Computed torque control is a control scheme used in motion control in robotics. It combines feedback linearization via a PID controller of the error with a dynamical model of the controlled robot.[1][2]
Let the dynamics of the controlled robot be described by
where
is the state vector of joint variables that describe the system,
is the inertia matrix,
is the vector Coriolis and centrifugal torques,
are the torques caused by gravity and
is the vector of joint torque inputs.
Assume that we have an approximate model of the system made up of
. This model does not need to be perfect, but it should justify the approximations
and
.
Given a desired trajectory
the error relative to the current state
is then
.
We can then set the input of the system to be
With this input the dynamics of the entire systems becomes
and the normal methods for PID controller tuning can be applied. In this way the complicated nonlinear control problem has been reduced to a relatively simple linear control problem.