# A closed-form solution for real-time ZMP gait generation and feedback stabilization

### Citation:

R. Tedrake, S. Kuindersma, R. Deits, and K. Miura, “A closed-form solution for real-time ZMP gait generation and feedback stabilization,” in IEEE-RAS International Conference on Humanoid Robots, Seoul, Korea, 2015.
 explicit-zmp.pdf 1.81 MB

### Abstract:

Here we present a closed-form solution to the continuous time-varying linear quadratic regulator (LQR) problem for the zero-moment point (ZMP) tracking controller. This generalizes previous analytical solutions for gait generation by allowing soft" tracking (with a quadratic cost) of the desired ZMP, and by providing the feedback gains for the resulting time-varying optimal controller. This enables extremely fast computation, with the number of operations linear in the number of spline segments representing the desired ZMP. Results are presented using the Atlas humanoid robot where dynamic walking is achieved by recomputing the optimal controller online.

Last updated on 05/27/2016