NUMERICALLY STABLE SOLUTION TO THE 6R PROBLEM OF INVERSE KINEMATICS.

Area of Science:

• Robotics
• Computational Geometry
• Applied Mathematics

Background:

• Inverse kinematics (IK) is crucial for robot motion planning.
• Existing IK algorithms often struggle with complex configurations and special cases.
• A stable and comprehensive solution for 6-revolute manipulator IK is needed.

Purpose of the Study:

• To develop a stable and accurate algorithm for computing all solutions to the inverse kinematics problem of a 6-revolute manipulator chain.
• To address limitations of current methods, particularly in handling problematic configurations.

Main Methods:

• Formulated a system of 20 equations based on closure conditions.
• Utilized singular value decomposition (SVD) to eliminate two joint angles stably.
• Converted the reduced system to a generalized eigenvalue problem to solve for three angles.
• Employed pseudoinverse for the remaining angles.
• Reduced the system to 10 complex equations for accelerated SVD computation.

Main Results:

• The algorithm successfully computes all solutions for the inverse kinematics problem.
• Demonstrated robustness through comparison with existing methods.
• Validated performance on challenging cases, including vanishing link lengths and 180-degree joint angles.

Conclusions:

• The proposed algorithm offers a stable and accurate approach to solving the 6-DOF manipulator inverse kinematics.
• The method's efficiency and robustness make it suitable for complex robotic applications.
• This work advances the state-of-the-art in robotic motion planning and control.