How do you resolve kinematic singularities in a 6-DOF robot arm during trajectory planning?

Kinematic singularities in a 6-DOF robot arm occur when the robot's joint configuration results in a loss of manipulability, meaning the robot cannot move its end-effector in certain directions or orientations, or requires infinite joint velocities to do so. A 6-DOF (Degrees of Freedom) robot arm has six joints that allow it to move its end-effector (the tool at the end of the arm) in three dimensions and rotate it about three axes. Singularities typically arise when two or more robot axes align, causing the robot's Jacobian matrix (which relates joint velocities to end-effector velocities) to become singular, i.e., non-invertible. During trajectory planning, which is the process of generating a smooth path for the robot to follow, singularities can cause problems like jerky movements, excessive joint velocities, or even complete loss of control. Several techniques can be used to resolve these issues. One approach is to avoid singularities altogether by designing trajectories that stay away from singular configurations. This can be achieved by limiting the robot's workspace or by using motion planning algorithms that explicitly avoid singular regions. Another method involves using damped least-squares inverse kinematics. This technique adds a damping factor to the Jacobian matrix during inverse kinematics calculations (the process of determining the joint angles required to achieve a desired end-effector pose). The damping factor prevents the Jacobian from becoming singular and helps to smooth out joint velocities near singularities, although it may introduce small errors in the end-effector position. A third approach is to use singularity-robust inverse kinematics. These methods are specifically designed to handle singularities by smoothly transitioning through singular configurations without generating excessive joint velocities. One example is the selective deactivation of degrees of freedom, where the robot temporarily restricts its movement to avoid the singular configuration. The selection of the most suitable technique depends on the specific application and the nature of the singularity encountered. Avoiding singularities through careful trajectory planning is generally preferred, but when that is not possible, damped least-squares or singularity-robust methods offer effective solutions.