On inverse kinematics with inequality constraints: new insights into minimum jerk trajectory generation

Graphical Abstract

Abstract

The problem of inverse kinematics is revisited in the present paper. The paper is focusing on the problem of solving the inverse kinematics problem while minimizing the jerk of the joint trajectories. Even though the conventional inverse kinematics algorithms have been proven to be efficient in many applications, it has been proven that constraints on the accelerations or the jerk cannot be guaranteed, and even yields to divergence or makes the problem unsolvable. The proposed algorithm yields smooth velocity and acceleration trajectories, which are highly desired features for industrial robots. The algorithm uses the joint jerk as the control parameter instead of the classical use of the joint velocity as result constraints on the jerk function can be easily incorporated. To validate the proposed approach, we have conducted several simulations scenarios. The simulation results have revealed that the proposed method can efficiently solve the inverse kinematics problem while considering constraints on the joint acceleration and jerk.

Keywords:

• Inverse kinematics
• acceleration limits
• smooth motions
• minimum jerk
• quadratic programming

Notes

No potential conflict of interest was reported by the authors.

A preliminary version of the paper has been presented at the Workshop on Whole-Body Control for Robots in the Real World, IROS 2014.

Additional information

Funding

This research is partially supported by a discovery grant (Prof. Wael Suleiman) from the Natural Sciences and Engineering Research Council of Canada (NSERC).