A Fast Numerical Solution for General Robotic Manipulators Using Parallel Processing

                                                                             by Siavash Farzan

 Introduction

   A general robotic manipulator is a combination of links and joints, where the joints are either prismatic (P) or revolute(R). In order to move the robotic end-effector along a certain path, the joint variables (t) must be controlled until the end-effector reaches the desired position and orientation (i.e. pose (t), where (t) = f((t)) ). Hence, given a desired pose (t), it is necessary to solve the inverse kinematics equation (t) = f^-1((t)).

   Here, we propose a robust and fast solution for the inverse kinematical 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 robot dependent 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 average of 20.48ms. The algorithm was implemented in C/C++ using 16 POSIX threads, and it can be easily expanded to use more threads and/or multi-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.

Figure 1. Visual representation of the proposed method in one dimension

Related work

From Computational Intelligence to Robotics: Using Evolutionary Algorithms to Solve the Inverse Kinematics Problem

                                                                             by Siavash Farzan

 Introduction

   Computational Intelligence has always had an impact on different areas including Robotics and Automation. In this project a robust and fast evolutionary-like solution for the inverse kinematic problem of general serial manipulators – i.e. any number and any combination of revolute and prismatic joints is proposed. It uses an iterative numerical approximation of the Inverse Jacobian and unlike other iterative methods, it is accurate and fast and works for any generic robotic manipulator –redundant or not- even at singular configuration of the joint variables.

   This approach is compared with some other evolutionary algorithms based on Genetic Algorithm to find the strengths and weaknesses of different CI methods for this problem.

   We demonstrate that high accuracy and the real time performance of our method by comparing it with two different approaches proposed in other papers, including a GPU-based one.

  Experimental results carried out on different robots showed that the new proposed approach is able to find a better solution compared to genetic algorithm methods; with fewer iterations, sub-millimeter accuracy and in real time.

   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.

Third place poster award, 6th annual MU IEEE Computational Intelligence Society (CIS) poster contest

    References

1. S. Farzan and G. N. DeSouza, "From D-H to Inverse Kinematics: A Fast Numerical Solution for General Robotic Manipulators Using Parallel Processing", Intelligent Robots and Systems (IROS), 2013 IEEE International Conference. (Submitted)