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--- ece4560:lynx6:03invkin [2017/11/04 19:48] – created pvela
+++ ece4560:lynx6:03invkin [2024/08/20 21:38] (current) – external edit 127.0.0.1
@@ Line 3: / Line 3: @@
 Using the link lengths of your manipulator as defined in its forward kinematics, work out the inverse kinematics for the Lynx-6 end-effector.  That is, given a desired end-effector configuration $g_e^* \in SE(3)$, figure out a joint configuration $\vec \alpha$ that places the manipulator end-effector there if it is possible to do so.  If it is not, then indicate as much.
+===== Dealing with Kinematic Insufficiency =====
+------------------------------------------------
+The Lynx-6 manipulator is not fully dextrous, so many end-effector configurations are simply not possible.  The first logical test is whether the wrist is achievable or not.  The next sensible test deals with the orientation at the wrist: the Lynx-6 cannot arbitrarily reorient.  Still work out the solution as though the wrist does have full $SO(3)$ control.  When you compute the rotation matrix of achievable orientations, you will get a special form.
+Explain what that special form is and describe what test should be performed to verify that the desired orientation is realizable. Incorporate this test into the inverse kinematics so that a failure flag is returned if it is not possible.
 ==== Checking Validity ====
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 A more fun option would be to use the ''lynx6'' display code to see if it really works out. To visualize the target end-effector configuration, plot it using the $SE(3)$ class, then see if the end-effector really ends up there.
+==== Debugging ====
+To debug your program for the inverse kinematics, it helps a lot to first compute the forward kinematics for easy angles.  Things like the zero configuration (your output should be the zero-vector for $\alpha$).  Then set $\alpha_1$ to something easy, like 45 or 30 degrees.  After that move on to $\alpha_3$ or some other joint that does sensible things, and use easy angles (like $\pm$90 degrees).
+===== Position Inverse Kinematics ====
+---------------------------------------
+//Not Required//
+An extra bonus would be to check if the position can be achieved even if the orientation cannot.  This requires identifying yet a different test that would indicate the hand can be set to point at the desired position even if the orientation cannot be achieved.  This one is a bit trickier.
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