Singularities occurwhen the rank of the robot’s Jacobian matrixis less than the maximum rank the Jacobian can reach in some configuration. Singularities exist for a particular robot configuration if the determinant of the Jacobian matrix is zero. All of these definitions say more or less the sam...
Once the robot’s joint angles are calculated using the inverse kinematics, a motion profile can be generated using the Jacobian matrix to move the end-effector from the initial to the target pose. The Jacobian matrix helps define a relationship between the robot’s joint parameters and the end...
The gradient is a vector representing the direction and rate of fastest increase of a scalar function, whereas the Jacobian is a matrix describing all first-order partial derivatives of a vector-valued function.