├── .gitignore ├── CONTRIBUTING.md ├── LICENSE.txt ├── README.md ├── controllers ├── impedance_6dof.py └── impedance_hyq_leg.py ├── data ├── js_data_jointimp.npy ├── js_data_taskimp.npy ├── js_terms.npy ├── ts_data_jointimp.npy └── ts_data_taskimp.npy ├── docs └── view.png ├── figures ├── angles_visualization.eps ├── angles_visualization.svg ├── ellipse_2d.eps ├── ellipse_2d.svg ├── jointspace_terms.eps ├── systems_1st_x_2nd.eps ├── systems_1st_x_2nd.svg ├── systems_K_x_KD.eps ├── systems_K_x_KD.svg ├── task_x_joint.eps └── task_x_joint.svg ├── matlab ├── ParametricCurveKDM.mlx └── README.md ├── parametric_analysis └── transforms_function.py └── plots ├── jointspace_terms.py ├── parametric3d.py └── subplots_figures.py /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | wheels/ 23 | share/python-wheels/ 24 | *.egg-info/ 25 | .installed.cfg 26 | *.egg 27 | MANIFEST 28 | 29 | # PyInstaller 30 | # Usually these files are written by a python script from a template 31 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 32 | *.manifest 33 | *.spec 34 | 35 | # Installer logs 36 | pip-log.txt 37 | pip-delete-this-directory.txt 38 | 39 | # Unit test / coverage reports 40 | htmlcov/ 41 | .tox/ 42 | .nox/ 43 | .coverage 44 | .coverage.* 45 | .cache 46 | nosetests.xml 47 | coverage.xml 48 | *.cover 49 | *.py,cover 50 | .hypothesis/ 51 | .pytest_cache/ 52 | cover/ 53 | 54 | # Translations 55 | *.mo 56 | *.pot 57 | 58 | # Django stuff: 59 | *.log 60 | local_settings.py 61 | db.sqlite3 62 | db.sqlite3-journal 63 | 64 | # Flask stuff: 65 | instance/ 66 | .webassets-cache 67 | 68 | # Scrapy stuff: 69 | .scrapy 70 | 71 | # Sphinx documentation 72 | docs/_build/ 73 | 74 | # PyBuilder 75 | .pybuilder/ 76 | target/ 77 | 78 | # Jupyter Notebook 79 | .ipynb_checkpoints 80 | 81 | # IPython 82 | profile_default/ 83 | ipython_config.py 84 | 85 | # pyenv 86 | # For a library or package, you might want to ignore these files since the code is 87 | # intended to run in multiple environments; otherwise, check them in: 88 | # .python-version 89 | 90 | # pipenv 91 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. 92 | # However, in case of collaboration, if having platform-specific dependencies or dependencies 93 | # having no cross-platform support, pipenv may install dependencies that don't work, or not 94 | # install all needed dependencies. 95 | #Pipfile.lock 96 | 97 | # poetry 98 | # Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control. 99 | # This is especially recommended for binary packages to ensure reproducibility, and is more 100 | # commonly ignored for libraries. 101 | # https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control 102 | #poetry.lock 103 | 104 | # pdm 105 | # Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control. 106 | #pdm.lock 107 | # pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it 108 | # in version control. 109 | # https://pdm.fming.dev/#use-with-ide 110 | .pdm.toml 111 | 112 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm 113 | __pypackages__/ 114 | 115 | # Celery stuff 116 | celerybeat-schedule 117 | celerybeat.pid 118 | 119 | # SageMath parsed files 120 | *.sage.py 121 | 122 | # Environments 123 | .env 124 | .venv 125 | env/ 126 | venv/ 127 | ENV/ 128 | env.bak/ 129 | venv.bak/ 130 | 131 | # Spyder project settings 132 | .spyderproject 133 | .spyproject 134 | 135 | # Rope project settings 136 | .ropeproject 137 | 138 | # mkdocs documentation 139 | /site 140 | 141 | # mypy 142 | .mypy_cache/ 143 | .dmypy.json 144 | dmypy.json 145 | 146 | # Pyre type checker 147 | .pyre/ 148 | 149 | # pytype static type analyzer 150 | .pytype/ 151 | 152 | # Cython debug symbols 153 | cython_debug/ 154 | 155 | # PyCharm 156 | # JetBrains specific template is maintained in a separate JetBrains.gitignore that can 157 | # be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore 158 | # and can be added to the global gitignore or merged into this file. For a more nuclear 159 | # option (not recommended) you can uncomment the following to ignore the entire idea folder. 160 | #.idea/ 161 | -------------------------------------------------------------------------------- /CONTRIBUTING.md: -------------------------------------------------------------------------------- 1 | # Contributing Guidelines 2 | Thank you for your interest in contributing to `impedance_control_benchmark`. 3 | Whether it's a bug report, new feature, correction, or additional 4 | documentation, we greatly value feedback and contributions from our community. 5 | 6 | Please read through this document before submitting any issues or pull requests 7 | to ensure we have all the necessary information to effectively respond to your 8 | bug report or contribution. 9 | 10 | ## Reporting Bugs/Feature Requests 11 | We welcome you to use the GitHub issue tracker to report bugs or suggest features. 12 | 13 | When filing an issue, please check [existing open][issues], or 14 | [recently closed][closed-issues], issues to make sure somebody else hasn't already 15 | reported the issue. Please try to include as much information as you can. Details 16 | like these are incredibly useful: 17 | 18 | * A reproducible test case or series of steps 19 | * The version of our code being used 20 | * Any modifications you've made relevant to the bug 21 | * Anything unusual about your environment or deployment 22 | 23 | ## Contributing via Pull Requests 24 | Contributions via pull requests are much appreciated. 25 | Before sending us a pull request, please ensure that: 26 | 27 | 1. Limited scope. Your PR should do one thing or one set of things. 