Which the best approach to solve inverse kinematic problem of 7 DOF industrial robot online such as Kuka LBR iiwa, I mean closed form solution by geometry method or numerical solution which is Jacobean based method
inverse kinematic of 7 DOF KUKA LBR iiwa
-
ali78141 -
November 25, 2016 at 3:13 AM -
Thread is marked as Resolved.
-
-
I went with a numerical IK solution as it allows you to impose a secondary objective easily (such as avoiding joint limits) and at the same time is fast enough to be implemented in real-time (I ran it at 1000Hz). Furthermore, it is fairly easy to implement using a standard matrix library such as Eigen. The algorithm that I used was a specific case of the algorithm described in this paper: https://pp.bme.hu/eecs/article/download/7163/6169, where a nonlinear joint transformation is used to optimally impose joint limit avoidance for a redundant manipulator like IIWA. The example that they give in this paper uses a tan(.) transformation, but I used a parabolic transformation instead .
Additionally, singularity avoidance can be done in a very simple way by setting the joint limits to the limits of the solution branch bracketed by singularities (with some margin of course!). There are 8 solution branches obtained by combination of A2 (+/-), A4(+/-) and A6(+/-) elbow configurations (2x2x2=8). If you must move between branches, then you may need to do either jump the singularities in joint space or modify the cartesian input to avoid computing solutions near singularities. -
Thank you very much for your reply, yes numerical solution is more general and flexible to add more objective, only it has more computational time in comparison with the analytical solution, and also analytical solution can only apply to a specific robot configuration such as a robot with spherical wrist robot. That is what I conclude from some Literature Revie. The challenge will how to deal with computational time, as the solution will be implemented in real time.
-
I implemented the IK solver in hard real-time (1000Hz loop rate, using a real-time patched linux). By using solution from previous iteration to seed the solver for current time step, you can expect very fast convergence (typically in 2-3 iterations). I was able to compute IK for 3 different cartesian trajectories at 1000Hz hard real time simultaneously. As far as I know, you cannot sense/command LBR IIWA faster than 1000Hz, so as long as your client machine is able to keep up, numerical IK should work out just fine.
-
I am starting doing PhD and my topic will be Online path planning optimization of redundant robot, now I am preparing my proposal, and I have to suggest approaches to design fast and simple algorithm to implement online. The optimization method should consider different criteria such as minimum cycle time and maximum redundancy; so far, I am still at the theoretical level. In future, I am going to work on Kuka LBR iiwa.