,          # Fine-tuning for accuracy
    'stiffness': 0.36,         # Small adjustment
    'mass': 20.0,
    'damping': 5.72            # Damping slightly increased for better alignment
}

# Optimized physical parameters for the martini_glass
physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.45,  # Slightly increased based on previous attempts
    'armature': 0.33,          # Fine-tuned for better alignment
    'stiffness': 0.88,         # Slightly adjusted
    'mass': 10.0,
    'damping': 8.25            # Adjusted for better trajectory prediction
}

# Optimized physical parameters for the wine_glass
physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.52,  # Small incremental adjustment
    'armature': 0.72,          # Fine-tuned for optimal trajectory
    'stiffness': 0.56,         # Minor adjustment for better result
    'mass': 4.0,
    'damping': 7.75            # Fine adjustment for accurate prediction
}

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
```

========

Based on the trajectories given in 'problem_trajectories.txt' and the previous parameter adjustments, we need to fine-tune the parameters again to achieve more accurate results. Let's make subtle adjustments while considering the error trends in previous attempts.

Here is the refined code:
```python
# Code to generate the new simulation

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 parameters (object_id=1)
physical_parameters_for_object_id_1 = {
    'sliding-friction': 0.16,  # Adjusted to slightly higher
    'armature': 0.25,          # Slightly reduced from the last attempt
    'stiffness': 0.37,         # Minor increase for better stability
    'mass': 20.0,
    'damping': 5.8             # Slightly increased for finer control
}

# Martini glass parameters (object_id=2)
physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.46,  # Increased subtly for more friction control
    'armature': 0.32,          # Retained for consistency
    'stiffness': 0.86,         # Adjusted slightly up from the last attempt
    'mass': 10.0,
    'damping': 8.4             # Improved slightly to reduce overshooting
}

# Wine glass parameters (object_id=3)
physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.53,  # Fine-tuned for more matched friction
    'armature': 0.70,          # Retained to maintain better control
    'stiffness': 0.55,         # Slightly adjusted for better accuracy
    'mass': 4.0,
    'damping': 7.7             # Adjusted to maintain damping consistency
}

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

# The trajectories are not included in this code section as per the instructions.
```

These adjusted physical parameters should help in minimizing the trajectory prediction error. Make sure to run the code in your simulation environment to validate the results and further fine-tune if necessary.

========

Below is an updated version of the code example, with refined physical parameters based on your information, with the goal of reducing the trajectory error even further. 

```python
# example_code_1.py

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

# Keeping the same parameters
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)

# Parameters tuned for bottle
physical_parameters_for_object_id_1 = { 
             'sliding-friction': 0.14,  # Reduced
             'armature': 0.24,          # Reduced
             'stiffness': 0.34,         # Reduced slightly
             'mass': 20.0,
             'damping': 5.65            # Adjusted slightly down
         }

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)

# Parameters tuned for martini_glass
physical_parameters_for_object_id_2 = { 
             'sliding-friction': 0.43,  # Adjusted down
             'armature': 0.30,          # Adjusted down
             'stiffness': 0.84,         # Adjusted more
             'mass': 10.0,
             'damping': 8.15            # Slight reduction
         }

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)

# Parameters tuned for wine_glass
physical_parameters_for_object_id_3 = {
             'sliding-friction': 0.51,  # Adjusted back to slightly lower
             'armature': 0.71,          # Slight reduction
             'stiffness': 0.54,         # Readjusted back
             'mass': 4.0,
             'damping': 7.74            # Slightly fine-tuned
         }

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)

# Generating the scene and running the simulation
sim.create_scene()
sim_out = sim.run_simulation()
del sim
```

You should run this updated code example to check if the trajectory prediction error is minimized further. The parameters have been refined considering your previous attempts and making slight, carefully considered changes to maximize the match with the given trajectory data in 'problem_trajectories.txt'.

========

Based on the previous error analysis, I'll make small adjustments to the parameters for each object to refine the approximation of the trajectories. Based on past attempts, we'll carefully adjust the sliding-friction, armature, stiffness, and damping to optimize the trajectory similarity.

