# Jerk Control of Floating Base Systems with Contact-Stable Parametrised Force Feedback

## TL;DR

This paper introduces a jerk-based control framework for floating base systems that incorporates contact stability constraints and force feedback, transforming constrained optimization into an unconstrained problem for smoother control.

## Contribution

It presents a novel jerk control architecture with a one-to-one contact stability manifold correspondence, enabling unconstrained optimization and improved force feedback integration.

## Key findings

- Successfully validated with simulations and experiments on iCub robot.
- Achieved contact-stable control with reduced discontinuities.
- Effectively incorporated FT sensor feedback into control loop.

## Abstract

Nonlinear controllers for floating base systems in contact with the environment are often framed as quadratic programming (QP) optimization problems. Common drawbacks of such QP based controllers are: the control input often experiences discontinuities; no force feedback from Force/Torque (FT) sensors installed on the robot is taken into account. This paper attempts to address these limitations using jerk based control architectures. The proposed controllers assume the rate-of-change of the joint torques as control input, and exploit the system position, velocity, accelerations, and contact wrenches as measurable quantities. The key ingredient of the presented approach is a one-to-one correspondence between free variables and an inner approximation of the manifold defined by the contact stability constraints. More precisely, the proposed correspondence covers completely the contact stability manifold except for the so-called friction cone, for which there exists a unique correspondence for more than 90% of its elements. The correspondence allows us to transform the underlying constrained optimisation problem into one that is unconstrained. Then, we propose a jerk control framework that exploits the proposed correspondence and uses FT measurements in the control loop. Furthermore, we present Lyapunov stable controllers for the system momentum in the jerk control framework. The approach is validated with simulations and experiments using the iCub humanoid robot.