NMT EE 589 UNM ME 482582 ROBOT ENGINEERING
NMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582
8. Manipulator Control q 8. 3 Independent Joint Control Simplified drive train model of a robot joint ○ Inertia “seen” by the motor ○ Torque amplification Ø For “high” gear ration the link Link k Load Inertia Motor inertia effect is relatively “small” q The motor can be modeled as U(s) ○ Motor Inertia (s) where B is viscous friction, Ka the scale factor from motor voltage (u) to current, and Km the torque constant Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 2 / 16
8. Manipulator Control q 8. 3 Independent Joint Control An example of independent joint control: ○ ○ Consider the PUMA 560 robot Video: Puma 560 - Gravity Compensation Open Loop Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 3 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Viscous Friction Dr. Stephen Bruder Coriolis & Centripetal ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 4 / 16
8. Manipulator Control q 8. 3 Independent Joint Control A simple position control example (Puma 560 the 2 ○ nd link) Approximate the inertia seen by the motor Ø G 2=107, Im 2=2 X 10 -4, D 22 2, hence, J=3. 7 X 10 -4 Outer Position Loop Dr. Stephen Bruder Inner Velocity Loop ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 5 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Speed Control Example ○ Kv=1. 5, 0. 5, 1. 0 Kv=1. 0 gives a reasonable system response Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 6 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Speed Control Example ○ What about the effect of gravity? Ø Varies with configuration! (-40 < G 2 < 40) Let’s add a gravity induced disturbance torque of 20 Nm Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 7 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Add a 20 Nm gravity induced disturbance Ø Needs some integral control!! q Disturbance Rejection!! Massive (1 rad/s) steady state error!! Ki=10 => No steady state error!! 20 Nm Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 8 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 9 / 16
8. Manipulator Control q q q 8. 3 Independent Joint Control This term will be treated as an unknown “small” disturbance, and temporarily neglected. Furthermore, it is simple to scale (8. 8) by a, therefore, no loss of generality occurs by letting a = 1. The model thus becomes (8. 9) By selecting the control law Dr. Stephen Bruder ME 482/582: Robotics Engineering (8. 10) Tuesday 27 th Nov 2012 Slide 10 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Model Based Control Law Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 11 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 12 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Servo Control Law Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 13 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 14 / 16
8. Manipulator Control q 8. 3 Independent Joint Control Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 15 / 16
8. Manipulator Control o o 8. 3 Independent Joint Control We can prove that these types of local control schemes actually do work, at least asymptotically. The simplest way to show this is by creating a Lyapunov function using the closed loop system resulting from the two stage control scheme described above. Dr. Stephen Bruder ME 482/582: Robotics Engineering Tuesday 27 th Nov 2012 Slide 16 / 16
- Slides: 16