```python
# Code to set up and run the simulation as described, with parameters adjusted

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

# Physical parameters for the tray
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 the bottle
physical_parameters_for_object_id_1 = {
    'sliding-friction': 0.16,  # Slightly increased for stability
    'armature': 0.25,          # Fine-tuning based on previous best results
    'stiffness': 0.36,         # Adjusted for better matching from best previous attempts
    'mass': 20.0,
    'damping': 5.75            # Fine-tuned based on best previous attempts
}
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 the martini_glass
physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.44,  # Adjusted based on the most accurate past attempts
    'armature': 0.32,          # Fine-tuned based on analysis
    'stiffness': 0.87,         # Based on best attempt
    'mass': 10.0,
    'damping': 8.2             # Kept around most accurate previous predictions
}
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 the wine_glass
physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.52,  # Based on results with lowest error previously
    'armature': 0.71,          # Fine-tuned from previous values
    'stiffness': 0.55,         # Small adjustment for better alignment
    'mass': 4.0,
    'damping': 7.75            # Fine adjustment for better accuracy
}
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
```
The parameters have been adjusted based on careful consideration of trends from previous attempts. The tuning has been focused on improving the friction, stiffness, armature, and damping parameters incrementally to reduce the overall error in trajectory prediction. This approach uses incremental changes to previous best parameters and avoids large shifts to ensure stability and convergence towards the desired trajectory.

========

### Updated Python Code with Refined Physical Parameters

Based on the previous attempts and analysis, here are the further refined physical parameters designed to reduce the prediction errors:

```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': 0.14,  # Reduced
    'armature': 0.26,          # Increased for better predictions
    'stiffness': 0.35,         # Fine-tuned
    'mass': 20.0,
    'damping': 5.72            # Fine-tuning for damping
}

physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.45,  # Remaining closer to previous best
    'armature': 0.34,          # Adjusted up slightly from previous
    'stiffness': 0.86,         # Slightly reduced from the last best
    'mass': 10.0,
    'damping': 8.3             # Fine-tuned
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.52,  # Reverting back to previous effective value
    'armature': 0.72,          # Fine-tuned
    'stiffness': 0.56,         # Slightly adjusted for better result
    'mass': 4.0,
    'damping': 7.75            # Fine-tuning based on previous calculations
}

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
```

In this refined version, we have:
1. **Adjusted sliding frictions** based on how they impacted the objects in previous tests.
2. **Fine-tuned armature values** which regulate the constraints between rotational motion versus the applied torque for better alignment.
3. **Tweaked stiffness values** to provide better control over the restitution properties.
4. **Modified damping** as this adjusts how the energy is dissipated in the system, crucial for ensuring the object stays stable.

These adjustments target reducing the overall trajectory errors and narrowing down the improvement process towards more precise alignment with the problem trajectories.

========

Certainly! Let's refine the physical parameters a bit more for each object to further reduce the error. Based on previous attempts, we'll make slight adjustments within the constraints of the first significant digit to progress towards a better match with the trajectories in 'problem_trajectories.txt'.

Here is the modified Python code with the refined physical parameters:

```python
# example_code_1.py

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

# Tray physical parameters remain the same as provided in the example
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 adjusted for stability
    'armature': 0.26,          # Slightly increased
    'stiffness': 0.36,         # Adjusted slightly
    'mass': 20.0,
    'damping': 5.75            # Fine-tuned damping value
}

# Refined physical parameters for martini_glass
physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.45,  # Adjusted based on previous analysis
    'armature': 0.33,          # Fine-tuned armature
    'stiffness': 0.87,         # Slightly adjusted stiffness
    'mass': 10.0,
    'damping': 8.25            # Fine adjustment in damping
}

# Refined physical parameters for wine_glass
physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.52,  # Based on effective values
    'armature': 0.72,          # Fine-tuned armature
    'stiffness': 0.56,         # Slightly adjusted stiffness
    'mass': 4.0,
    'damping': 7.75            # Fine-tuning based on previous good values
}

# Create objects in the scene using these refined parameters
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)

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

This code adjusts the physical parameters for each object slightly based on the observed previous attempts to better match the trajectories provided. Specifically, we have made minor adjustments to the `sliding-friction`, `armature`, `stiffness`, and `damping` values to create a closer approximation of the desired trajectories. The changes aim to improve the overall alignment and minimize the trajectory prediction error.

Run this refined code in your simulator and observe the result. If necessary, you can continue making small adjustments to each parameter to achieve even closer alignment.

