# Switching between Limit Cycles in a Model of Running Using Exponentially Stabilizing Discrete Control Lyapunov Function

arXiv: https://arxiv.org/abs/1807.02696 · HTML: https://mlsanity.com/paper/1807.02696/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2018.

## Built on by (most cited first, 1 of 1)

- [Hybrid Systems Neural Control with Region-of-Attraction Planner](https://mlsanity.com/paper/2303.10327/) (2023)

## Abstract (arXiv)

This paper considers the problem of switching between two periodic motions, also known as limit cycles, to create agile running motions. For each limit cycle, we use a control Lyapunov function to estimate the region of attraction at the apex of the flight phase. We switch controllers at the apex, only if the current state of the robot is within the region of attraction of the subsequent limit cycle. If the intersection between two limit cycles is the null set, then we construct additional limit cycles till we are able to achieve sufficient overlap of the region of attraction between sequential limit cycles. Additionally, we impose an exponential convergence condition on the control Lyapunov function that allows us to rapidly transition between limit cycles. Using the approach we demonstrate switching between 5 limit cycles in about 5 steps with the speed changing from 2 m/s to 5 m/s.