Chapter3. Motion Control

Given by: Dr. Hamid Sadeghian

Motion Control of Robot Manipulators

Kinematic control: providing reference trajectory in the joint space from the task space and follow independently by each motor
Dynamic control: calculate the command torque from the task directly and apply to joint motors simulatenously

Task specification $\rightarrow$ end-effector motion and forces $\rightarrow$ operational space.

Control actions $\rightarrow$ joint actuator generalized forces $\rightarrow$ joint space.

Operational space control

Formulation inverse kinematics is embedded into the feedback control loop. Its advantage lies in its ability to act directly on errors in workspace variables.

Joint space control

Manipulator inverse kinematics is solved to transform the motion requirements $x_d$ from the operational space into the corresponding motion $q_d$ in the joint space. Then, a joint space control control scheme is designed that allows the actual motion q to track the reference input.

Basic methods

Robot dynamics:

M(q)\ddot{q} + C(q,\dot{q})\dot{q} + F\dot{q} + g(q) = \tau

PD+gravity Control

constant desired configuration $q_d$ . The following coontroller brings the system to the desired posture:

\begin{align*} \tau &= g(q) + K_P\tilde{q} - K_D\dot{q}\\ \tilde{q} &= q_d - q \end{align*}

The closed-loop(time independent) dynamics is:

M(q)\ddot{q} + C(q,\dot{q})\dot{q} + F\dot{q} = K_P\tilde{q} - K_D\dot{q}