Abstract

The direct kinematics problem for parallel robots can be stated as follows: given values of the joint variables, the corresponding Cartesian variable values, the pose of the end-effector, must be found. Most of the times the direct kinematics problem involves the solution of a system of non-linear equations. The most efficient methods to solve such kind of equations assume convexity in a cost function which minimum is the solution of the non-linear system. In consequence, the capacity of such methods depends on the knowledge about an starting point which neighboring region is convex, hence the method can find the global minimum. This article propose a method based on probabilistic learning about an adequate starting point for the Dogleg method which assumes local convexity of the function. The proposed method efficiently avoids the local minima, without need of human intervention or apriori knowledge, thus it shows a more robust performance than the simple Dogleg method or other gradient based methods. To demonstrate the performance of the proposed hybrid method, numerical experiments and the respective discussion are presented. The proposal can be extended to other structures of closed-kinematics chains, to the general solution of systems of non-linear equations, and to the minimization of non-linear functions.