R3. Inverse kinematics

1. Info
2. Preparation
3. Tasks
- Task 1: Inverse kinematics of a double pendulum
- Task 2: Inverse kinematics of a spatial robot
4. Summary

1 Info

The assignment presents inverse kinematics for serial robot. To calculate IK Newton method and Robotics Toolbox functions are used.

The points marked with (*) are optional (not obligatory).

2 Preparation

Before the classes recall from the lecture definitions of robot inverse kinematics and singularities. Study the Newton algorithm applied to the inverse kinematics task. Design your implementation of the Newton algorithm. Consider which functions from standard Matlab libraries and the robotic toolbox will may be used to solve given tasks.

3 Tasks

Task 1: Inverse kinematics of a double pendulum

Write kinematics of a planar double pendulum with arm lengths l₁=1m and l₂=0.5m.
(*) Determine the work-space of the manipulator (note: use geometry properties of the robot shape or a scatter plot for possible joint angles)
Select an arbitrary point P=(x,y), find q₁ and q₂ for which K(q)=P.
For a square defined by two vertices from a diagonal: A=(0.5,-0.25),B=(1,0.25) use Newton method to find inverse kinematics for all vertices.
(*) use a solution from the previous item to simulate a motion of the manipulator between the vertices (test interpolation of intermediate points both in the joint-space and the task-space).

To report:
1. Include kinematics equations of the manipulator
2. Attach code of the algorithm and a chosen example (point P and the IK solution for it).
3. Is the solution to the IK task unique? Under what conditions?
4. Present solution of IK for the square vertices
5*. Present the result of interpolation. What is a difference between the task-space and joint-space solution? 6*. Comment on repeatability of the motion. Why it is important?

Task 2: Inverse kinematics of a spatial robot

Use kinematics of the 3R or KUKA(*) robot from the previous assignment.
Define the output variables of the robot (what is the output dimension?).
Find a solution of the inverse kinematics for a selected point.
Define a circle in the task-space. Select at least 6 evenly placed points on the circle. Determine the inverse kinematic solution for those points (note: one can use own implementation or toolbox function for the manipulator defined as SerialLink).
To report:
1. Include an equation of the circle and coordinates of the selected points
2. Include the code and the solution for those points
3*. Add the code and the plot presenting the configuration of the manipulator in the defined points.

4 Summary

The report should include the result of the tasks and answers to the questions.
Please do not forget to indicate the author of the report!
The report in PDF format should be submitted before the beginning of next classes using a method defined by the instructor.