Feedback Control of Flexible Robotic Arms. Mohsin Waqar Intelligent Machine Dynamics Lab Georgia Institute of Technology January 26, 2007. My Background in Brief. Education: BS Degree in Mechanical Engineering, Cum Laude, May 2006
Intelligent Machine Dynamics Lab
Georgia Institute of Technology
January 26, 2007
BS Degree in Mechanical Engineering, Cum Laude, May 2006
San Jose State University, San Jose, California
Senior Design Project: Injection Molding Machine Tending Robot
RAININ INSTRUMENT LLC, Oakland, CA, June 2005 – July 2006
Truck Assembly Maintenance Co-op
NEW UNITED MOTOR MANUFACTURING INC, Fremont, CA, January – August 2004
1) Manipulators with very large workspaces (long reach):
Example - handling of nuclear waste.
2) Manipulators with constraints on mass:
Example – space manipulators.
3) Manipulators with improved performance:
Examples - “truly high precision,” quicker motion, less energy requirement, and lower cost.
Source: Shabana, A. A. Vibration of Discrete and Continuous Systems. 1997.
Source: Cannon, R.H. and Schmitz, E. “Initial Experiments on the End-Point Control of a Flexible One-Link Robot.” 1984.
Accurate knowledge of natural frequencies and damping ratios becomes a requirement.
Mashner (2002) Beargie (2002)
Noise Covariance Matrices Q and R – measure of uncertainty in plant and in measurements, respectively. Higher values for a matrix element means lots of uncertainty in a process state or in a measurement.
Error Covariance Matrix P - measure of uncertainty in state estimates. Higher elements mean high uncertainty in pre-measurement estimate so weight measurements heavier. Depends on process noise.
Kalman Matrix K - determines how much to weight fresh estimates based on a recent measurement (correcting estimate). Depends on Error Covariance Matrix P.
How it works:
Step 1. Declare Initial Conditions:
Error Covariance Matrix P, initial state guess x.
Step 2. Declare Filter Parameters:
Noise Covariance Matrices Q and R.
Step 3. Predict States x based on Plant Dynamics
Step 4. Update Error Covariance Matrix P (increase)
Step 5. Update Kalman Matrix K
Step 6. Correct State Estimate x based on measurement
Step 7. Update Error Covariance Matrix P (decrease)
Iterate through Steps 3 – 7 ….
At Steady State: P, K become constant. If Q, R and system matrices A, B, C already constant: can use steady state Kalman filter.
R = 0.1
R = 1
R = 0.01
Commanded Tip Position
Other State Estimates
Estimate for Tip Position
This has been done before by Beargie and Mashner in 2002!