Main Content

Compute joint configurations to achieve an end-effector pose

**Library:**Robotics System Toolbox / Manipulator Algorithms

The Inverse Kinematics block uses an inverse kinematic (IK) solver to
calculate joint configurations for a desired end-effector pose based on a specified rigid body
tree model. Create a rigid body tree model for your robot using the `rigidBodyTree`

class. The rigid body tree model defines all the joint constraints
that the solver enforces.

Specify the `RigidBodyTree`

parameter and the desired end effector inside
the block mask. You can also tune the algorithm parameters in the **Solver
Parameters** tab.

Input the desired end-effector **Pose**, the **Weights**
on pose tolerance, and an **InitialGuess** for the joint configuration. The
solver outputs a robot configuration, **Config**, that satisfies the
end-effector pose within the tolerances specified in the **Solver
Parameters** tab.

[1] Badreddine, Hassan, Stefan
Vandewalle, and Johan Meyers. "Sequential Quadratic Programming (SQP) for Optimal Control in
Direct Numerical Simulation of Turbulent Flow." *Journal of Computational
Physics*. 256 (2014): 1–16. doi:10.1016/j.jcp.2013.08.044.

[2] Bertsekas, Dimitri P.
*Nonlinear Programming*. Belmont, MA: Athena Scientific,
1999.

[3] Goldfarb, Donald. "Extension of
Davidon’s Variable Metric Method to Maximization Under Linear Inequality and Equality
Constraints." *SIAM Journal on Applied Mathematics*. Vol. 17, No. 4
(1969): 739–64. doi:10.1137/0117067.

[4] Nocedal, Jorge, and Stephen
Wright. *Numerical Optimization*. New York, NY: Springer,
2006.

[5] Sugihara, Tomomichi.
"Solvability-Unconcerned Inverse Kinematics by the Levenberg–Marquardt Method."
*IEEE Transactions on Robotics*. Vol. 27, No. 5 (2011): 984–91.
doi:10.1109/tro.2011.2148230.

[6] Zhao, Jianmin, and Norman I.
Badler. "Inverse Kinematics Positioning Using Nonlinear Programming for Highly Articulated
Figures." *ACM Transactions on Graphics*. Vol. 13, No. 4 (1994): 313–36.
doi:10.1145/195826.195827.