From D-H to inverse kinematics: A fast numerical solution for general robotic manipulators using parallel processing

Abstract

We propose a robust and fast solution for the inverse kinematic problem of general serial manipulators -i.e. any number and any combination of revolute and prismatic joints. The algorithm only requires the Denavit-Hartenberg (D-H) representation of the robot as input and no training or robotdependent optimization function is needed. In order to handle singularities and to overcome the possibility of multiple paths in redundant robots, our approach relies on the computation of multiple (parallel) numerical estimations of the inverse Jacobian while it selects the current best path to the desire configuration of the end-effector. But unlike other iterative methods, our method achieves sub-millimeter accuracy in 20.48ms in average. The algorithm was implemented in C/C++ using 16 POSIX threads, and it can be easily expanded to use more threads and/or many-core GPUs. We demonstrate the high accuracy and the real-time performance of our method by testing it with five different robots, at both non-singular and singular configurations, including a 7-DoF redundant robot.

A parallel evolutionary solution for the inverse kinematics of generic robotic manipulators

“…First, we ran our algorithm using four different robots and compared the proposed parallel evolutionary method with the method presented in the previous work [1]. For the second experiment, we performed a comparison between the proposed method and two Genetic Algorithm approaches presented in [3] and [30], which were also discussed in Section II.…”

“…However, instead of choosing a single individual for the position of the end-effector,ˆ X -as in [1] u individuals are now chosen. The entire process above is performed in parallel, using:…”

“…The method relies on estimates of the actual Jacobian matrix, eliminating the need to find an analytical solution for the inverse Jacobian, which for many robots is not even feasible. However, unlike our previous greedy method [1], this parallel evolutionary method addresses the problem of selecting one single estimate at each iteration of the algorithm. Instead, by evaluating an entire generation of individuals in each iteration, the evolutionary method proposed here can better handle non-monotonic Forward/Inverse Kinematics functions while trying to achieve the fewest possible iterations to get end-effector to the desired position.…”

“…In our previous work [1], we presented a fast and accurate method using an iterative numerical approximation of the inverse Jacobian. In this paper, we improve our previous method by employing an evolutionary approach, while further reducing the number of iterations, keeping its real-time applicability to generic robot manipulators -i.e.…”

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This paper is an improvement of our previous work [1]. It provides a robust, fast and accurate solution for the inverse kinematics problem of generic serial manipulators -i.e.

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