# Distributed Feedback Controllers for Stable Cooperative Locomotion of Quadrupedal Robots: A Virtual Constraint Approach

## TL;DR

This paper develops distributed feedback control algorithms enabling stable cooperative locomotion of quadrupedal robots with holonomic constraints, using virtual constraints and nonlinear control, demonstrated through extensive numerical simulations.

## Contribution

It introduces a novel approach to distributed control of cooperative legged robots using virtual constraints and quadratic programming, addressing complex hybrid dynamical models.

## Key findings

- Successful stabilization of cooperative locomotion in simulations
- Development of optimal distributed feedback controllers
- Handling complex hybrid dynamical models with high-dimensional states

## Abstract

This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. The paper then generates modified and local virtual constraints for each agent that allow stable collaborative locomotion. Optimal distributed feedback controllers, based on nonlinear control and quadratic programming, are developed to impose the local virtual constraints. To demonstrate the power of the analytical foundation, an extensive numerical simulation for cooperative locomotion of two quadrupedal robots with robotic manipulators is presented. The numerical complex hybrid model has 64 continuous-time domains, 192 discrete-time transitions, 96 state variables, and 36 control inputs.