The generalized momentum of the robotic arm is an important physical quantity that describes the motion state of the robotic arm, and represents the amount of motion of each joint of the robotic arm.
For a manipulator with n degrees of freedom, its generalized momentum is defined as: p = M(q)q̇
Among them: q: generalized coordinates of the robotic arm, indicating the angle of each joint
q̇: Generalized speed of the robotic arm, representing the angular velocity M(q) of each joint:
The inertia matrix of the robotic arm is an nxn matrix, which depends on the joint angle qp:
The generalized momentum of the robotic arm is an nx 1 vector. It can be seen that the generalized momentum is directly related to the generalized speed, but it is also related to the inertia matrix M. The generalized momentum of the manipulator reflects the motion state of the entire mechanical system and plays a key role in kinematic analysis, dynamics analysis and control planning. For example, in genetic algorithm planning, generalized momentum is often used as one of the optimization objectives. Calculating and controlling the generalized momentum of the robotic arm can better understand and guide the movement of the robotic arm and achieve efficient and fast motion control.