28 | Avoid adding “random fixes” to PRs. Put those on separate PRs. 29 | 2. Give your PR a descriptive title. Add a short summary, if required. 30 | 3. Don’t be afraid to request reviews from maintainers. 31 | 32 | To send us a pull request, please: 33 | 34 | 1. Fork the repository. 35 | 2. Modify the source; please focus on the specific change you are contributing. 36 | If you also reformat all the code, it will be hard for us to focus on your change. 37 | 3. Commit to your fork using clear commit messages. 38 | 4. Send a pull request, answering any default questions in the pull request interface. 39 | 5. Pay attention to any automated CI failures reported in the pull request, 40 | and stay involved in the conversation. 41 | 42 | GitHub provides additional documentation on [forking a repository](https://help.github.com/articles/fork-a-repo/) 43 | and [creating a pull request](https://help.github.com/articles/creating-a-pull-request/). 44 | 45 | ## Finding contributions to work on 46 | Looking at the existing issues is a great way to find something to contribute on. 47 | As this project, by default, uses the default GitHub issue labels 48 | (enhancement/bug/duplicate/help wanted/invalid/question/wontfix), 49 | looking at any ['help wanted'][help-wanted] issues is a great place to start. 50 | 51 | ## Licensing 52 | Any contribution that you make to this repository will be under the GNU General Public License v3.0, as dictated by that [license]: 53 | 54 | ~~~ 55 | Impedance Control Benchmark 56 | Copyright (C) 2024, leggedrobotics-usp 57 | 58 | This program is free software: you can redistribute it and/or 59 | modify it under the terms of the GNU General Public License 3.0, 60 | or later version. 61 | 62 | This program is distributed in the hope that it will be useful, 63 | but WITHOUT ANY WARRANTY; without even the implied warranty of 64 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 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But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Impedance Control Benchmark 2 | Welcome to the Impedance Control Benchmark project. This project is dedicated to characterizing the impedance control method in robotics. 3 | 4 | 5 | [impedance_control_demo.webm](https://github.com/leggedrobotics-usp/impedance_control_benchmark/assets/44267124/6fbf650b-2feb-4efe-84b0-c8472888b0c4) 6 | 7 | 8 | 9 | The primary focus is on proposing a Python-based toolset that relies on the Pinocchio rigid body dynamics library (Python wrappers), Numpy, and Matplotlib. 10 | The aim is to increase the reachability using this programming language without losing the theoretical background. 11 | 12 | ## Installation and Dependencies 13 | 14 | The source code was developed on Ubuntu 22.04 with: 15 | 16 | 1. Python 3.10 17 | 2. [Pinocchio](https://stack-of-tasks.github.io/pinocchio/download.html#Install_1) 2.6.20 18 | 3. Matplotlib 3.6.2 19 | 4. Numpy 1.23.5 20 | 21 | Versions are recommended, but not strictly. 22 | Once installed these dependencies, clone the repo: 23 | ```sh 24 | git clone git@github.com:leggedrobotics-usp/impedance_control_benchmark.git 25 | ``` 26 | This is it! 27 | 28 | ## Usage 29 | 30 | The simulation setup was design to rely on the `MeshcatVisualizer` running 31 | on a web browser. Once the simulation starts a new window on your browser will 32 | display the robot arm and peform the movement according to the [simulation script](./controllers/impedance_6dof.py). 33 | 34 | Browser window url: `http://127.0.0.1:7000/static/` 35 | 36 | Run the simulation on interactive mode for better experience: 37 | 38 | ```sh 39 | python3 -i controllers/impedance_6dof.py 40 | ``` 41 | 42 | Simulation logs are stored in the [data](./data/) directory. Graphs using these logs can be seen on [plots](./plots/). 43 | Please consider this directory struct for your usage and development. Data files are here for exemplification only. 44 | **Do not open PR with data/log files.** 45 | 46 | ## Contributing 47 | 48 | - Fork the repo 49 | - 50 | - Check out a new branch and name it regarding your changes: 51 | - ````bash 52 | git checkout -b 53 | ```` 54 | - Commit your changes with relevant and proper messages; 55 | 56 | - Push to your fork branch; 57 | 58 | - Open a pull request (PR)! 59 | 60 | See [CONTRIBUTING](./CONTRIBUTING.md) for extended guidelines. 61 | 62 | ## License 63 | 64 | GNU GPLv3 65 | 66 | Permissions of this strong copyleft license are conditioned on making available the complete source code of licensed works and modifications, which include larger works using a licensed work, under the same license. 67 | Copyright and license notices must be preserved. Contributors provide an express grant of patent rights. 68 | 69 | ## Funding 70 | 71 | The source code and associated publications were developed with the support from the São Paulo Research Foundation (FAPESP), grant numbers 2018/15472-9, and 2021/09244-6. 72 | -------------------------------------------------------------------------------- /controllers/impedance_6dof.py: -------------------------------------------------------------------------------- 1 | # Impedance Control Benchmark 2 | # Copyright (C) 2024, leggedrobotics-usp 3 | # Leonardo F. dos Santos, Cícero L. A. Zanette, and Elisa G. Vergamini 4 | # 5 | # This program is free software: you can redistribute it and/or 6 | # modify it under the terms of the GNU General Public License 3.0, 7 | # or later version. 