Accurate Robot Positioning using Corrective Learning

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 • 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.