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Common technique to generate trajectory in robotics

but it has some performance problems..

more efficient technique to generate trajectory is the trapezoidal profile..

however it has a problem that robot can be unstable because of its discrete acc/deceleration.

(generally, this has lower bandwidth relatively.. it can be ignored)

* Ref :

[1] https://moocs.qut.edu.au/courses/814/learn

linear interpolation 방식으로 position은 간단하게 interpolation할 수 있었으나

orientation의 경우, rotation matrix를 interpolation하면 아래와 같은 문제가 발생한다. 

따라서 Euler angle이나 RPY를 interpolation해야 하는데, 이 경우에도 문제는 있다..

바로 아래와 같은 direction problem이다.

그렇다면 우리는 효율적인 orientation interpolation 방법에 대해 궁금해질 차례이다.

아래를 보면 그 해답을 알 수 있다.

* Ref :

[1] https://moocs.qut.edu.au/courses/814/learn

KINEMATIC control of a robot manipulator consists of solving the control problem in two stages, i.e., the desired task trajectory is transformed via the inverse kinematics into corresponding joint trajectories, which then constitute the reference inputs to some joint space control scheme [1]. This approach differs from operational space control [2] in the sense that manipulator kinematics is handled outside the control loop, thus allowing the problem of kinematic singularities and/or redundancy to be solved separately from the motion control problem. Moreover, most built-in controllers of industrial robots are based on joint servos and, thus, they can be easily embedded into a kinematic control strategy.

* Ref

[1] Fabrizio Caccavale, Student Member, IEEE, Stefano Chiaverini, and Bruno Siciliano, Senior Member, IEEE, Second-Order Kinematic Control of Robot Manipulators with Jacobian Damped LeastSquares Inverse: Theory and Experiments, IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 2, NO. 3, SEPTEMBER 1997.

to reduce..

- the peak acceleration on the robot mechanism

- vibration in the structure of the robot

- the size of the motors required to drive the robot

* Ref :

[1] https://moocs.qut.edu.au/courses/814/learn

path

a set of points in space 

trajectory

a set of points in space and a schedule for reaching each point

* Ref :

[1] https://moocs.qut.edu.au/courses/814/learn

* Ref :

[1] https://moocs.qut.edu.au/courses/814/learn

* Ref :

[1] https://moocs.qut.edu.au/courses/814/learn

* Ref :

[1] https://moocs.qut.edu.au/courses/814/learn

* Ref :

[1] https://moocs.qut.edu.au/courses/814/learn

A singularity occurs when the middle rotation in the sequence makes the rotation axes of the first and third rotations parallel.

(A singularity in a three-angle sequence is sometimes referred to as gimbal lock.)

Think about the PUMA560 robot whose 4th joint and 6th joint are aligned. If 4th joint increases and 6th joint decreases with same rates at the same time, the orientation of end effector will not be changed.

So, we lose some degree of freedom!

* Ref :

[1] https://moocs.qut.edu.au/courses/814/learn