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fix README.md
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Signed-off-by: Takayuki Murooka <takayuki5168@gmail.com>
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takayuki5168 committed Dec 20, 2022
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30 changes: 15 additions & 15 deletions planning/obstacle_cruise_planner/README.md
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Expand Up @@ -175,7 +175,7 @@ This includes not only cruising a front vehicle, but also reacting a cut-in and
The safe distance is calculated dynamically based on the Responsibility-Sensitive Safety (RSS) by the following equation.

$$
d_rss = v_{ego} t_{idling} + \frac{1}{2} a_{ego} t_{idling}^2 + \frac{v_{ego}^2}{2 a_{ego}} - \frac{v_{obstacle}^2}{2 a_{obstacle}},
d_{rss} = v_{ego} t_{idling} + \frac{1}{2} a_{ego} t_{idling}^2 + \frac{v_{ego}^2}{2 a_{ego}} - \frac{v_{obstacle}^2}{2 a_{obstacle}},
$$

assuming that $d_rss$ is the calculated safe distance, $t_{idling}$ is the idling time for the ego to detect the front vehicle's deceleration, $v_{ego}$ is the ego's current velocity, $v_{obstacle}$ is the front obstacle's current velocity, $a_{ego}$ is the ego's acceleration, and $a_{obstacle}$ is the obstacle's acceleration.
Expand All @@ -190,22 +190,22 @@ These values are parameterized as follows. Other common values such as ego's min
The detailed formulation is as follows.

$$
d_error = d - d_rss
d_normalized = lpf(d_error / d_obstacle)
d_quad_normalized = sign(d_normalized) *d_normalized* d_normalized
v_pid = pid(d_quad_normalized)
v_additional = v_pid > 0 ? v_pid * w_acc : v_pid
v_target = v_target = max(v_ego + v_additional, v_min_cruise)
d_{error} = d - d_{rss} \\
d_{normalized} = lpf(d_{error} / d_{obstacle}) \\
d_{quad, normalized} = sign(d_{normalized}) *d_{normalized}*d_{normalized} \\
v_{pid} = pid(d_{quad, normalized}) \\
v_{add} = v_{pid} > 0 ? v_{pid}* w_{acc} : v_{pid} \\
v_{target} = max(v_{ego} + v_{add}, v_{min, cruise})
$$

| Variable | Description |
| -------------- | --------------------------------------- |
| `d` | actual distane to obstacle |
| `d_rss` | ideal distance to obstacle based on RSS |
| `lpf(val)` | apply low-pass filter to `val` |
| `v_min_cruise` | `min_cruise_target_vel` |
| `w_acc` | `output_ratio_during_accel` |
| `pid(val)` | apply pid to `val` |
| Variable | Description |
| ----------------- | --------------------------------------- |
| `d` | actual distane to obstacle |
| `d_{rss}` | ideal distance to obstacle based on RSS |
| `v_{min, cruise}` | `min_cruise_target_vel` |
| `w_{acc}` | `output_ratio_during_accel` |
| `lpf(val)` | apply low-pass filter to `val` |
| `pid(val)` | apply pid to `val` |

## Implementation

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