Inverse Kinematics and Robot Motion
In the last lecture, we talked about robot forward kinematics, and forward kinematics is the relationship between the robot joint angles, which we represent by a vector I call 'Q, and the pose of the robot end effector.
We can describe this in terms of a mathematical function. We can describe forward kinematics as the function curly K of the robot joint angles, and the return value of that function is the pose of the end effector. This is very very useful in robotics, but more useful is what's called the 'Inverse Kinematics.'
This is the function that tells us that joint angles that we need in order to achieve a particular robot end effector pose.
So say we want the robots end effector to be at this particular pose in space, then what should the joint angles be set to in order for the robot end effector to get to that particular pose? This is called the 'Inverse Kinematics Problem' that's really key to arm type robots.
We will learn about inverse kinematics, that is, how to compute the robot’s joint angles given the desired pose of their end-effector and knowledge about the dimensions of its links. We will also learn about how to generate paths that lead to smooth coordinated motion of the end-effector.
High school mathematics
This content assumes an understanding of high school-level mathematics, e.g. trigonometry, algebra, calculus, physics (optics) and some knowledge/experience of programming (any language).
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A spray painting robot is planted on on a basement that allows it to freely move at least 1800. If the lower arm has a length of 0.96m, and a weight of 10kg. The upper arm bearing the end effector is 1.36m and 12 kg.
i. Estimate the angles at the two joints (Inverse Kinematics)
ii Using the joint angles in i above, find the coordinate position of the end effector (Forward Kinematics)
iii. Sketch the position of the end effector at that position