State propagation from uncertain control input

Robotics Asked by Astghik Hakobyan on October 3, 2021

Consider a nonlinear system $x(k+1)=f(x(k),u(k))$, where $x(k)inmathbb{R}^{n}$ is the state, $u(k)inmathbb{R}^m$ is the control input. Here $u(k)$ is normally distributed RV with mean $mu_u(k)$ and variance $Sigma_u(k)$. I want to find the distribution of $x(k)$ starting from some deterministic $x(0)$ for some horizon $K$.
Then can the ordinary EKF update equation be used for the prediction in the below way?

Sigma_x(k+1)&=nabla_x f(mu_x(k),mu_u(k))Sigma_x(k)nabla_x f(mu_x(k),mu_u(k))^top+nabla_u f(mu_x(k),mu_u(k))Sigma_u(k)nabla_u f(mu_x(k),mu_u(k))^top

One Answer

Yes. This approach is commonly used when IMUs are present because they measure the rate of state change with some uncertainty.

Answered by holmeski on October 3, 2021

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