8 | # 9 | # This program is distributed in the hope that it will be useful, 10 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | # GNU General Public License for more details. 13 | 14 | import pinocchio as pin 15 | import numpy as np 16 | import time as tm 17 | import math 18 | from math import pi 19 | import matplotlib.pyplot as plt 20 | from pinocchio.visualize import MeshcatVisualizer 21 | import example_robot_data 22 | 23 | 24 | controller = 4 # Choose the impedance controller 25 | plotting = False # dismiss plot if false 26 | savefile = False # dismiss log save if false 27 | open_viewer = ( 28 | False # false if the viewer tab is already open (http://127.0.0.1:7000/static/) 29 | ) 30 | 31 | robot = example_robot_data.load("ur5") 32 | viz = MeshcatVisualizer() 33 | 34 | robot.setVisualizer(viz) 35 | robot.initViewer(open=open_viewer) 36 | robot.loadViewerModel() 37 | NQ, NV = robot.model.nq, robot.model.nv 38 | end_effector = robot.model.getFrameId("ee_link") 39 | 40 | q = np.array([0.00, -1.00, 1.2, -(pi + 0.2), -pi / 2, 0]) 41 | dq = np.zeros(robot.model.nv) 42 | ddq = np.zeros(robot.model.nv) 43 | tau = np.zeros(robot.model.nq) 44 | 45 | sim_dt = 0.010 # [s] simulation time step 46 | 47 | # Cartesian Impedance Control 48 | # Rotational Impedance (Roll, Pitch, Yaw): 49 | Ree_des = pin.rpy.rpyToMatrix(0, 0, 0) 50 | 51 | if controller == 2: 52 | sim_dt = 0.001 # [s] 53 | Kd = np.diag([1000, 7000, 7000, 200, 200, 200]) # Stiffness 54 | wn = np.diag([250, 50, 50, 30, 30, 30]) # natural freq. 55 | Md = Kd @ np.linalg.inv(wn @ wn.T) # M = K/w² 56 | Md_inv = np.linalg.inv(Md) 57 | # Damping design, D = 2 * sqrt(K*M) * zeta: 58 | zeta = 1.0 59 | Dd = 2 * np.sqrt(Kd @ Md) * zeta # Damping 60 | if controller == 3 or controller == 4: # 1st order impedance 61 | Kd = np.diag([900, 2500, 2500, 150, 150, 188]) # Stiffnes 62 | Dd = np.diag([60, 100, 100, 0.6, 0.6, 0.8]) # Damping 63 | if controller == 1 or controller == 5: 64 | q_des = q 65 | dq_des = np.zeros(robot.model.nv) 66 | ddq_des = np.zeros(robot.model.nv) 67 | 68 | # Simulation time parameters 69 | sim_duration = 4.00 # [s] 70 | sim_steps = int(sim_duration / sim_dt) 71 | 72 | # Initiate the x_des according to the q0 73 | pin.forwardKinematics(robot.model, robot.data, q) 74 | x_desired = robot.framePlacement(q, end_effector).translation 75 | v_desired = np.zeros(6) 76 | a_desired = np.zeros(6) 77 | 78 | # Singularity Avoidance Potential 79 | Vm, Vm_last = 0, 0 80 | dVm = np.zeros(NV) 81 | k_sap = 1.00 82 | m_dyn0 = 8.58e-2 # experimental threshold 83 | 84 | singularity_avd = False 85 | dynamic_ref = False 86 | 87 | # Disturbance 88 | disturbance_t = 0.01 89 | ur5_payload = 5.00 # [Kg] 90 | fe_amp = 9.80665 * ur5_payload 91 | fe_angf = 3.00 # [Hz] 92 | tau_ext = np.zeros(NQ) 93 | force_ext = np.array([-fe_amp, 0, 0, 0, 0, 0]) 94 | 95 | delta_t = [] 96 | JTpinv = np.zeros((3, NQ)) # 97 | 98 | # Logging 99 | log_fee = [] # force_ext logging data 100 | log_xee = [] # ee pos error logging data 101 | log_vee = [] # ee vel error logging data 102 | log_aee = [] # ee acc error logging data 103 | log_time = [] # time logging data 104 | # Log JS states 105 | log_torque = [] 106 | log_joints = [] 107 | 108 | tau_id_full_j1 = [] 109 | tau_id_full_j3 = [] 110 | 111 | tau_id_part_j1 = [] 112 | tau_id_part_j3 = [] 113 | 114 | tau_nle_j1 = [] 115 | tau_nle_j3 = [] 116 | 117 | viz.display(q) 118 | input( 119 | "Wait the visualizer loading on the browser window or reload it if already open.\n" 120 | + "Then, press any key here to start." 121 | ) 122 | try: 123 | print(f"Simulation started, Controller {controller}. Press CTRL+C to stop.") 124 | tic = tm.time() 125 | for k in range(sim_steps): 126 | dt = sim_dt 127 | sim_time = k * dt 128 | 129 | ## Compute Terms ## 130 | # Compute: FK | crba | nle | Jacobians | CoM | K+U Energies 131 | pin.computeAllTerms(robot.model, robot.data, q, dq) 132 | M = robot.mass(q) # get the Inertia Matrix 133 | h = robot.nle(q, dq) # get Nonlinear Effects (C+g) 134 | g = robot.gravity(q) # get Gravitational vector 135 | 136 | # Get the end-effector Jacobian 137 | J = pin.computeFrameJacobian( 138 | robot.model, robot.data, q, end_effector, pin.ReferenceFrame.LOCAL_WORLD_ALIGNED 139 | ) 140 | 141 | # End-effector Jacobian derivative (dJ/dt) 142 | dJ = pin.frameJacobianTimeVariation( 143 | robot.model, robot.data, q, dq, end_effector, pin.ReferenceFrame.LOCAL_WORLD_ALIGNED 144 | ) 145 | 146 | # Get ee kinematic data: 147 | pin.updateFramePlacement(robot.model, robot.data, end_effector) 148 | x = robot.data.oMf[end_effector].translation # 3x1 149 | v = J @ dq 150 | ddx = dJ @ dq + J @ ddq 151 | 152 | Ree = robot.data.oMf[end_effector].rotation 153 | rpy = pin.rpy.matrixToRpy( 154 | robot.data.oMf[end_effector].rotation 155 | ) # useful for orientation check 156 | 157 | if singularity_avd: 158 | dVm = np.zeros(NV) 159 | # Singularity Avoidance Potential: 160 | m_dyn = math.sqrt(np.linalg.det(J @ J.T)) # manipulability measure 161 | if m_dyn < m_dyn0: 162 | Vm = k_sap * (m_dyn - m_dyn0) ** 2 163 | for k in range(NV): 164 | if dq[k] > 1e-6: 165 | dVm[k] = (Vm - Vm_last) / (dq[k] * sim_dt) 166 | else: 167 | dVm[k] = (1.0 - 1e-6) * dVm[k] 168 | else: 169 | Vm = 0 170 | Vm_last = Vm 171 | 172 | if dynamic_ref: 173 | ref_freq = 0.3 174 | ref_ampl = 0.10 175 | mov_ee_angle = 2 * pi * ref_freq * sim_time 176 | x_desired[1] = ref_ampl * math.cos(mov_ee_angle) + 0.1091 177 | x_desired[2] = ref_ampl * math.sin(mov_ee_angle) + 0.5414 178 | v_desired[1] = -(2 * pi * ref_freq) * ref_ampl * math.sin(mov_ee_angle) 179 | v_desired[2] = (2 * pi * ref_freq) * ref_ampl * math.cos(mov_ee_angle) 