使用する数式


[1]$$\mathbf λ=-\mathbf K\begin{bmatrix}\mathbf x_{cog}\\ \mathbf h\end{bmatrix}+\mathbf k(\mathbf x_{ref},\mathbf h_{ref})\hspace{20mm}(1)$$
[2
]Capture Point(the only point where the CoM can come to rest)
$$\mathbf ξ=\mathbf x+\frac{1}{\omega}\dot{\mathbf x}$$
[3
]QP

\({min}_{/dot{\mathbf v}_d,\mathbf ρ}\;J_{\dot{\mathbf h}_d}+J_{\mathbf J}+J_{\mathbf ρ}+J_{\dot{\mathbf v}_d}\)
\({s.t.}\;\;\mathbf A\dot{\mathbf v}_d+\dot{\mathbf A}\mathbf v=\mathbf W_{\mathbf g}+\mathbf B_{COM}\mathbf ρ+\sum_i\mathbf W_{ext,i}\)
\(\mathbf ρ_{min}\leq\mathbf ρ\)
\(\dot{\mathbf v}_{min}\leq\dot{\mathbf v}_d\leq\dot{\mathbf v}_{max}\)
目的関数の項は次のように定義される.
Momentum Objective:   \(J_{\dot{\mathbf h}_d}=||\mathbf P_{\dot{\mathbf h}}(\mathbf A\dot{\mathbf v}_d-\mathbf b)||^2\)
Motion Objective:   \(J_{\mathbf J}=||\mathbf P_{\mathbf J}(\mathbf J\dot{\mathbf v}_d-\mathbf p||^2\)
Contact Force Cost:   \(J_{\mathbf ρ}=||\mathbf P_{\mathbf ρ}\mathbf ρ||^2\)
Joint Acceleration Cost:   \(J_{\dot{\mathbf v}_d}=||\mathbf P_{\dot{\mathbf v}_d}\dot{\mathbf v}_d||^2\)
[4]DCM, 重心軌跡計画
$$\dot{\mathbf p}_{DCM}(t)=\frac{1}{T}(\mathbf p_{DCM}(t)-\mathbf p_{VRP}(t))$$
$$\dot{\mathbf p}_G(t)=-\frac{1}{T}(\mathbf p_G(t)-\mathbf p_{DCM}(t))$$

 

【参考文献】
[1]https://arxiv.org/pdf/1410.7284.pdf
[2]http://homepages.laas.fr/soueres/Papiers/Koroibot/Ramos-2014c.pdf
[3]https://arxiv.org/pdf/1709.03660.pdf
[4]https://www.jstage.jst.go.jp/article/jrsj/36/2/36_36_122/_pdf/-char/ja
[5]