On inverse kinematics with nonlinear criteria: Trajectory relaxation

The concept of trajectory relaxation of Inverse Kinematics (IK) problem is thoroughly investigated in this pa­per. Trajectory relaxation refers to relaxing the hard-constraint of following a desired trajectory, hence the robot is allowed to deviate from that trajectory. The main advantages of this concept is improving the robustness of the IK solver and efficiently allowing the optimization of additional nonlinear criteria, for instance maximizing the manipulability index of the robot. We propose different formulations of the trajectory relax­ation as well as several functions to control the stiffness of the relaxed constraint. We conducted experiments in simulation to compare the proposed formulations and identify their strengths and weaknesses, we also validated the results on a Baxter research robot.