180 | a_desired[1] = ( 181 | -((2 * pi * ref_freq) ** 2) * ref_ampl * math.cos(mov_ee_angle) 182 | ) 183 | a_desired[2] = ( 184 | -((2 * pi * ref_freq) ** 2) * ref_ampl * math.sin(mov_ee_angle) 185 | ) 186 | 187 | # Disturbance: 188 | if sim_time > disturbance_t: 189 | force_ext[0] = -fe_amp * math.sin(fe_angf * sim_time) 190 | tau_ext = J.T @ force_ext 191 | 192 | ## Control ## 193 | x_err = np.concatenate([x_desired - x, pin.rpy.matrixToRpy(Ree_des @ Ree.T)]) 194 | v_err = v_desired - v 195 | 196 | if controller == 0: # No controller 197 | tau = np.zeros(NQ) + h 198 | 199 | if controller == 1: 200 | # [T. Boaventura, 2012]: Joint Space PD 201 | Kp = 100 * np.eye(NQ) 202 | Kd = 20 * np.eye(NQ) 203 | joint_impedance = Kp.dot(q_des - q) + Kd.dot(dq_des - dq) 204 | tau_id_part_j1.append(joint_impedance[0]) 205 | tau_id_part_j3.append(joint_impedance[2]) 206 | joint_impedance = M @ joint_impedance 207 | tau_id_full_j1.append(joint_impedance[0]) 208 | tau_id_full_j3.append(joint_impedance[2]) 209 | tau = M @ ddq_des + h + joint_impedance 210 | 211 | if controller == 2: 212 | # [Ott,2008]: Classical Impedance Controler Eq. 3.14 213 | Ji = np.linalg.inv(J) 214 | impedance_force = Kd.dot(x_err) + Dd.dot(v_err) 215 | IR = M @ Md_inv # Inertial Ratio 216 | interaction_port = (J.T @ IR) @ ( 217 | impedance_force + force_ext 218 | ) - J.T @ force_ext 219 | inverse_dyn = M @ J @ a_desired + (h - g - M @ Ji @ dJ) @ Ji @ v_desired 220 | tau = inverse_dyn + interaction_port 221 | 222 | if controller == 3: 223 | # [Ott,2008]: Classical Impedance Controler (No Inertia) Eq. 3.18 224 | Ji = np.linalg.inv(J) 225 | impedance_force = Kd.dot(x_err) + Dd.dot(v_err) 226 | interaction_port = J.T @ impedance_force 227 | inverse_dyn = M @ J @ a_desired + (h - g - M @ Ji @ dJ) @ Ji @ v_desired 228 | tau = inverse_dyn + interaction_port 229 | 230 | if controller == 4: 231 | # [Ott,2008]: Classical Impedance Controler (No Inertia), and a_d = v_d = 0 232 | impedance_force = Kd.dot(x_err) + Dd.dot(v_err) 233 | tau = J.T @ impedance_force 234 | 235 | if controller == 5: 236 | # Joint Space impedance (Tutorial): 237 | Kq = np.diag([1000, 1000, 1000, 500, 500, 200]) 238 | wq = np.eye(6) * 250 239 | Mq = Kq @ np.linalg.inv(wq @ wq.T) 240 | Dq = 2 * np.sqrt(Kq @ Mq) # zeta = 1 241 | tau_impedance = ( 242 | Kq.dot(q_des - q) + Dq.dot(dq_des - dq) + Mq.dot(ddq_des - ddq) 243 | ) 244 | tau = tau_impedance 245 | 246 | ## Simulate Dynamics ## 247 | # Forward Dynamics (Articulated-Body Algorithm): 248 | ddq = pin.aba(robot.model, robot.data, q, dq, tau + g + tau_ext + dVm) 249 | # Integration: 250 | dq = dq + dt * ddq 251 | q = pin.integrate(robot.model, q, dt * dq) 252 | 253 | viz.display(q) 254 | 255 | ## Logging ## 256 | log_time.append(sim_time) 257 | log_fee.append(-force_ext[0]) 258 | log_xee.append(x_desired[0] - x[0]) 259 | log_vee.append(v_desired[0] - v[0]) 260 | log_aee.append(a_desired[0] - ddx[0]) 261 | 262 | log_joints.append(q) 263 | log_torque.append(tau) 264 | 265 | tau_nle_j1.append(g[0] + h[0]) 266 | tau_nle_j3.append(g[2] + h[2]) 267 | 268 | ellapsed_time = tm.time() - tic 269 | print(f"\nSimulation ended. ({ellapsed_time:.2f} s)\n") 270 | 271 | except KeyboardInterrupt: 272 | exit 273 | 274 | if plotting: 275 | plt.figure() 276 | plt.plot(log_xee[2:], log_fee[2:]) 277 | plt.grid() 278 | # figure wont close running in interactive mode 279 | plt.show(block=False) 280 | 281 | ax = plt.figure().add_subplot(projection="3d") 282 | ax.plot(log_xee[2:], log_vee[2:], log_fee[2:]) 283 | plt.show(block=(not open_viewer)) 284 | 285 | if savefile: 286 | np.save("data/ts_data", np.array([log_time, log_xee, log_vee, log_fee, log_aee]).T) 287 | time = np.array([log_time]).T 288 | joints = np.array(log_joints) 289 | torque = np.array(log_torque) 290 | js_log = np.hstack((time, joints, torque)) 291 | np.save("data/js_data", js_log) 292 | if controller == 1: 293 | np.save( 294 | "data/js_terms", 295 | np.array( 296 | [ 297 | log_time, 298 | tau_nle_j1, 299 | tau_id_part_j1, 300 | tau_id_full_j1, 301 | tau_nle_j3, 302 | tau_id_part_j3, 303 | tau_id_full_j3, 304 | ] 305 | ).T, 306 | ) 307 | -------------------------------------------------------------------------------- /controllers/impedance_hyq_leg.py: -------------------------------------------------------------------------------- 1 | # Impedance Control Benchmark 2 | # Copyright (C) 2024, leggedrobotics-usp 3 | # Leonardo F. dos Santos, Cícero L. A. Zanette, and Elisa G. Vergamini 4 | # 5 | # This program is free software: you can redistribute it and/or 6 | # modify it under the terms of the GNU General Public License 3.0, 7 | # or later version. 8 | # 9 | # This program is distributed in the hope that it will be useful, 10 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | # GNU General Public License for more details. 13 | 14 | import pinocchio as pin 15 | import numpy as np 16 | import time as tm 17 | import math 18 | from math import pi 19 | import matplotlib.pyplot as plt 20 | from pinocchio.visualize import MeshcatVisualizer 21 | import example_robot_data 22 | 23 | 24 | controller = 0 # Choose the impedance controller 25 | open_viewer = ( 26 | False # false if the viewer tab is already open (http://127.0.0.1:7000/static/) 27 | ) 28 | 29 | robot = example_robot_data.load("hyq") 30 | viz = MeshcatVisualizer() 31 | 32 | robot.setVisualizer(viz) 33 | robot.initViewer(open=open_viewer) 34 | robot.loadViewerModel() 35 | NQ, NV = robot.model.nq, robot.model.nv 36 | # foot frames (left/right, front/hind): lf_foot, rf_foot, lh_foot, rh_foot 37 | end_effector = robot.model.getFrameId("lf_foot") 38 | 39 | # q(0,1,2) -> trunk translations 40 | # q(3,4,5,6) -> trunk rotations (quat ?) 