diff --git a/README.md b/README.md index 9f205c8..32c5f2d 100644 --- a/README.md +++ b/README.md @@ -22,9 +22,9 @@ The library implements two controllers: The controllers have the following form -| Proportional Controller | Proportional Derivative Controller | -|:-----------------------:|:-------------:| -| ![img-f6214bd2482f678b](https://user-images.githubusercontent.com/16744101/89174620-77c5b100-d586-11ea-88f7-318343c13b0f.png) | ![img-40c85670ed9bec65](https://user-images.githubusercontent.com/16744101/89174628-7b593800-d586-11ea-8219-d3ea2cb70901.png) | +| Proportional Controller | Proportional Derivative Controller | +|:---------------------------------------------------------------:|:-------------------------------------------------------------------------------------------------------------:| +| $\psi = \psi^d + k_p \text{Log}\left(X^d \circ X^{-1}\right)$ | $\dot{\psi} = \dot{\psi}^d + k_d \left(\psi^d - \psi \right) + k_p \text{Log}\left(X^d \circ X^{-1}\right)$ | where `X` and `Xᵈ` are elements of a Lie group. `∘` is the group operator. `ψ` represents an element in the Lie algebra of the Lie group whose coordinates are expressed in `ℝⁿ`.