# Analytic Model for Quadruped Locomotion Task-Space Planning

## TL;DR

This paper introduces a simplified analytical model for quadruped locomotion planning that reduces computational complexity by modeling the system as two bipeds connected at their centers of mass, enabling potential real-time trajectory generation.

## Contribution

The novel contribution is extending an algebraic bipedal model to quadrupeds by leveraging gravitational attractor topology for efficient task-space planning.

## Key findings

- Generated trajectories align with previous studies
- Model reduces computational cost for trajectory planning
- Potential for real-time complex action planning in unstructured environments

## Abstract

Despite the extensive presence of the legged locomotion in animals, it is extremely challenging to be reproduced with robots. Legged locomotion is an dynamic task which benefits from a planning that takes advantage of the gravitational pull on the system. However, the computational cost of such optimization rapidly increases with the complexity of kinematic structures, rendering impossible real-time deployment in unstructured environments. This paper proposes a simplified method that can generate desired centre of mass and feet trajectory for quadrupeds. The model describes a quadruped as two bipeds connected via their centres of mass, and it is based on the extension of an algebraic bipedal model that uses the topology of the gravitational attractor to describe bipedal locomotion strategies. The results show that the model generates trajectories that agrees with previous studies. The model will be deployed in the future as seed solution for whole-body trajectory optimization in the attempt to reduce the computational cost and obtain real-time planning of complex action in challenging environments.