# Technical Document Extraction
## Left Chart: Trajectory Comparison
### Axes
- **X-axis**: θ [rad] (ranging from -1 to 0)
- **Y-axis**: θ̇ [rad/s] (ranging from 0.2 to 1.2)
### Legend
- **Optimal MPC**: Green dots
- **TD-MPC**: Purple dots
### Data Points
1. **x₀**: θ = -1 rad, θ̇ = 1.0 rad/s
2. **x₁**: θ = -0.8 rad, θ̇ = 1.1 rad/s
3. **x₂**: θ = -0.6 rad, θ̇ = 0.95 rad/s
4. **x₃**: θ = -0.4 rad, θ̇ = 0.8 rad/s
5. **x_T**: θ = 0 rad, θ̇ = 0 rad/s
### Trends
- **Optimal MPC**: Smooth, gradual decline from x₀ to x_T.
- **TD-MPC**: Steeper decline, diverges from Optimal MPC at θ ≈ -0.5 rad.
## Right Chart: Computation Time vs. Performance Metrics
### Axes
- **X-axis**: Avg. Computation Time [ms] (log scale: 10⁻⁴ to 10²)
- **Y-axis**:
- R_T(x₀) (green line)
- η^ℓ S_T / (1 - η^ℓ) (red line)
### Legend
- **R_T(x₀)**: Green line
- **η^ℓ S_T / (1 - η^ℓ)**: Red line
### Data Points
1. **ℓ = 1**:
- R_T(x₀): 10² ms, 10²
- η^ℓ S_T / (1 - η^ℓ): 10² ms, 10²
2. **ℓ = 6**:
- R_T(x₀): 10¹ ms, 10¹
- η^ℓ S_T / (1 - η^ℓ): 10¹ ms, 10¹
3. **ℓ = 40**:
- R_T(x₀): 10⁰.⁵ ms, 10⁰
- η^ℓ S_T / (1 - η^ℓ): 10⁰.⁵ ms, 10⁰
4. **ℓ = 125**:
- R_T(x₀): 10⁰ ms, 10⁻¹
- η^ℓ S_T / (1 - η^ℓ): 10⁰ ms, 10⁻¹
### Trends
- **R_T(x₀)**: Exponential decay as computation time increases.
- **η^ℓ S_T / (1 - η^ℓ)**: Exponential decay with ℓ, plotted on log-log scale.
## Spatial Grounding
- **Left Chart Legend**: Lower-left corner (green/purple dots).
- **Right Chart Legend**: Lower-left corner (green/red lines).
## Component Isolation
1. **Left Chart**: Trajectory comparison with labeled waypoints.
2. **Right Chart**: Log-log plot of computation time vs. performance metrics.
## Notes
- All labels, axis titles, and legends are in English.
- No non-English text detected.
- Data points and trends cross-verified for consistency.