========

To produce better results based on your previous attempts, it's essential to make incremental, calculated adjustments to the physical parameters. Here is another attempt with minor, but potentially impactful, adjustments:

```python
# New attempt to generate closer trajectories.

physical_parameters_for_object_id_1 = {
    'sliding-friction': 0.15,  # Further adjust based on previous trends
    'armature': 0.27,          # Maintain stability and alignment
    'stiffness': 0.37,         # Slightly increased for better control
    'mass': 20.0,
    'damping': 5.74            # Fine-tuning damping for stability
}

physical_parameters_for_object_id_2 = {
    'sliding-friction': 0.44,  # Slightly reduced based on previous best
    'armature': 0.34,          # Retained the value close to best attempt
    'stiffness': 0.86,         # Slightly decreased for better match
    'mass': 10.0,
    'damping': 8.23            # Fine adjustment in damping
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.51,  # Reverting to slightly lower value
    'armature': 0.71,          # Fine-tuning armature
    'stiffness': 0.56,         # Slightly adjusted for better alignment
    'mass': 4.0,
    'damping': 7.74            # Fine-tuned damping value
}
```
In this attempt:
- I've adjusted the sliding-friction, stiffness, and damping values based on the trends seen in the previous attempts. 
- The changes are carefully chosen to provide better stability and control, aiming to reduce the trajectory error.

Run the simulation with the new parameters and check the trajectory errors. If needed, further minor adjustments can be made in subsequent attempts.

========

Given the previous attempts and their results, it appears that we need a refined tuning approach. It seems the adjustments have not resulted in a significant improvement. So, I'll take the parameters from attempt 14 and make slight, nuanced adjustments to better align with the desired trajectory. 

### 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)

physical_parameters_for_object_id_1 = { 
    'sliding-friction': 0.15,  # Slightly adjusted for further refinement
    'armature': 0.26,          # Maintaining good result value
    'stiffness': 0.36,         # Small increment
    'mass': 20.0,
    'damping': 5.74            # Slightly adjusted damping
}

physical_parameters_for_object_id_2 = { 
    'sliding-friction': 0.44,  # Reduced slightly
    'armature': 0.33,          # Slightly reduced
    'stiffness': 0.87,         # Adjusted up minimally
    'mass': 10.0,
    'damping': 8.24            # Adjusted slightly for better control
}

physical_parameters_for_object_id_3 = {
    'sliding-friction': 0.51,  # Adjusted slightly down
    'armature': 0.71,          # Small adjustment
    'stiffness': 0.55,         # Restored previous best slight change
    'mass': 4.0,
    'damping': 7.74            # Fine-tuning damping value
}

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
```

### Explanation of Adjustments:
- **bottle**:
  - **Sliding Friction**: Slightly adjusted for refinement at 0.15.
  - **Armature**: 0.26 based on previous best attempt.
  - **Stiffness**: Small increment to 0.36.
  - **Damping**: Slightly adjusted down to 5.74.
- **martini_glass**:
  - **Sliding Friction**: Small reduction to 0.44.
  - **Armature**: Reduced to 0.33.
  - **Stiffness**: Increased minimally to 0.87.
  - **Damping**: Fine-tuning slightly down to 8.24.
- **wine_glass**:
  - **Sliding Friction**: Small decrement to 0.51.
  - **Armature**: Adjusted down to 0.71.
  - **Stiffness**: Restored previous effective value 0.55.
  - **Damping**: Fine-tuned to 7.74.

Let's test these adjustments and see if they reduce the trajectory error effectively. Hopefully, these fine-tuned step changes incrementally enhance the trajectory predictions.

========

Certainly! I'll attempt some fine-tuning based on the error in previous attempts:

### Attempt #17:

physical_parameters_for_object_id_1:
* Sliding Friction: 0.15
* Armature: 0.26
* Stiffness: 0.35
* Mass: 20.0
* Damping: 5.73

physical_parameters_for_object_id_2:
* Sliding Friction: 0.44
* Armature: 0.33
* Stiffness: 0.87
* Mass: 10.0
* Damping: 8.23

physical_parameters_for_object_id_3:
* Sliding Friction: 0.51
* Armature: 0.71
* Stiffness: 0.55
* Mass: 4.0
* Damping: 7.73

Here is the code incorporating the above parameters:

```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': 0.15,
             'armature': 0.26,
             'stiffness': 0.35,
             'mass': 20.0,
             'damping': 5.73
         }
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': 0.44,
             'armature': 0.33,
             'stiffness': 0.87,
             'mass': 10.0,
             'damping': 8.23
         }
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': 0.51,
             'armature': 0.71,
             'stiffness': 0.55,
             'mass': 4.0,
             'damping': 7.73
         }
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
```

By refining the parameters further, especially by paying close attention to significant but minor adjustments, we aim to reduce the error margin. Run the provided simulation to see if these fine-tuned parameters reduce the trajectory prediction error.