Yankov K. Inverse Kinematics for Educational Robot MOVER 4

Статья- Applied Researches in Technics, Technologies and Education ARTTE.- 2017- Vol. 5,- No.3, pp.212-224.
he solution of inverse kinematics is a necessary condition to realize the control of a manipulation robot. Generally, this is an undefined optimization task, and therefore it is a subject of constant interest from the authors of robot software. The object of this work is to discuss several possible solutions of the inverse problem for the MOVER 4 robot. The kinematics equations are generated in analytic form with the CINDY program. These equations are the source to obtain the closed form solution. This is the approach that creates the fastest and most economical computer-memory algorithms. The disadvantage is that closed-form solutions are possible for a class of manipulation systems (MS) with a limited number of degrees of freedom. The second approach is more general and applies to MS where a closed-form solution is not possible. The goal function that must be minimized is the distance between the end-effector coordinates and the target point and the constraint is that decision must belong to the joint space coordinates. The task is solved applying the Lagrange multipliers. The disadvantage of the method is the probability to fall into a singular configuration where the Jacobian is zero. The third approach is the cyclic coordinate descent method. In this case, the multiparametric optimization is reduced to a one-parametric. The minimum of the goal function depends on only one degree of freedom at a time to move the end effector to the target point. This method is applicable to manipulation systems with an unlimited number of degrees of freedom. The disadvantage is that the solution is a local rather than a global minimum.