1. Accurate Robot Positioning using Corrective Learning
Ram Subramanian
ECE 539
Course Project
Fall 2003

2. Outline Motivation Two Link Manipulators Kinematics
Corrective Learning
Experimental Setup
Results & Conclusion

3. Motivation
The human motor control mechanism works by initiating a motion in the general direction of the target. Then subsequently produces corrective movements to reach the target with a good degree of accuracy.

4. The 2 Link Manipulator Simple kinematics link2
Easy to setup control parameters
Easy to Model
link2 2
link1 1

5. Kinematics
The forward kinematics of a robot are used to determine the position of the end effecter for a given set of joint angles
The Inverse kinematics are used to determine appropriate joint angles for a particular end effecter position.

6. Problem with Inverse Kinematics
Mapping from Cartesian space of the end effecter to the joint angles of the robot is
Non linear
Potentially degenerate
(leading to multiple solutions)
This causes complications when controlling the manipulator. Modeling other parameters like friction etc. increases the non linearity of the system further

7. Corrective Learning The Learning Process Initiate a movement
Determine the position error between the end effecter and the target
Adjust the joint angles based on a heuristic
Repeat until the target position is reached

8. Corrective Learning (cont’d)
Once the joint angles corresponding to a particular target position is learned, subsequent visits to the same target point use the already learned values.
This technique allows the positioning of the robot without accurate knowledge of all the link parameters

9. Experimental Setup Target Position Look up Table (1,2 ) (x,y) (x,y)
Controller
Two Link
Robot
Initial
Position
Learner
Error
(1, 2)

10. Results & Conclusions
The average error between the final position of the robot end effecter and the target was found to be 3.21, with a standard deviation of 0.8 .
The first reach to every target position takes one order of magnitude longer in time than the subsequent reaches to the same target position.

11. Future Work
Comparison between this learning technique, a model developed with a Back Propagation neural network and the computed torque technique.
Adapt the learning technique for manipulators with larger number of links.