ZiMPedance

Code for ZiMPedance: Impedance-Aware ZMP Modeling and Control for Payload Carrying with Quadruped Robots (Giovanni B. Dessy, Lorenzo Amatucci, Claudio Semini, Victor Barasuol).

Overview

A quadruped carrying a payload through a passive spring-based arm: the arm's dynamics store and release energy during locomotion and move the ZMP. This repository contains the MuJoCo simulation of the paper and the controller it proposes:

• ZiMPedance MPC (mpc_params['type'] = 'zimpedance', the paper's ARMPC): an MPC on the single rigid body dynamics extended with the passive-arm joint states, their springs and dampers and the base-arm inertial coupling, with a ZMP constraint. It is written with acados and Pinocchio.
• Single-robot tasks on an Aliengo with a 3-DoF passive arm: locomotion on flat and rough terrain, disturbances on the arm's end effector, and end-effector tracking and reaching with the arm.
• Standalone PACC model: the two passive arms on fixed blocks, sharing a payload.
• Two-robot collaborative carrying: a leader and a follower that carry a payload between their arms; the follower is guided by its arm deflection. Both robots run the PACC collaborative MPC ('collaborative'), not ZiMPedance.
• Passive arm hardware: printable STLs of the arm and the Arduino sketch of its joint encoders (hardware/passive_arm).

The controller framework is derived from Quadruped-PyMPC and the simulation environment from gym-quadruped; both are reduced here to what this code uses.

Dependencies

• Linux (tested on Ubuntu 24.04, x86-64), conda or mamba, and a C compiler
• Python 3.12, MuJoCo 3.4.0, Pinocchio 4.0 (must be >= 4.0), casadi 3.7.2, liecasadi, gymnasium, numpy, scipy, matplotlib: see installation/environment.yml
• acados v0.4.0, as a git submodule, built by the setup script

Installation

git clone --recurse-submodules https://github.com/iit-DLSLab/ZiMPedance.git
cd ZiMPedance
bash installation/setup_env.sh          # --lock for the exact tested versions
conda activate zimpedance

The setup script creates the zimpedance conda environment, builds acados in quadruped_pympc/acados and sets PYTHONPATH, LD_LIBRARY_PATH and ACADOS_SOURCE_DIR when the environment is activated. Nothing is pip-installed. The first run of each controller and robot generates and compiles its acados solver (about 1 min); later runs reuse it.

How to run

Single robot, ZiMPedance MPC (simulation/zimpedance_sim.py):

python simulation/zimpedance_sim.py --task figure_eight_tracking
python simulation/zimpedance_sim.py --task locomotion --headless --export run.npz
python simulation/zimpedance_sim.py                    # interactive: arrow keys set the velocity command

Task	Robot	What it does
locomotion	leader	crawl forward, turn in place, backward, stop
rough_terrain	leader	crawl forward over tilted boxes up to 0.1 m
disturbance_rejection	leader	crawl under eight 30 N impulses on the end effector (EEF)
disturbance_sinusoidal	leader	crawl under a 15 N, 1 Hz force on the EEF
pull_release	leader	standing, the EEF is pulled sideways and released four times
y_tracking	follower	standing, lateral EEF sine, 0.1 m at 0.4 Hz (paper Fig. 6)
yz_reaching	follower	y-z EEF targets, held 2 s each
circular_tracking	follower	EEF circle in the y-z plane, radius 0.1 m
figure_eight_tracking	follower	EEF figure eight, drawn by the arm while the base stays nearly still
moving_target_reaching	follower	EEF follows a target moving at 0.05 m/s
spatial_reaching	follower	four fixed EEF targets, then a moving one
xy_reaching	follower	walks to put the EEF on x-y targets up to 0.6 m away

The leader has the arm at the rear, the follower at the front. The end-effector tasks use a soft arm (joint 1 nearly undamped) so the arm motion is visible. Presets, weights and arm impedance: simulation/zimpedance_tasks.py. Options: --duration S, --scene rough|stairs|ramp|..., --headless, --export run.npz.

Standalone PACC and two-robot carrying:

python simulation/pacc_standalone_sim.py                         # passive arms on blocks, shared payload
python simulation/collaborative_carrying_sim.py --scenario straight
    # scenarios: stand, straight, stop, turn, turn_right, turn_slow, turn_stop, showcase
    # --payload-preset light_2kg (default) | medium_5kg | heavy_7kg (experimental)

Regression checks (about 6 and 3.5 min on 16 cores; see simulation/validation/README.md):

python simulation/validation/regression_zimpedance.py
python simulation/validation/regression_collaborative.py

Repository layout

Path	Content
quadruped_pympc/config.py	controller and simulation parameters, ZiMPedance weight profiles
quadruped_pympc/controllers/zimpedance/	ZiMPedance MPC (acados OCP and Pinocchio model)
quadruped_pympc/controllers/collaborative/	PACC collaborative MPC (two-robot carrying)
quadruped_pympc/ (rest)	gait generator, foothold and swing control, passive-arm wrench estimate
gym_quadruped/	MuJoCo environments and robot models: aliengo_leader, aliengo_follower, aliengo_two_robots
simulation/	the simulations above, their task presets and the regression checks
hardware/passive_arm/	arm STLs (mm) and encoder sketch
installation/	conda environment and setup script

Citing this work

If you use this code, please cite:

@article{dessy2026zimpedance,
  author  = {Dessy, Giovanni B. and Amatucci, Lorenzo and Semini, Claudio and Barasuol, Victor},
  title   = {{ZiMPedance}: Impedance-Aware {ZMP} Modeling and Control for Payload Carrying with Quadruped Robots},
  journal = {IEEE Robotics and Automation Letters},
  year    = {2026}
}

License

BSD 3-Clause, see LICENSE.

Maintainer

This repository is maintained by Giovanni B. Dessy (giovanni.dessy@outlook.com).