An inverse kinematics solution with trajectory scaling for redundant manipulators

Abstract

Kinematic redundancy offers robots many useful capabilities, such as an ability to fulfill several tasks simultaneously. However, the inverse kinematics (IK) problem for redundant manipulators is not trivial. Often, pseudoinverse-based methods are used, allowing for the projection of the desired joint space velocity vector on the null space of the manipulator’s Jacobian. Unfortunately, it is not straightforward to include in the solution the joint position, velocity and acceleration bounds. On the other hand, the IK problem can be formulated as an optimization problem. A quadratic programming (QP) formulation is especially attractive for an online implementation, since it is computationally much lighter than nonlinear optimization methods. In a QP IK formulation, the joint constraints can be easily included. However, if the desired end effector trajectory becomes too demanding, then the joint space solution might not exist. To overcome this obstacle, we propose a QP IK formulation with trajectory scaling. The method is successfully tested on a model of KUKA LWR4+ 7-DOF manipulator; the joint constraints are satisfied and the motion is slowed down only when it is necessary.