# Feasible Region: an Actuation-Aware Extension of the Support Region

## TL;DR

This paper introduces the Feasible Region, an actuation-aware extension of the support region for legged robots, ensuring static stability and torque feasibility for locomotion on rough terrains.

## Contribution

It defines a new feasible region that accounts for actuation limits, improving foothold and trajectory planning for stable legged locomotion.

## Key findings

- Efficient iterative algorithm for feasible region computation
- Successful robot experiments negotiating obstacles with payload
- Enhanced stability and torque feasibility in locomotion planning

## Abstract

In legged locomotion the projection of the robot Center of Mass (CoM) being inside the convex hull of the contact points is a commonly accepted sufficient condition to achieve static balancing. However, some of these configurations cannot be realized because the joint torques required to sustain them would be above their limits (actuation limits). In this manuscript we rule out such configurations and define the Feasible Region, a revisited support region that guarantees both global static stability in the sense of tipover and slippage avoidance and of existence of a set of joint-torques that are able to sustain the robot body weight. We show that the feasible region can be employed for the selection of feasible footholds and CoM trajectories to achieve static locomotion on rough terrains, also in presence of load intensive tasks. Key results of our approach include the efficiency in the computation of the feasible region thanks to an Iterative Projection algorithm. This allowed us to carry out successful experiments on the HyQ robot, that was able to negotiate obstacles of moderate dimensions while carrying an extra 10 kg payload.