Generation and optimal choice of joint trajectories using all solutions of inverse kinematics of general 6-R robots

ABSTRACT

In this article, an algorithm is presented that transforms a given trajectory of a general 6-R Robot in Cartesian task space (position and orientation) into all possible joint space trajectories. It is shown how all solutions of the inverse kinematics can be used to obtain continuous joint trajectories. Inverse kinematics yields up to 16 different solution paths in joint space and these joint paths are compared using different optimality criteria. To achieve this goal the Cartesian trajectory is discretized and at each instant the inverse kinematics is computed using a fast algorithm developed in Pfurner and Husty et al. In the set of joint angles corresponding to the inverse kinematics solutions coherent paths are determined and interpolated with quintic splines. Different boundary conditions for the construction of the splines are discussed. Using the splines some possibilities for the optimal choice among the paths using different criteria are presented.

KEYWORDS:

• 6-R robots
• inverse kinematics
• joint trajectory
• optimization

Acknowledgments

The research presented in this article was supported by the Translational Research project “KineControl” of theStandortagentur Tirol, Austria. M. Husty acknowledges the support of FWF project P 23831-N13, “Algebraic Methods in Collision Detection and Path Planning.” Mathias Brandstötter (UMIT Hall) is acknowledged for providing the data of the second example and the Figs. 8 and 9.

Appendix A

Notes

¹The trajectory in this example had been chosen such that the manipulator hits its boundary which can be seen clearly because of the gap in all joint trajectories.

A detailed discussion of this issue is subject to further research.