Inverse kinematics

The inverse kinematics ( often abbreviated as IK ) or reverse transformation is a term used in robotics. It allows the determination of the joint angle of the arm members on the basis of the pose ( position and orientation) of the end effector in an industrial robot (English: the tool center point TCP). Hence it plays an important role in the movement of industrial robots and computer animation of characters. It is the logical counterpart to the direct kinematics.

In the inverse kinematics of the last element of the kinematic chain, known as the end effector is moved and brought into the desired position. The other links in the chain have to take in accordance with the degrees of freedom of their joints matching documents.

You can compare this with the human arm, which is also such a kinematic chain with its joints: Bring one example, the hand in a certain position, automatically take the wrist, elbow and shoulder also certain positions a. Exactly this ( joint angle ) positions must be determined through the inverse kinematics.

The correlations tries to clarify the following picture:

Trouble

The following problems occur in the calculation of inverse kinematics:

Solutions

To solve the inverse kinematic problem, there is no generally applicable method. Since the calculation of the joint angles must be done very quickly, in practice solutions are commonly found, which are optimized and adapted to the specific robot.

There are the following basic methods:

  • Algebraic methods
  • Geometric methods
  • Numerical methods

Algebraic methods

By successive inversion of the Denavit -Hartenberg transformation and thus solving the following system of equations can be calculated according to the individual joint angles vector components and after:

A homogeneous matrix, which describes the position and orientation of the end effector.

Geometric methods

Based on knowledge about the geometry of the robot is trying, for example by means of cosine or sine rule to calculate the joint angle vector.

Numerical Methods

Using numerical methods is iteratively tries to find a solution for the joint angle vector. Local minima or the determination of a suitable starting value, however, are problematic here.

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