add State-only Foot Placement Constraints

matheecs · Aug 25, 2021 · 60e5d1a · 60e5d1a
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diff --git a/README.md b/README.md
@@ -17,6 +17,7 @@
     - [算法](#算法)
     - [约束处理方法](#约束处理方法)
     - [实现细节](#实现细节)
+  - [State-only Foot Placement Constraints [TODO]](#state-only-foot-placement-constraints-todo)
   - [References](#references)
 
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@@ -453,6 +454,13 @@ void GaussNewtonDDP::runIteration(bool unreliableControllerIncrement) {
 }
 ```
 
+## State-only Foot Placement Constraints [TODO]
+
+<img src="https://render.githubusercontent.com/render/math?math=\mathbf{h}_{i}^{s w}(\mathbf{x}, t)=\mathbf{A}_{i} \cdot \mathbf{p}_{E_{i}}(\mathbf{x})+\mathbf{b}_{i}+s(t) \cdot \mathbf{1} \geq \mathbf{0}">
+
+> For each contact phase within the MPC horizon, the terrain segment is selected that is closest to the reference end-effector position determined by <img src="https://render.githubusercontent.com/render/math?math=\mathbf{x}_{ref}(t)">, evaluated at the middle of the stance phase.
+
+![](images/cbf_mpc.png)
 ## References
 
 - [Tutorial on OCS2 Toolbox](https://www.youtube.com/watch?v=RYmQN9GbFYg)

diff --git a/images/cbf_mpc.png b/images/cbf_mpc.png