Predictive inverse kinematics with trajectory scaling for redundant manipulators based on quadratic optimization

Abstract

Redundant robots display unique capabilities, presenting equally unique challenges at the same time. The solution to the inverse kinematics (IK) problem needs to account for a greater number of unknowns (joint variables) than equations. The classic Jacobian pseudoinverse-based methods are well established and often used to solve the IK problems. However, they usually do not support the inclusion of joint position, velocity, and acceleration constraints. On the other hand, the constraints can be easily included when the IK is formulated as an optimization problem. Our method, the PQPIK-S (Predictive Quadratic Programming Inverse Kinematics with Scaling), is based on a quadratic programming formulation and includes trajectory scaling to slow down the desired manipulator motion if no solution satisfying the velocity and acceleration constraints can be found. As an extension over our previous QPIK-S method, the PQPIK-S computes the solution for several future steps inside the prediction window. The PQPIK-S is successfully tested in simulations utilizing a model of the KUKA LWR 4+ 7-DOF manipulator as well as in experiments using a real robot.