stewart_platform_sim

ROS 2 Python simulation of a six-DoF Stewart platform (or Stewart-Gough platform^1,2), which is a parallel manipulator comprising a fixed base platform, a moving end-effector platform, and six serial SPS sturctures².

The inverse kinematics (IK) and differential kinematics (DK) problems are solved as to obtain the required leg lengths and leg velocities for driving the robot to achieve a desired motion in $SE(3)$.

The map for IK, $f_{\mathrm{ik}}:\ SE(3) \to \mathbb{R}^6$ is provided, where

• $\boldsymbol{s} = f_{\mathrm{ik}}(^b\boldsymbol{\xi}_e)$
• $\boldsymbol{s} \in \mathbb{R}^6$ is the leg length
• $^b\boldsymbol{\xi}_e \in SE(3)$ is the end-effector pose w.r.t. base.

The inverse Jacobian for DK, $J_b^{-1}:\ se(3) \to \mathbb{R}^6$ is also provided, where

• $\dot{\boldsymbol{s}} = J_b^{-1} \cdot \mathcal{V}_b = J_b^{-1} \cdot \mathrm{Ad}(^b\boldsymbol{\xi}_e) \cdot \mathcal{V}_e$
• $\dot{\boldsymbol{s}} \in \mathbb{R}^6$ is the leg velocity
• $J_b^{-1} \in \mathbb{R}^{6\times 6}$ and $\mathcal{V}_b \in se(3)$ are the base inverse Jacobian and base twist, respectively
• $\mathcal{V}_e \in se(3)$ is the end-effector twist (spatial velocity for both linear and angular) that can be transformed into $\mathcal{V}_b$ through the adjoint map $\mathrm{Ad}(^b\boldsymbol{\xi}_e) \in \mathbb{R}^{6\times 6}$.

Simulation (visualised in ROS 2 RViz2)

Demo

Run the simulation in ros2:

# Simulate in ros2 and visualise in rivz2
cd ~/stewart_platform_sim && python3 sim_ros2.py
rviz2

Bibliography

• Picture of the Stewart-Gough platform mechanism:

  • [1] J.-P. Merlet, C. Gosselin, and Tian Huang. Parallel mechanisms. In B. Siciliano and O. Khatib, editors, Handbook of Robotics, Second Edition, pages 443–461. Springer-Verlag, 2016.

• Stewart platform IK and DK:

  • [2] K. M. Lynch and F. C. Park, Modern Robotics: Mechanics, Planning, and Control. Cambridge University Press, 2017.

Contact

• Author: Wei-Hsuan Cheng ([email protected])
• Homepage: wei-hsuan-cheng
• GitHub: wei-hsuan-cheng