Dynamics and Control of Robotic Manipulators with Contact and Friction

2Fundamentals of Robot Dynamics and Control

2.1 Robot Kinematics

Robot kinematics is classified into two categories: forward kinematics and inverse kinematics. Forward kinematics is used to determine the posture of the robot's hand based on the of displacement or velocity inputs from each joint. Inverse kinematics is used to calculate the value of each joint variable (its angular displacement, linear displacement, or velocity) given the specific point and gesture of the robot end. A matrix is used to establish the representation method of object position, object gesture and object motion, and then the forward and inverse kinematics of different robot configurations, such as Cartesian coordinates, cylindrical coordinates, and spherical coordinates are studied. The Denavit‐Hartenberg (D‐H) method [1] is used to derive the forward and inverse kinematic equations for all possible robot configurations.

2.1.1 Matrix Description of Robot Kinematics

Matrices can be used to represent points, vectors, coordinate systems, translations, rotations, and transformations, and can represent objects and other moving elements in the coordinate system.

The spatial point P (shown in Figure 2.1) can be represented by its three coordinates relative to the reference coordinate system:

(2.1)

where (a_x, b_y, c_z) is the coordinate of that point in the reference coordinate system.

Figure 2.1The represent ...