This article takes a step to provide humanoid robots with adaptive morphology abilities. We present a systematic approach for enabling robotic covers to morph their shape, with an overall size fitting the anthropometric dimensions of a humanoid robot. More precisely, we present a cover concept consisting of two main components: a skeleton, which is a repetition of a basic element called node, and a soft membrane, which encloses the cover and deforms with its motion. This article focuses on the cover skeleton and addresses the challenging problems of node design, system modeling, motor positioning, and control design of the morphing system. The cover modeling focuses on kinematics, and a systematic approach for defining the system kinematic constraints is presented. Then, we apply genetic algorithms to find the motor locations so that the morphing cover is fully actuated. Finally, we present control algorithms that allow the cover to morph into a time-varying shape. The entire approach is validated by performing kinematic simulations with four different covers of square dimensions and having 3x3, 4x8, 8x8, and 20x20 nodes, respectively. For each cover, we apply the genetic algorithms to choose the motor locations and perform simulations for tracking a desired shape. The simulation results show that the presented approach ensures the covers to track a desired shape with good tracking performances.

The code in this repo requires MATLAB and the MATLAB's Curve Fitting Toolbox, make sure that you have them installed on your machine.

To quickly install those dependencies with mpm, you can run:

mpm install --release=R2024b --products=MATLAB Curve_Fitting_Toolbox

To install the software in this repo, follow the instructions in either the "Traditional Installation" or the "Pixi installation" section.

1. Clone the repository and mystica:

git clone https://github.com/ami-iit/paper_bergonti_2022_tro_kinematics-control-morphingcovers.git
git clone https://github.com/ami-iit/mystica.git --branch v2022.06.0

mystica is a matlab library to simulate the kinematics and dynamics of multibody systems.

2. Run in matlab the function install() stored in mystica:

install()

The function install() downloads mambaforge. mambaforge is a package manager that downloads and configures our dependencies in conda enviroment called mystica.

If you already have pixi installed in your machine, just run pixi run matlab from inside the repo:

cd paper_bergonti_2022_tro_kinematics-control-morphingcovers
pixi run matlab

This will install all required dependencies, and launch matlab with the dependencies added in the path.

To launch one of experiments of the paper, you can also just run:

cd paper_bergonti_2022_tro_kinematics-control-morphingcovers
pixi run sim1

where in place of sim1 you can also run sim2, sim3 or sim4 depending on the experiment you want to run.

This repository stores:

• the algorithm for evaluating an optimal motor positioning for structures with closed kinematic loops (see Sec.IV of the paper);
• the instantaneous controller that evaluates motors speed to make the cover skeleton moves toward the desired shape (see Sec.V of the paper);
• the scripts for reproducing the simulations described in Sec.VI of the paper.

Reproducing simulations results

1. If you have completed the installation procedure successfully, a file setup.m is generated in mystica\deps. You have to open Matlab and run the script setup.m to configure MATLABPATH.

2. Run one of the four scripts stored in this folder. For example, to reproduce the result of the first scenario you have to run:

cd paper_bergonti_2022_tro_kinematics-control-morphingcovers
cd scripts
run('sim1')

If you open the script, you can modify the config.simulation_with_noise parameter deciding whether to apply noise. Instead, the parameter config.run_only_controller allows you to choose if you want to run only the controller without evaluating a new motor placement.

#	mesh	script	pixi command	$t_{run}$*	result
1	3x3	sim1.m	pixi run sim1	30s
2	8x8	sim2.m	pixi run sim2	5min
3	20x20	sim3.m	pixi run sim3	2h
4	4x8	sim4.m	pixi run sim4	3min

* $t_{run}$ is the script running time evaluated with a PC with Intel Xeon Gold 6128 3.40GHz and RAM 128GB.

If you find the work useful, please consider citing:

@ARTICLE{9793615,
  author={Bergonti, Fabio and Nava, Gabriele and Fiorio, Luca and L’Erario, Giuseppe and Pucci, Daniele},
  journal={IEEE Transactions on Robotics},
  title={Modeling and Control of Morphing Covers for the Adaptive Morphology of Humanoid Robots},
  year={2022},
  volume={38},
  number={5},
  pages={3300-3313},
  doi={10.1109/TRO.2022.3170281}}

This repository is maintained by:

	@FabioBergonti