41 | # q(7,8,9) -> left front leg 42 | # q(10,11,12) -> left hind leg 43 | # q(13,14,15) -> right front leg 44 | # q(16,17,18) -> rigth hind leg 45 | 46 | q = np.zeros(NQ) 47 | q[2] = 0.577 # trunk height (z) 48 | q[7] = -0.15 49 | q[8] = 1.0 50 | q[9] = -2.0 51 | 52 | q[10] = -0.15 53 | q[11] = -0.8 54 | q[12] = 1.6 55 | 56 | q[13] = -0.15 57 | q[14] = 0.8 58 | q[15] = -1.6 59 | 60 | q[16] = -0.15 61 | q[17] = -0.8 62 | q[18] = 1.6 63 | 64 | q0 = q 65 | 66 | dq = np.zeros(NV) 67 | ddq = np.zeros(NV) 68 | tau = np.zeros(NV) 69 | 70 | sim_dt = 0.010 # [s] simulation time step 71 | 72 | # Cartesian Impedance Control 73 | # Rotational Impedance (Roll, Pitch, Yaw): 74 | Ree_des = pin.rpy.rpyToMatrix(0, 0, 0) 75 | 76 | if controller == 2: 77 | sim_dt = 0.001 # [s] 78 | Kd = np.diag([1000, 7000, 7000, 200, 200, 200]) # Stiffness 79 | wn = np.diag([250, 50, 50, 30, 30, 30]) # natural freq. 80 | Md = Kd @ np.linalg.inv(wn @ wn.T) # M = K/w² 81 | Md_inv = np.linalg.inv(Md) 82 | # Damping design, D = 2 * sqrt(K*M) * zeta: 83 | zeta = 1.0 84 | Dd = 2 * np.sqrt(Kd @ Md) * zeta # Damping 85 | if controller == 3 or controller == 4: # 1st order impedance 86 | Kd = np.diag([900, 2500, 2500, 150, 150, 188]) # Stiffnes 87 | Dd = np.diag([60, 100, 100, 0.6, 0.6, 0.8]) # Damping 88 | if controller == 1 or controller == 5: 89 | q_des = q 90 | dq_des = np.zeros(robot.model.nv) 91 | ddq_des = np.zeros(robot.model.nv) 92 | 93 | # Initiate the x_des according to the q0 94 | pin.forwardKinematics(robot.model, robot.data, q) 95 | x_desired = robot.framePlacement(q, end_effector).translation # 3x1 96 | v_desired = np.zeros(3) 97 | 98 | # Disturbance 99 | disturbance_t = 0.02 100 | fe_amp = 20 101 | fe_angf = math.pi # [rad/s] 102 | tau_ext = np.zeros(NV) 103 | force_ext = np.array([0, 0, 0, 0, 0, 0]) 104 | 105 | # Simulation time parameters 106 | sim_duration = 4.0 + disturbance_t # [s] 107 | sim_steps = int(sim_duration / sim_dt) 108 | 109 | # Joint space controller gain matrices 110 | Kp_q = np.eye(9) * 188 111 | Kd_q = np.eye(9) * 2.7 112 | 113 | # Cartesian impedance controller gain matrices 114 | Kd = np.diag([250, 250, 250]) # Stiffnes 115 | Dd = np.diag([10.0, 10.0, 10.0]) # Damping 116 | 117 | delta_t = [] 118 | 119 | viz.display(q) 120 | input( 121 | "Wait the visualizer loading on the browser window or reload it if already open.\n" 122 | + "Then, press any key here to start." 123 | ) 124 | try: 125 | print(f"Simulation started, Controller {controller}. Press CTRL+C to stop.") 126 | tic = tm.time() 127 | for k in range(sim_steps): 128 | dt = sim_dt 129 | sim_time = k * dt 130 | 131 | ## Compute Terms ## 132 | # Compute: FK | crba | nle | Jacobians | CoM | K+U Energies 133 | pin.computeAllTerms(robot.model, robot.data, q, dq) 134 | M = robot.mass(q) # get the Inertia Matrix 135 | h = robot.nle(q, dq) # get Nonlinear Effects (C+g) 136 | g = robot.gravity(q) # get Gravitational vector 137 | 138 | # Get the end-effector Jacobian 139 | J = pin.computeFrameJacobian( 140 | robot.model, robot.data, q, end_effector, pin.ReferenceFrame.LOCAL_WORLD_ALIGNED 141 | ) 142 | 143 | # End-effector Jacobian derivative (dJ/dt) 144 | dJ = pin.frameJacobianTimeVariation( 145 | robot.model, robot.data, q, dq, end_effector, pin.ReferenceFrame.LOCAL_WORLD_ALIGNED 146 | ) 147 | 148 | # Get ee kinematic data: 149 | pin.updateFramePlacement(robot.model, robot.data, end_effector) 150 | x = robot.data.oMf[end_effector].translation # 3x1 151 | v = J @ dq 152 | 153 | # Disturbance: 154 | if sim_time > disturbance_t: 155 | force_ext[2] = fe_amp * math.sin(fe_angf * sim_time) 156 | #force_ext[2] = -20 157 | tau_ext = J.T @ force_ext 158 | 159 | # joint space controller on the other legs 160 | tau_js = Kp_q.dot(q0[10:] - q[10:]) + Kd_q.dot(np.zeros(9,) - dq[9:]) 161 | tau = np.concatenate([np.zeros(9,), tau_js]) 162 | 163 | # [Ott,2008]: Classical Impedance Controler (No Inertia), and a_d = v_d = 0 164 | x_err = x_desired - x 165 | v_err = v_desired - v[:3] 166 | impedance_force = Kd.dot(x_err) + Dd.dot(v_err) 167 | tau[6:9] = J[:3,6:9].T @ impedance_force 168 | 169 | #Kd = np.diag([40, 40, 40]) 170 | #Dd = np.diag([0.1, 0.1, 0.1]) 171 | #tau[6:9] = Kd.dot(q0[7:10] - q[7:10]) + Dd.dot(-dq[7:10]) 172 | 173 | ## Restrict the dynamic simulation to one leg only (left front) 174 | tau_ext[0:6] = np.zeros(6,) 175 | tau_ext[9:] = np.zeros(9,) 176 | 177 | ## Simulate Dynamics ## 178 | # Forward Dynamics (Articulated-Body Algorithm): 179 | ddq = pin.aba(robot.model, robot.data, q, dq, tau + g + tau_ext) 180 | # Integration: 181 | dq = dq + dt * ddq 182 | q = pin.integrate(robot.model, q, dt * dq) 183 | 184 | viz.display(q) 185 | 186 | ellapsed_time = tm.time() - tic 187 | print(f"\nSimulation ended. ({ellapsed_time:.2f} s)\n") 188 | 189 | except KeyboardInterrupt: 190 | exit 191 | -------------------------------------------------------------------------------- /data/js_data_jointimp.npy: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/leggedrobotics-usp/impedance_control_benchmark/55822473c5336ab92f15e17fb26203c657e25960/data/js_data_jointimp.npy -------------------------------------------------------------------------------- /data/js_data_taskimp.npy: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/leggedrobotics-usp/impedance_control_benchmark/55822473c5336ab92f15e17fb26203c657e25960/data/js_data_taskimp.npy -------------------------------------------------------------------------------- /data/js_terms.npy: -------------------------------------------------------------------------------- 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The elliptical curve is at the so called impedance space defined by the 5 | position deviation, the velocity deviation, and the input force. Plots are shown for both time and frequency domain 6 | parameter sets. On the time domain set are stiffness, damping, and mass. On the frequency domain set are stiffness, 7 | damping factor, and natural frequency. 