Algorithm for Determining the Types of Inverse Kinematics Solutions for Sequential Planar Robots and Their Representation in the Configuration Space

The work defines in a new way the different types of solutions of the inverse kinematics (IK) problem for planar robots with a serial topology and presents an algorithm for solving it. The developed algorithm allows the finding of solutions for a wide range of robots by using a geometric approach, representing points in a polar coordinate system. Inverse kinematics, which is one of the most important, most studied and challenging problems in robotics, aims to calculate the values of the joint variables, given the desired position and orientation of the robot’s end effector. Configuration space is defined by joint angles and is the basis of most motion planning algorithms. Areas in the working and configuration space are generated that are reachable with different types of solutions. Programs are created that use the proposed algorithm for robots with two and three rotational degrees of freedom, and graphically present the results in the workspace and configuration space. The possibility of transitioning from one type of solution to another by passing through a singular configuration is discussed. The results are important for planning motions in the workspace and configuration space, as well as for the design and kinematic analysis of robots.