Null-Space Minimization of Center of Gravity Displacementof a Redundant Aerial Manipulator

Abstract

Displacements of the base during trajectory tracking are a common issue in the control of aerial manipulators. These are caused by reaction torques transferred to the base due to the manipulator motion and, in particular, to the motion of its center of gravity. We present a novel approach to reduce base displacements of a kinematically redundant aerial manipulator by using null-space projection in the inverse kinematic control. A secondary objective function minimizes the horizontal displacement of the manipulator center of gravity. We test this algorithm on different trajectories for both three and four degrees of freedom (DOF) manipulators in a simulation environment. The results comparing our algorithm with inverse kinematic control without the null-space projection show up to an 80% reduction in the end-effector position error and an average of about 56% reduction in maximum base displacement. The simulation implementation also runs faster than in real-time in our code implementation. We provide a workspace analysis based on multiple stopping criteria such as excessive base displacement, joint velocities and end-effector position error for the 3 and 4 DOF manipulators. As expected, the 4 DOF manipulator has a larger workspace.

Trajectory Tracking Control of an Aerial Manipulator in the Presence of Disturbances and Model Uncertainties

“…However, a minimum joint velocity solution can be found replacing the inverse of the Generalized Jacobian with its pseudoinverse in Equation (19). In this case, it is also possible to adopt the method of the Extended Generalized Jacobian or the null-space projection method developed in [9] and [8], respectively.…”

“…Certain approaches aim to reduce the base motion at the mechanical design level, employing counter-balancing mechanisms or mass distribution strategies [7], while other methods exploit the kinematic redundancy of the manipulator to minimize the dynamic disturbance transferred from the manipulator to the UAV [8,9]. On the other hand, in space robotics, the control of floating-base manipulators has been addressed assuming the conservation of momentum [10] to compensate for base motions.…”