8 | -------------------------------------------------------------------------------- /parametric_analysis/transforms_function.py: -------------------------------------------------------------------------------- 1 | # Impedance Control Benchmark 2 | # Copyright (C) 2024, leggedrobotics-usp 3 | # Leonardo F. dos Santos, Cícero L. A. Zanette, and Elisa G. Vergamini 4 | # 5 | # This program is free software: you can redistribute it and/or 6 | # modify it under the terms of the GNU General Public License 3.0, 7 | # or later version. 8 | # 9 | # This program is distributed in the hope that it will be useful, 10 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | # GNU General Public License for more details. 13 | 14 | import numpy as np 15 | from math import sin, cos, atan, asin, sqrt 16 | 17 | def transforms(arg_dict): 18 | """Compute the ellipse-based transforms representing a 2º order LTI system 19 | under sinusoidal input. 20 | 21 | Args: 22 | arg_dict (str, double): lumped parameters values dictionary: 23 | -- Kd: equivalent stiffness; 24 | -- Dd: equivalent damping; 25 | -- Md: equivalent inertia; 26 | -- wu: input angular frequency; 27 | 28 | Returns: 29 | np.array((3,3)), np.array((3,3)), np.array((3,2)): 30 | sequential transformations Tx, Ty, and Tz, respectively. 31 | """ 32 | K = arg_dict.get("Kd") 33 | D = arg_dict.get("Dd") 34 | M = arg_dict.get("Md") 35 | wu = arg_dict.get("wu") 36 | 37 | binormal_vector = np.array([K - M * wu**2, D, -1]) 38 | 39 | rho = atan(D) 40 | phi = asin(-binormal_vector[0] / np.linalg.norm(binormal_vector)) 41 | 42 | Tx = np.array( 43 | [ 44 | [1, 0, 0], 45 | [0, cos(rho), -sin(rho)], 46 | [0, sin(rho), cos(rho)], 47 | ] 48 | ) 49 | Ty = np.array( 50 | [ 51 | [cos(phi), 0, sin(phi)], 52 | [0, 1, 0], 53 | [-sin(phi), 0, cos(phi)], 54 | ] 55 | ) 56 | 57 | sigma_1 = sqrt(D**2 + 1) 58 | sigma_2 = K - M*wu**2 59 | 60 | R11 = sqrt(1 + (sigma_2/sigma_1)**2) 61 | R12 = 0 62 | R21 = D * sigma_2 / sigma_1 63 | R22 = wu * sigma_1 64 | 65 | Tz = np.array([[R11, R12, 0], [R21, R22, 0], [0, 0, 1]]) 66 | 67 | return Tx, Ty, Tz 68 | -------------------------------------------------------------------------------- /plots/jointspace_terms.py: -------------------------------------------------------------------------------- 1 | # Impedance Control Benchmark 2 | # Copyright (C) 2024, leggedrobotics-usp 3 | # Leonardo F. dos Santos, Cícero L. A. Zanette, and Elisa G. Vergamini 4 | # 5 | # This program is free software: you can redistribute it and/or 6 | # modify it under the terms of the GNU General Public License 3.0, 7 | # or later version. 8 | # 9 | # This program is distributed in the hope that it will be useful, 10 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | # GNU General Public License for more details. 13 | 14 | import matplotlib.pyplot as plt 15 | from matplotlib import colormaps 16 | import numpy 17 | 18 | js_terms = numpy.load("data/js_terms.npy") 19 | time = js_terms[:,0] 20 | 21 | id_full = colormaps['tab20c'](0) 22 | id_partial = colormaps['tab20c'](4) 23 | grav_comp = colormaps['tab20c'](17) 24 | font = { 25 | "family": "serif", 26 | "math_fontfamily": "cm", 27 | "color": "black", 28 | "weight": "bold", 29 | "size": 13, 30 | } 31 | 32 | subplot_cols = 2 33 | subplot_rows = 1 34 | 35 | fig = plt.figure(figsize=[9.51, 3.74]) 36 | 37 | ax1 = plt.subplot2grid((subplot_rows, subplot_cols), (0, 0), colspan=1, fig=fig) 38 | ax1.plot(time, js_terms[:,1], color=grav_comp, linestyle="-.") 39 | ax1.plot(time, js_terms[:,2], color=id_partial, linestyle="--") 40 | ax1.plot(time, js_terms[:,3], color=id_full, linestyle="-") 41 | 42 | ax2 = plt.subplot2grid((subplot_rows, subplot_cols), (0, 1), colspan=1, fig=fig) 43 | ax2.plot(time, js_terms[:,4], color=grav_comp, linestyle="-.") 44 | ax2.plot(time, js_terms[:,5], color=id_partial, linestyle="--") 45 | ax2.plot(time, js_terms[:,6], color=id_full, linestyle="-") 46 | 47 | for ax in fig.get_axes(): 48 | ax.tick_params(direction='in') 49 | ax.set_xlabel("$time \hspace{0.5} [s]$", fontdict=font, va='center') 50 | ax.set_ylabel(r"$\tau \hspace{0.5} [N.m]$", fontdict=font, va='center') 51 | 52 | plt.subplots_adjust(left=0.06, bottom=0.09, right=0.94, top=0.98, wspace=0.16, hspace=0.70) 53 | plt.show(block=True) 54 | -------------------------------------------------------------------------------- /plots/parametric3d.py: -------------------------------------------------------------------------------- 1 | # Impedance Control Benchmark 2 | # Copyright (C) 2024, leggedrobotics-usp 3 | # Leonardo F. dos Santos, Cícero L. A. Zanette, and Elisa G. Vergamini 4 | # 5 | # This program is free software: you can redistribute it and/or 6 | # modify it under the terms of the GNU General Public License 3.0, 7 | # or later version. 8 | # 9 | # This program is distributed in the hope that it will be useful, 10 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | # GNU General Public License for more details. 