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Inverse Kinematics
In most of case, robots have to fulfill tasks defined in a 3D Cartesian space. However, the commands sent to the motor are angles, the problem to find the Joint Angles given the position of the end effector is called inverse kinematics. When the problem is under constraint (when, for example, we have more Joint Angles than Cartesian coordinates) there is a infinity of solutions. To solve this problem, some additional constraints are added to the system. The constraints are extracted from a set of demonstrations and used to optimize the position control of the arm.
Constraints-based Optimization
A Cost Function has been defined which is a weighted linear combination of errors between the demonstration and the reproduction of the Joint Angle trajectory, of the Cartesian trajectory related to the robot and of the Cartesian trajectory related to the goal. Using Lagrange optimisation to derive the cost function, we obtain a extended Inverse Kinematics algorithm which is used to reproduce the learned movement. The robot is then able to reproduce the movement for different goal positions.
Acknowledgment
This work was supported in part by the Swiss National Science Foundation, through grant no 620-066127 of the SNF Professorships program and by the European Commission Division FP6-IST Future and Emerging Technologies under Contract FP6-002020, EU Integrated Project COGNIRON.
Videos
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| Learning and reproducing the grasping of a chess piece (1:10) DivX, 6.3Mb |
Learning to grab a ball with two hands (1:18) DivX, 7.2Mb |
learning to hit a dot using a hammer (1:13) DivX, 6.2Mb |
Selected Publications
People involved in this project