Verifying Safe Transitions between Dynamic Motion Primitives on Legged Robots

TL;DR

This paper introduces a formal framework for verifying safe transitions between dynamic motion primitives on legged robots, enabling complex autonomous behaviors through a graph-based approach.

Contribution

It formalizes a process to determine safe transition conditions for dynamic primitives, integrating them into a graph structure for planning and verification.

Findings

Successfully implemented transitions between standing, walking, and jumping on a quadrupedal robot.

Demonstrated the use of a motion primitive graph for planning safe behavior sequences.

Validated the framework's effectiveness in real-world robotic experiments.

Abstract

Functional autonomous systems often realize complex tasks by utilizing state machines comprised of discrete primitive behaviors and transitions between these behaviors. This architecture has been widely studied in the context of quasi-static and dynamics-independent systems. However, applications of this concept to dynamical systems are relatively sparse, despite extensive research on individual dynamic primitive behaviors, which we refer to as "motion primitives." This paper formalizes a process to determine dynamic-state aware conditions for transitions between motion primitives in the context of safety. The result is framed as a "motion primitive graph" that can be traversed by standard graph search and planning algorithms to realize functional autonomy. To demonstrate this framework, dynamic motion primitives -- including standing up, walking, and jumping -- and the transitions between these behaviors are experimentally realized on a quadrupedal robot.