13 | 14 | import numpy as np 15 | import math 16 | import matplotlib.pyplot as plt 17 | from parametric_analysis.transforms_function import * 18 | 19 | task_impedance_ts = np.load("data/ts_data_taskimp.npy")[700:, :] 20 | 21 | # font dictionary to standardize 22 | font = { 23 | "family": "serif", 24 | "math_fontfamily": "cm", 25 | "color": "black", 26 | "weight": "normal", 27 | "size": 14, 28 | } 29 | 30 | Amp = 9.80665 * 5 / 1000 # [m] 31 | wu = 3.00 # [Hz] 32 | dt = 0.01 33 | steps = math.ceil(2 * math.pi / (dt * wu)) 34 | 35 | simulation_params = {"Kd": 1000, "Dd": 8, "Md": 0.016, "wu": wu} 36 | parameters_set = [ 37 | {"Kd": 12, "Dd": 0, "Md": 0, "wu": wu}, 38 | {"Kd": 12, "Dd": 2, "Md": 0, "wu": wu}, 39 | {"Kd": 0, "Dd": 2, "Md": 0, "wu": wu}, 40 | {"Kd": 12, "Dd": 2, "Md": 0, "wu": wu}, 41 | ] 42 | 43 | # 1st dim: time, 2nd dim: parameters_set, 3rd dim: {x,y,z} 44 | curves = np.zeros( 45 | (steps, len(parameters_set), 3) 46 | ) 47 | # Generate Curves: 48 | for j, param in enumerate(parameters_set): 49 | for k in range(steps): 50 | Tx, Ty, Tz = transforms(param) 51 | T = Tx @ Ty @ Tz 52 | curves[k, j, :] = (Amp * T @ 53 | np.array([math.cos(wu * k * dt), math.sin(wu * k * dt), 0]).T 54 | ) 55 | 56 | # 2D Plots 57 | ax = plt.subplot2grid((1, 2), (0, 0), colspan=1) 58 | ax.plot(curves[:, 0, 0], curves[:, 0, 2], label="$k_d$ = 12, $d_d$ = 0") 59 | ax.plot(curves[:, 1, 0], curves[:, 1, 2], label="$k_d$ = 12, $d_d$ = 2") 60 | ax.set_xlabel("$e [m]$", fontdict=font, va='center') 61 | ax.set_ylabel("$f_{int} [N]$", fontdict=font, va='center') 62 | ax.tick_params(axis='both', direction='in') 63 | plt.legend(loc="upper center", fontsize="small", ncols=1, bbox_to_anchor=(0.3, 1.0)) 64 | 65 | ax2 = plt.subplot2grid((1, 2), (0, 1), colspan=1, yticklabels=[]) 66 | ax2.plot(curves[:, 2, 1], curves[:, 2, 2], label="$k_d$ = 0, $d_d$ = 2") 67 | ax2.plot(curves[:, 3, 1], curves[:, 3, 2], label="$k_d$ = 12, $d_d$ = 2") 68 | ax2.set_xlabel("$\dot{e} [m/s]$ ", fontdict=font, va='center') 69 | ax2.tick_params(axis='both', direction='in') 70 | #ax2.set_ylabel("$f_{int}$", fontdict=font, va='center') 71 | plt.legend(loc="upper center", fontsize="small", ncols=1, bbox_to_anchor=(0.3, 1.0)) 72 | 73 | plt.tight_layout() 74 | plt.show(block=False) 75 | 76 | # 3D plot with projections: 77 | ax = plt.figure().add_subplot( 78 | projection="3d", xticklabels=[], yticklabels=[], zticklabels=[] 79 | ) 80 | ax.set_proj_type("ortho") 81 | 82 | curve_color = ["silver" ,"green", "darkviolet", "blue"] 83 | projections_offset = 1.45 84 | projections_alpha = 0.0 85 | plot_type = 'surface' 86 | 87 | x_off = np.max(curves[:, 0, 0]) * projections_offset 88 | y_off = np.max(curves[:, 0, 1]) * projections_offset 89 | z_off = np.min(curves[:, 0, 2]) * projections_offset 90 | 91 | for c in range(len(parameters_set)): 92 | x_off_new = np.max(curves[:, c, 0]) * projections_offset 93 | y_off_new = np.max(curves[:, c, 1]) * projections_offset 94 | z_off_new = np.min(curves[:, c, 2]) * projections_offset 95 | if x_off_new > x_off: 96 | x_off = x_off_new 97 | if y_off_new > y_off: 98 | y_off = y_off_new 99 | if z_off_new < z_off: 100 | z_off = z_off_new 101 | 102 | for c, pset in enumerate(parameters_set): 103 | k_val, d_val = pset["Kd"], pset["Dd"] 104 | label_string = ( 105 | "$K_d$ = " + f"{k_val}, " + 106 | "$D_d$ = " + f"{d_val}" 107 | ) 108 | ax.plot(curves[:, c, 0], curves[:, c, 1], 109 | curves[:, c, 2], color=curve_color[c], 110 | label=label_string) 111 | 112 | if plot_type == "contour": 113 | ax.plot(curves[:, c, 0], curves[:, c, 2], 114 | zs=y_off, zdir="y", color=curve_color[c], 115 | linestyle="--", alpha=projections_alpha, 116 | ) 117 | ax.plot(curves[:, c, 1], curves[:, c, 2], 118 | zs=x_off, zdir="x", color=curve_color[c], 119 | linestyle="--", alpha=projections_alpha, 120 | ) 121 | if plot_type == "surface": 122 | ax.plot_trisurf(curves[:, c, 0], curves[:, c, 1], 123 | curves[:, c, 2], color=curve_color[c], 124 | linewidth=0.3, antialiased=True, alpha=0.5 125 | ) 126 | 127 | 128 | # Log from Pinocchio simulation 129 | ax.plot(task_impedance_ts[:, 1], 130 | task_impedance_ts[:, 2], 131 | task_impedance_ts[:, 3], 132 | color="k", linestyle=":", 133 | alpha=0.0) 134 | 135 | ax.xaxis.set_rotate_label(False) 136 | ax.yaxis.set_rotate_label(False) 137 | ax.zaxis.set_rotate_label(False) 138 | ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) 139 | ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) 140 | ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) 141 | ax.set_ylabel("$\dot{e}_x$", fontdict=font) 142 | ax.set_zlabel("$f_{ext}$", fontdict=font) 143 | ax.set_xlabel("$e_x$", fontdict=font) 144 | plt.legend(loc="upper center", fontsize="small", 145 | ncols=1, bbox_to_anchor=(0.07, 1.00) 146 | ) 147 | plt.show(block=False) 148 | 149 | ax2 = plt.figure().add_subplot( 150 | projection="3d", xticklabels=[], yticklabels=[], zticklabels=[] 151 | ) 152 | ax2.set_proj_type("ortho") 153 | ax2.set_aspect("equal") 154 | 155 | parameters_set = [ 156 | {"Kd": 0, "Dd": 0.0, "Md": 0, "wu": 1.5}, 157 | {"Kd": 1, "Dd": 0.0, "Md": 0, "wu": 1.5}, 158 | {"Kd": 1, "Dd": 0.3, "Md": 0, "wu": 1.5}, 159 | ] 160 | 161 | ax2.plot([0, 1], [0, 0], [0, 0], linestyle="-", color="blue") 162 | ax2.plot([0, 0], [0, 1], [0, 0], linestyle="-", color="blue") 163 | ax2.plot([0, 0], [0, 0], [0, 1], linestyle="-", color="blue") 164 | 165 | Tx, Ty, Tz = transforms(parameters_set[0]) 166 | Basis = Tx @ Ty @ Tz 167 | 168 | ax2.plot([0, Basis[0,0]], [0, Basis[0,1]], [0, Basis[0,2]], linestyle="--", color="grey") 169 | ax2.plot([0, Basis[1,0]], [0, Basis[1,1]], [0, Basis[1,2]], linestyle="--", color="grey") 