Inverse Kinematics: New Method for Minimum Jerk Trajectory Generation

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 joints trajectories. Even-though the conventional inverse kinematics algorithms have been proven to be efficient in many applications, no contraintes on the accelerations or the jerk of the obtained trajectories can be guaranteed. The proposed algorithm yields smooth velocity and acceleration trajectories, which are mostly important in the case of humanoid robots as the balance is directly related to the joint accelerations. The algorithm is using the joints jerk as the control parameter instead of the classical use of the joints velocity, as a result constraints of the jerk function can be easily incorporated. To validate the proposed approach, a simulation scenario of a boxing motion with the humanoid robot HRP-2 has been conducted. The simulation results have revealed the effectiveness of the proposed method to solve the inverse kinematics problem while considering the joint jerks efficiently. I. INVERSE KINEMATICS PROBLEM: REVISITED The inverse kinematics problem is one of the most studied problems in robotics. Many efficient and robustness algorithms have been proposed for solving the inverse kinematics problem [1], [2]. The inverse kinematics problem was originally formulated as follows: min q̇ q̇t Qq̇t