Addverb Bi-Manual Manipulation

This is a ongoing research please don’t share any content on this page without prior permission from the author. (Debojit Das : [email protected])

GitHub Repositories

https://github.com/Debojit-D/Dual_Arm_Manipulation-Addverb_and_IITGN_Robotics.git

https://github.com/Debojit-D/Addverb_Heal_and_Syncro_Hardware.git

Contains the MuJoCo and Gazebo simulations. Also the ROS packages for dual arm control.

Contains the Hardware ROS Packages for Addverb. Heal and Syncro Robots.

Task 1 : Hold and move / shift large objects with two hands (large objects that do not have handles)

<aside> 💡

[ ] Dual - Arm Object Impedance Control
- [ ] Redundancy Optimisation
- [ ] Collision Avoidance Using Redundancy Optimisation / Bounding Volume Hierarchies </aside>

Dual - Arm Object Impedance Formulation

$$ \begin{equation} \boldsymbol{\tau}_{\text{desired}} = \mathbf{J}H^{T} \mathbf{F}{\text{ext}} \end{equation}

$$ \begin{equation} \boldsymbol{\tau}{\text{desired}} = \mathbf{J}H^{T} (\mathbf{F}{\text{impedance}} + \mathbf{F}{\text{null space}}) \end{equation} $$

$$ \begin{equation} \mathbf{F}_{\text{impedance}} = \mathbf{G}^{+} \big[ \mathbf{K}_p (\mathbf{q}_d - \mathbf{q}) + \mathbf{K}_d (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) \big) \end{equation}

$$ \begin{equation} \mathbf{F}{\text{nullspace}} = (\mathbf{I} - \mathbf{G}^{+} \mathbf{G}) \Phi{\text{o}} \end{equation}

$$ \begin{equation}\boldsymbol{\tau}_{\text{desired}} = \mathbf{J}_H^{T} \bigg[ \mathbf{G}^{+} \Big( \mathbf{K} (\mathbf{q}_d - \mathbf{q}) + \mathbf{K}_d (\dot{\mathbf{q}}d - \dot{\mathbf{q}}) \Big) + (\mathbf{I} - \mathbf{G}^{+} \mathbf{G}) \Phi{\text{o}} \bigg]\end{equation} $$

In the formulation above and the once generated on this page :-

$\mathbf{G}$ is the grasp matrix.
$\mathbf{J}_H$is the hand Jacobian.
$\mathbf{K_p}$ and $\mathbf{K_d}$ are the proportional and derivative gain arrays.
$\mathbf{q_d}$ and $\mathbf{q}$ are the desired and current object pose, respectively; that is being manipulated.
$\dot{\mathbf{q_d}}$ and $\dot{\mathbf{q}}$ are the desired and current object velocities, respectively.

If we assume a soft contact model (assuming full G matrix),