Manipulability in trajectory tracking for constrained redundant manipulators via sequential quadratic programming

Abstract

Trajectory tracking methods for constrained redundant manipulators are presented in this thesis, where the end-effector of a redundant serial manipulator has to track a desired trajectory while some points on its kinematic chain satisfy one or more constraints. In addition, two manipulability indexes are taken into account in order to optimize the trajectory. The first index is defined in terms of the geometric Jacobian of the manipulator in the constrained configuration. The second index is based on the constrained Jacobian, which maps velocities from joint space to task space, taking into account the holonomic constraints. Three methods for solving the trajectory tracking problem are discussed. The first two, kinematic control (KC) and quadratic programming (QP), are widely discussed in literature. The third, sequential quadratic programming (SQP), is a new approach, unlike KC or QP, has as advantages (despite some shortcomings) not explicitly depend on pseudoinverse Jacobian, derivative from the desired trajectory and linearization of indexes or constraints. A discussion of these three methods is presented in terms of tracking error, constraint violation, singularity distance, among others through experiments performed on a Baxter collaborative robot.