1. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 ROBOT CONTROL T. Bajd and M. Mihelj

2. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Robot control deals with computation of the forces or torques which must be generated by the actuators in order to successfully accomplish the robot task. The robot task can be –execution of the motion in a free space, where position control is performed, or –in contact with the environment, where control of the contact force is required. The choice of the control method depends on –the robot task, –the mechanical structure of the robot mechanism. Robot control usually takes place in the world coordinate frame, which is defined by the user and is called also the coordinate frame of the robot task. Robot control

3. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 General control approach End-effector pose PositionOrientation RPY notation of the orientation

4. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Control loop is closed separately for each particular degree of freedom Less suitable for robotic systems characterized by nonlinear and time varying behavior Position error computation –Reference positions –Measured robot joint positions –Position error PD position control

5. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Control law; computation of control variable (torque, velocity) Actuation of robot motors is proportional to the error Velocity feedback loop introduces damping into the system Velocity error can be introduced into the control law (faster system response) leading to PD position control

6. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Block schemes

7. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Robot inverse dynamic model In static conditions can be simplified to Estimated gravity term part of the control law PD position control with gravity compensation

8. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 PD position control with gravity compensation

9. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Robot inverse dynamic model Robot forward dynamic model Define new variable leading to Robot dynamic model

10. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Assume that the robot dynamic model is known –inertial matrix is an approximation of real values, – represents an approximation of Consider the following control law where input y will be defined later. Inverse dynamics control

11. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Inverse dynamics control block scheme y represents computed acceleration in joint space

12. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 position error velocity error control law error dynamics PD position control

13. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Controller block scheme

14. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Definition of pose error Control based on the transposed Jacobian matrix Control based on the inverse Jacobian matrix Robot control in external coordinates

15. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 End-effector position Differential kinematics Manipulator Jacobian matrix Jacobian matrix

16. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Jacobian matrix Manipulator Jacobian matrix

17. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Inverse velocity relation For a square matrix of dimension two Inverse velocity relation Inverse Jacobian matrix equals Inverse Jacobian matrix

18. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Robot in contact with the environment (contact force f ) Find resulting joint torques In matrix form Transposed Jacobian matrix

19. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Velocity relation Force/torque relation Transposed matrix Force/torque relation Transposed Jacobian matrix

20. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Pose error in external coordinates Control law formulation (control variable in external coordinates) Control variable in joint space Transposed Jacobian matrix based Control

21. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Velocity relation Relation for small displacements Relation for small pose errors Control law in joint space Inverse Jacobian matrix based Control

22. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 PD position control with gravity compensation in external coordinates Control law

23. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Inverse dynamics Velocity relation Acceleration relation Computed acceleration for external coordinates control Inverse dynamics control in external coordinates

24. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Pose error Velocity error Acceleration error Error dynamics Control law Inverse dynamics control in external coordinates

25. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Inverse dynamics control in external coordinates – block scheme

26. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 control of end-effector desired pose while the robot is in contact with the environment –case of robot assembly (inserting a peg into a hole) –robot movement assures minimal contact force during action robot end-effector exerts a predetermined force on the environment –case of machining parts with robot (grinding) –robot movement depends on the difference between the desired and the actual contact force. Control of contact force with environment

27. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Dynamic model with contact force Define new variable leading to Robot dynamics with contact result of interaction with the environment

28. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Inverse dynamics with contact Forward dynamics with contact Control law Inverse dynamics control with contact

29. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Force control is based on position control Reference values for acceleration, velocity and pose are computed from force error Force control

30. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Force error Predefined manipulator behavior via inertia and damping matrices and Reference trajectory Force control

31. T. Bajd, M. Mihelj, J. Lenarčič, A. Stanovnik, M. Munih, Robotics, Springer, 2010 Parallel composition assumes force control in certain direction and pose control in other directions Parallel composition