C04 – 2009.02.12 Advanced Robotics for Autonomous Manipulation

1. Department of Mechanical Engineering ME 696 – Advanced Topics in Mechanical Engineering C04– 2009.02.12 Advanced Robotics for Autonomous Manipulation Giacomo Marani Autonomous Systems Laboratory, University of Hawaii http://www2.hawaii.edu/~marani 1

2. ME696 - Advanced Robotics – C04 Contents 1. Vectors deriv. 2. Angular velocity 3. Derivative for P. 4. Generalized Vel. 5. Derivative for R 6. Joint Kinematics 7. Simple kin. Joint Summary Kinematics of robotics structures Forward kinematics Inverse kinematics Closing the loop Kinematics – Part A 2

3. ME696 - Advanced Robotics – C04 Recap if geometric problem: Kinematics of robotic structures 3

4. ME696 - Advanced Robotics – C02 Kinematic problems Kinematics of robotic structures 4

5. ME696 - Advanced Robotics – C02 Direct kinematic problem (Forward kinematics) Direct kinematic problem 5

6. ME696 - Advanced Robotics – C02 Direct kinematic problem 6

7. ME696 - Advanced Robotics – C02 Kinematics of the joints 7

8. Contents RMRC: General issues Resolved Motion Rate Control (RMRC) is a local method for solving inverse kinematics problems. It uses the Jacobian J of the forward kinematics to describe a change of the endeffector’s position as: This equation can be solved for using pseudo-inverse methods: • Introduction • Theory • RMRC • Feedback loop • Position prior orient. • Singularity avoidance • Manipulability • Joint saturation • Path planner • Software architecture • Conclusion Theory Resolved Motion Rate Control 8

9. Contents In real situation, Resolved Motion Rate Control needs feedback loop to work in presence of various uncertainties.The objective of the control scheme is fundamentally that of making the global error asymptotically converging toward zero. • Introduction • Theory • RMRC • Feedback loop • Position prior orient. • Singularity avoidance • Manipulability • Joint saturation • Path planner • Software architecture • Conclusion Theory Closing the feedback loop The inputs is the target transformation matrix T*. Block Qf, translates the end effector cartesian velocity X* control signal into a corresponding set of seven joint velocity reference inputs. 9

10. Contents Position prior orientation In autonomous robotic systems, the subtask decomposition between position and orientation is advantageous, because it will enlarge the reachable workspace of the first-priority manipulation variable (position) by allowing incompleteness for the second priority subtask (orientation). • Introduction • Theory • RMRC • Feedback loop • Position prior orient. • Singularity avoidance • Manipulability • Joint saturation • Path planner • Software architecture • Conclusion Theory Local optimization: position prior orientation 10

11. Contents Theoretically, equation for changes as following: • Introduction • Theory • RMRC • Feedback loop • Position prior orient. • Singularity avoidance • Manipulability • Joint saturation • Path planner • Software architecture • Conclusion First manipulation variable. Theory  Contribution of the second manipulation variable, without disturbing r1  Third manipulation variable, mapped onto a subspace that affects neither r1 nor r2 Local optimization: position prior orientation Overall 11

12. Contents Singularity avoidance In autonomous system the main problem is to ensure a reliable motion everywhere in the workspace, in order to avoid any locking of the system or unwanted motions when approaching to singularity configurations. Because the human intervention is limited or absent, the controller should be capable of a “smart” choice of best solution in order to ensure completeness of the required task when it has solution. Yoshikawa (1984) proposed a continuous measure that can be considered as a kind of distance from singularity points: • Introduction • Theory • RMRC • Feedback loop • Position prior orient. • Singularity avoidance • Manipulability • Joint saturation • Path planner • Software architecture • Conclusion Theory Singularity avoidance 12

13. Singularity point Mom = constant Trajectory r(t) Contents The proposed method allows to avoid singularities by moving, when approaching to them, along surfaces where Mom is constants: • Introduction • Theory • RMRC • Feedback loop • Position prior orient. • Singularity avoidance • Manipulability • Joint saturation • Path planner • Software architecture • Conclusion Theory Singularity avoidance This is done projecting the error on the surface where mom is constant. 13

14. Contents Local maximization of manipulability We can use redundancy in order to maximize the manipulability. The method uses a potential function as third manipulation variable: • Introduction • Theory • RMRC • Feedback loop • Position prior orient. • Singularity avoidance • Manipulability • Joint saturation • Path planner • Software architecture • Conclusion Theory Local maximization of manipulability This may help to keep the manipulator as far as possible from singularity configurations. Without Maximization of Mom With Maximization of Mom 14

15. End of presentation