Hi Christoph,
As you noted, the analyticalInverseKinematics solver is presently limited to 6-DoF robots with a wrist. Other solutions (general 6-DoF solutions and solutions for robots with less than 6 DoF) are certainly possible, and we are looking to include those in future enhancements. We chose to focus initially on the 6-DoF + wrist because it is a prominent configuration in industrial serial manipulators, and because for many users, a numerical solver that is not limited by robot topology is more appropriate. You can learn more about our numerical solvers here.
While your robot is not technically a valid form for analyticalInverseKinematics, since you are looking at a 3-DoF revolute robots and care only about position (not orientation), this is a subset of the supported robots and can be made to work with some light modifications. To do this, add 3 intersecting revolute joints to the end. Then the resultant robot can be passed to analyticalInverseKinematics.
Here's an example: We start by building a 3-DoF robot. To minimize lines of code, I'll just start with a 6-DoF robot and remove the last three joints.
robot = loadrobot('fanucM16ib',DataFormat="row");
removeBody(robot, 'link_4');
tgtConfig = [pi/4 pi/4 pi/4];
show(robot, tgtConfig, Visuals="off"); % Preview robot
This is your typical 3-DoF robot. Now make a copy of this and add the 3 placeholder revolute joints at the end.
robotWithExtraBodies = copy(robot);
jtRotations =[0 pi/2 -pi/2];
for i = 1:3
rb{i}=rigidBody("extraBody"+num2str(i));
rb{i}.Joint = rigidBodyJoint("J"+num2str(i), "revolute");
setFixedTransform(rb{i}.Joint, axang2tform([1 0 0 jtRotations(i)]));
addBody(robotWithExtraBodies, rb{i}, robotWithExtraBodies.BodyNames{end});
end
% Visualize and see that it's the same except there are some extra
% frames at the end
show(robotWithExtraBodies, [tgtConfig 0 0 0], Visuals="off");
You can now call analyticalInverseKinematics on the robot with the the extra DoF and generate a solver:
aik = analyticalInverseKinematics(robotWithExtraBodies);
ik=generateIKFunction(aik, "ikFcn");
Given the solver, compute an IK solution for a pose
% Use a pose that we know will work
feasiblePose=getTransform(robot, tgtConfig,robot.BodyNames{end});
computedConfigs = ik(feasiblePose,false)
% Since we only care about the first three joints, get the unique values
% and throw out the extra dimensions
[~, isUniqueValidRowIdx] = unique(computedConfigs(:,1:3), 'rows');
configs = computedConfigs(isUniqueValidRowIdx,1:3)
This works because the method we employ is based on Pieper [1968] (see the citation at the bottom of the doc page), which recognizes that if the last three joints form a wrist, then the orientation and pose problem can be decoupled.
You could actually look at the generated solver and extract just the pose problem -- it's the output of a function called solveFirstThreeDHJoints, but be aware that there is some additional mapping that you will need to do to succeed.
If you do want a completely symbolic solution for a 3DoF manipulator, this is a solved problem. I would recommend looking at Pieper [1968] or a similar but more specialized paper. I gave some additional comments to this effect in the above comment thread.
