We address the challenge of effectively controlling the locomotion of legged robots by incorporating precise frequency and phase characteristics, which is often ignored in locomotion policies that do not account for the periodic nature of walking. We propose a hierarchical architecture that integrates a low-level phase tracker, oscillators, and a high-level phase modulator. This controller allows quadruped robots to walk in a natural manner that is synchronized with external musical rhythms. Our method generates diverse gaits across different frequencies and achieves real-time synchronization with music in the physical world. This research establishes a foundational framework for enabling real-time execution of accurate rhythmic motions in legged robots. The video and code are available at https://music-walker.github.io/.

In this paper, we propose an efficient Multi-Circle detector which follows the fixed search order. The method makes use of horizontal and vertical search to realize circle detection, which is named as HVCD. First, this method computes edge areas in a given image. The edge areas could be divided into some regions by means of region growing. Each of regions could be efficiently searched to achieve not only one-pixel wide edges but edge segments as well. Next, the candidate circles can be extracted from every edge segment. Finally, the circle candidates could be validated with the help of Helmholtz principle. Experimental results demonstrate that HVCD could effectively detect circles on synthetic and natural images on the one hand; on the other hand, HVCD here could solve the weakness in the process of circle Hough transform implementation and EDcircles implementation.