Analytical Inverse Kinematic Solution for Original Robotic Manipulator Construction

Author Name(s): Alexey D. Shamraev, Igor P. Balabanov, Rustem R. Ziyatdinov
Author Email: shamraev.leha@mail.ru

Abstract

During robot development, one of the main problems is the problem of more weight transfer to the greatest distance. The article discusses the robot kinematics, where all the movers are located as close as possible to the carrier link axis. All link engines perform rotational movements. This can significantly increase the payload of the robot. Due to kinematic relationships, the motion of one robot link is difficult to describe both in the Cartesian coordinate system and in the spherical one. The article proposes the solution to the problem of the robot intermediate link position determination, with a known position of the end unit. We analyzed such options for the problem solution as the inverse transformation method, the analytical method, the interval method, the finite rotation and displacement method, the biquaternion solution, Mesh-based Inverse Kinematics, and FABRIK. The analytical method was optimal for the kinematics of the manipulator under consideration. Mathematical formulas are obtained that allow one to obtain the position of the intermediate links after the method application. The resulting mathematical models will allow you to get the position of the manipulator intermediate links, to create a virtual manipulator and debug a control program on stationary computing systems. The resulting mathematical models are quite simple. Their calculation can be entrusted to a low-power computing system. This will allow the creation of autonomous adaptive systems using artificial intelligence.

Introduction

During robot design, one of the main problems is the problem of more weight transfer to the greatest distance. They try to solve the restrictions imposed by the laws of physics mainly by propulsion power increase. But it is obvious that a lot of power leads to weight increase and the robot is already engaged in its own weight transfer. For example, KUKA KR AGILUS manipulators are designed in this way [1]. The second way is to design the kinematics of the manipulator in an original way. To transfer the robot weight to the center of rotation in balanced way, and spend energy on useful work. For example, ABB IRB-460 manipulators are constructed in this way [2]. The first type of robot is quite easily described by mathematical equations in a spherical coordinate system. The second type of robot is quite difficult to describe both in spherical and Cartesian coordinate system. Since we are used to think in Cartesian coordinate system, this is the way of coordinate representation that should be preferred. The robots like IRB-460 are quite simple to design. Increasingly, such manipulators are designed and manufactured in a single copy by small companies for private use in small industries. The manipulator design is simple. Low cost of the manipulator manufacturing and maintenance are the main advantages of these robots. But the system for the final link position calculation is complicated. At the moment, mathematical models to control the robots like IRB-460 are hidden from an average user. The user creates a robot movement program using a practical method more and more often. It outputs the end unit to the starting point and remembers the position of the intermediate units. The number of key points can reach several hundred. This way of programming a robot is extremely inefficient. This article proposes the methodology for calculating the position of the intermediate units for the manipulator of IRB460 type.

Conclusion

The inverse kinematics problem of the non-trivial structure of a robot-manipulator with three degrees of freedom has been solved analytically, admissible values of generalized coordinates have been found.

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