Online Running-Gait Generation for Bipedal Robots with Smooth State Switching and Accurate Speed Tracking

. 2023 Mar 10;8(1):114. doi: 10.3390/biomimetics8010114

Algorithm 1 Iterative computation for target footholds

1:
Commanded translational speed: ${\dot{c}}_{c m d}^{x, y};$
2:
Using (5) and (6) to plan the vertical trajectory: $c_{j + 1}^{z}, {\ddot{c}}_{j + 1}^{z};$
3:
Given nominal ZMP trajectory of next step: $p_{n o m, j + 1}^{x, y};$
4:
With (13) and capturability constraints of CoM velocity ( ${\dot{c}}_{j + 1}^{x, y} (t_{0}) = {\dot{c}}_{j}^{x, y} (t_{f}), {\dot{c}}_{j + 1}^{x, y} (t_{f}) = {\dot{c}}_{c m d}^{x, y}$ ), get temporary horizontal CoM trajectory: $c_{t e m p, j + 1}^{x, y};$
5:
for $i \in \{x, y\}$ do
6:
$Δ c^{i} = c_{t e m p, j + 1}^{i} (t_{0}) - c_{j}^{i} (t_{f});$
7:
if $|Δ c^{i}| \leq t o l$ then
8:
$\begin{matrix} p_{t g t, j + 1}^{i} = p_{n o m, j + 1}^{i}; c_{t g t, j + 1}^{i} = c_{t e m p, j + 1}^{i}; \end{matrix}$
9:
else
10:
$i t e r \leftarrow 0;$
11:
$p_{t e m p, j + 1}^{i} = p_{n o m, j + 1}^{i};$
12:
while $|Δ c^{i}| > t o l$ do
13:
$p_{t e m p, j + 1}^{i} = p_{t e m p, j + 1}^{i} - Δ c^{i};$
14:
$i t e r \leftarrow i t e r + 1;$
15:
Repeat Line 4 $\to c_{t e m p, j + 1}^{i}$ ;
16:
$Δ c^{i} = c_{t e m p, j + 1}^{i} (t_{0}) - c_{j}^{i} (t_{f});$
17:
end while
18:
$\begin{matrix} p_{t g t, j + 1}^{i} = p_{t e m p, j + 1}^{i}; c_{t g t, j + 1}^{i} = c_{t e m p, j + 1}^{i}; \end{matrix}$
19:
end if
20:
end for