tutorial_inverse-kinematic
Tutorial on Inverse Kinematic
This tutorial builds on top tutorial_impedance-control to implement a simple inverse kinematic controller. The robot will try to move the end effector (left hand) in a desired configuration. The inverse kinematic is resolved using quadratic programming via osqp. The optimisation problem is formulated as
$$ \begin{align} \min_{\mathbf{\nu} = \begin{bmatrix} v_b \\ \dot{s} \end{bmatrix}} & \quad \frac{1}{2} {|| J_{ee}^{pos} \nu - v^{\star} ||}_ 2^ 2 + k_{\nu} {|| \nu ||}_ 2^ 2 \ \text{s.t.} \quad & J_B \nu = 0 \ & \dot{s}^{-} \leq \dot{s} \leq \dot{s}^{+} \ & v^{\star} = -K_p \left( x_{ee} - x_{ee}^{des} \right) \end{align} $$
$\nu$ is the vector of configuration velocities, $v_b$ is the base velocity, $\dot{s}$ is the joint velocity. $J_{ee}^{pos}$ is the Jacobian of the end effector position, $J_B$ is the Jacobian of the base. $\dot{s}^{-}$ and $\dot{s}^{+}$ are the lower and upper bounds on the joint velocity. $x_{ee}$ is the end effector position and $x_{ee}^{des}$ is the desired end effector position, and $K_p$ is the proportional gain.
Installation
- Install and Configure ironcub-mk1-software
- Build the repository
mkdir build
cd build
cmake ..
make install
Usage
- run yarpserver
yarpserver
- run yarpmanager
yarpmanager
- open the application
tutorial_inverse-kinematic-system.xmlin yarpmanager and run all the modules - open the application
tutorial_inverse-kinematic-app.xmlin yarpmanager and run the controller