Module 9 : Robot Dynamics & controls
Lecture 34 : Trajectory tracking control ( feed forward, computed torque and inverse dynamics approach)
Trajectory Tracking using PD+Feedforward :
  In this & are computed along the trajectory at various instants of time & these terms are feed forwarded . This is the basis of Feed forward algorithm. Along predefined path we can find out ,,. We can also estimate& at various points along trajectory. So along given trajectory, actuator(i.e. motor) have to overcome following torques.
  .= Effective inertia force.
  .= Effective damping force.
  This information is feed forwarded in this technique.
 

Figure 34.3 PP +Feedforward control
  Now Linear form with disturbance
 
  but
Controller Equation
  Substituting this controller equation , system dynamics becomes
  Define
  we get
For zero disturbance by choosing & such that whatever settling time chosen,
 
  One can now easily say that the tracking error is due to term.
  Substituting this controller equation , system dynamics becomes
 
  Here the trackting error is further reduced,
Nonlinear Coriolis, centripetal gravitational forces have to be computed, hence more comutational load.
Again, so far we have not seen any non-linear analysis or design of controllers .
Non-linear analysis & design necessary to further improve the performance.
   
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