170 | ax2.plot([0, Basis[2,0]], [0, Basis[2,1]], [0, Basis[2,2]], linestyle="--", color="grey") 171 | 172 | Tx, Ty, Tz = transforms(parameters_set[1]) 173 | Basis = Tx @ Ty @ Tz 174 | 175 | ax2.plot([0, Basis[0,0]], [0, Basis[0,1]], [0, Basis[0,2]], linestyle="--", color="green") 176 | ax2.plot([0, Basis[1,0]], [0, Basis[1,1]], [0, Basis[1,2]], linestyle="--", color="green") 177 | ax2.plot([0, Basis[2,0]], [0, Basis[2,1]], [0, Basis[2,2]], linestyle="--", color="green") 178 | 179 | Tx, Ty, Tz = transforms(parameters_set[2]) 180 | Basis = Tx @ Ty @ Tz 181 | 182 | ax2.plot([0, Basis[0,0]], [0, Basis[0,1]], [0, Basis[0,2]], linestyle="--", color="darkviolet") 183 | ax2.plot([0, Basis[1,0]], [0, Basis[1,1]], [0, Basis[1,2]], linestyle="--", color="darkviolet") 184 | ax2.plot([0, Basis[2,0]], [0, Basis[2,1]], [0, Basis[2,2]], linestyle="--", color="darkviolet") 185 | 186 | plt.show(block=True) 187 | -------------------------------------------------------------------------------- /plots/subplots_figures.py: -------------------------------------------------------------------------------- 1 | # Impedance Control Benchmark 2 | # Copyright (C) 2024, leggedrobotics-usp 3 | # Leonardo F. dos Santos, Cícero L. A. Zanette, and Elisa G. Vergamini 4 | # 5 | # This program is free software: you can redistribute it and/or 6 | # modify it under the terms of the GNU General Public License 3.0, 7 | # or later version. 8 | # 9 | # This program is distributed in the hope that it will be useful, 10 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | # GNU General Public License for more details. 13 | 14 | import matplotlib.pyplot as plt 15 | from matplotlib import colormaps 16 | import numpy 17 | import math 18 | 19 | rad2deg = 180 / math.pi 20 | t_begin = 700 # samples [dt = 0.001 s] 21 | joint_impedance_js = numpy.load("data/js_data_jointimp.npy")[t_begin:, :] 22 | joint_impedance_ts = numpy.load("data/ts_data_jointimp.npy")[t_begin:, :] 23 | task_impedance_js = numpy.load("data/js_data_taskimp.npy")[t_begin:, :] 24 | task_impedance_ts = numpy.load("data/ts_data_taskimp.npy")[t_begin:, :] 25 | 26 | ts_color = colormaps['tab20c'](0) 27 | js_color = colormaps['tab20c'](4) 28 | font = { 29 | "family": "serif", 30 | "math_fontfamily": "cm", 31 | "color": "black", 32 | "weight": "bold", 33 | "size": 13, 34 | } 35 | 36 | subplot_cols = 2 37 | subplot_rows = 3 38 | ieee_width_in = 7 # + 0.25 + 3.5 39 | aspect_ratio = 9 / 16 40 | 41 | scaling = math.e 42 | joint_impedance_ts[:, 1] = scaling * joint_impedance_ts[:, 1] 43 | joint_impedance_ts[:, 2] = scaling * joint_impedance_ts[:, 2] 44 | 45 | fig = plt.figure(figsize=[ieee_width_in, aspect_ratio * ieee_width_in]) 46 | 47 | ax1 = plt.subplot2grid( 48 | (subplot_rows, subplot_cols), (1, 0), colspan=1, xticklabels=[], yticklabels=[], fig=fig 49 | ) 50 | ax1.plot(task_impedance_ts[:, 1], task_impedance_ts[:, 3], color=ts_color) 51 | ax1.plot(joint_impedance_ts[:, 1], joint_impedance_ts[:, 3], color=js_color, linestyle="--") 52 | ax1.set_xlabel("$e_x$", fontdict=font, va='center') 53 | ax1.set_ylabel("$f_{int}$", fontdict=font, va='center') 54 | 55 | joint = 1 56 | ax2 = plt.subplot2grid( 57 | (subplot_rows, subplot_cols), (0, 0), colspan=1, xticklabels=[], yticklabels=[] 58 | ) 59 | ax2.plot( 60 | rad2deg * task_impedance_js[:, joint], 61 | task_impedance_js[:, joint + 6], 62 | color=colormaps['tab20c'](1), 63 | ) 64 | ax2.plot( 65 | rad2deg * joint_impedance_js[:, joint], 66 | joint_impedance_js[:, joint + 6], 67 | color=colormaps['tab20c'](5), 68 | linestyle="--", 69 | ) 70 | ax2.set_xlabel("$q$", fontdict=font, va='center') 71 | ax2.set_ylabel(r"$\tau$", fontdict=font, va='center') 72 | 73 | 74 | ax3 = plt.subplot2grid( 75 | (subplot_rows, subplot_cols), 76 | (0, 1), 77 | rowspan=2, 78 | projection="3d", 79 | xticklabels=[], 80 | yticklabels=[], 81 | zticklabels=[], 82 | ) 83 | 84 | ax3.set_proj_type("ortho") 85 | ax3.plot( 86 | task_impedance_ts[:, 1], 87 | task_impedance_ts[:, 2], 88 | task_impedance_ts[:, 3], 89 | color=ts_color, 90 | ) 91 | ax3.plot( 92 | joint_impedance_ts[:, 1], 93 | joint_impedance_ts[:, 2], 94 | joint_impedance_ts[:, 3], 95 | color=js_color, 96 | linestyle="--", 97 | ) 98 | ax3.set_xlabel("$e_x$", fontdict=font) 99 | ax3.set_ylabel("$\dot{e}_x$", fontdict=font) 100 | ax3.set_zlabel("$f_{int}$", fontdict=font) 101 | ax3.view_init(elev=20, azim=-20) 102 | 103 | ax4 = plt.subplot2grid( 104 | (subplot_rows, subplot_cols), (2, 0), colspan=1, xticklabels=[], yticklabels=[] 105 | ) 106 | ax4.plot(task_impedance_ts[:, 1], task_impedance_ts[:, 2], color=ts_color) 107 | ax4.plot(joint_impedance_ts[:, 1], joint_impedance_ts[:, 2], color=js_color, linestyle="--") 108 | ax4.set_ylabel("$\dot{e}_x$", fontdict=font, va='center') 109 | ax4.set_xlabel("$e_x$", fontdict=font, va='center') 110 | 111 | ax5 = plt.subplot2grid( 112 | (subplot_rows, subplot_cols), (2, 1), colspan=1, xticklabels=[], yticklabels=[] 113 | ) 114 | ax5.plot(task_impedance_ts[:, 2], task_impedance_ts[:, 3], color=ts_color) 115 | ax5.plot(joint_impedance_ts[:, 2], joint_impedance_ts[:, 3], color=js_color, linestyle="--") 116 | ax5.set_ylabel("$f_{int}$", fontdict=font, va='center') 117 | ax5.set_xlabel("$\dot{e}_x$", fontdict=font, va='center_baseline') 118 | 119 | for ax in fig.get_axes(): 120 | ax.tick_params(direction='in') 121 | 122 | plt.subplots_adjust( 123 | left=0.06, bottom=0.09, right=0.94, top=0.98, wspace=0.16, hspace=0.35 124 | ) 125 | plt.show(block=True) 126 | --------------------------------------------------------------------------------