1. Basilio Bona DAUIN – Politecnico di Torino
13/06/2018
ROBOTICS 01PEEQW
Basilio Bona
DAUIN – Politecnico di Torino
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2. Planar 2 DOF manipulator Reference planner: a numerical example
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

3. Planar two-arm manipulator – 1
This simple manipulator
cannot provide 3 DOF,
since it has only two joints
We will compute below
the kinematics functions
This is the third
Euler angle
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

4. Planar two-arm manipulator – 2
Direct position KF, assuming
Direct velocity KF
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

5. Planar two-arm manipulator – 3
Analytical Jacobian
Geometric Jacobian, assuming
All joints are revolute, hence:
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

6. Reference planner – sampled time
Use the approach
Use the s-function planner
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

7. Accelerations Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

8. Velocities
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

9. Example: angles Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

10. Cartesian space velocities
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

11. Cartesian space positions
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

12. Cartesian space velocities
Vmax = 2.0
Vmax = 1.5
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016

13. Joint space
Basilio Bona - DAUIN - PoliTo
ROBOTICS 01PEEQW /2016