A number of strategies exist to reduce the effect of these coupling torques between the joints, from introducing a gearbox between the motor and the joint, to advanced feedforward strategies.
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Electric motors are typically quite weak, they produce a low torque, so it’s very common to add a reduction gearbox.
We will use Simulink to create a dynamic model of a single robot joint and simulate its operation.
We can model a DC motor as a resistor and a voltage source, and then understand the implications of controlling either the voltage or current supplied to the motor. We also learn about common methods for motor control such as the H-bridge driver and pulse width modulation.
Actuators have finite capability, that is they have a maximum torque, velocity and power rating.
We will introduce resolved-rate motion control which is a classical Jacobian-based scheme for moving the end-effector at a specified velocity without having to compute inverse kinematics.
We describe the velocity coupling terms of the robot as a matrix which represents how the torque on one joint depends on the velocity of other joints.
We describe inertia of the robot as a matrix which represents how inertia of a joint depends on the position of all the joints, and how the torque on one joint depends on the acceleration of other joints.
We can factorise the joint torque expression into an elegant matrix equation with terms that describe the effects of inertia, Coriolis and centripetal and gravity effects.
We start by considering the effect of gravity acting on a robot arm, and how the torque exerted will disturb the position of the robot controller leading to a steady state error. Then we discuss a number of strategies to reduce this error.