Zero Reaction Torque Trajectory Tracking of an Aerial Manipulator through Extended Generalized Jacobian

Abstract

Aerial manipulators are used in industrial and service robotics tasks such as assembly, inspection, and maintenance. One of the main challenges in aerial manipulation is related to the motion of the UAV base caused by manipulator disturbance torques and forces, which jeopardize the precision of the robot manipulator. In this paper, we propose two novel inverse kinematic control methods used to track a trajectory with an aerial manipulator while also considering resultant UAV base motions. The first method is adapted from the generalized Jacobian formulation used in space robotics and includes the change in system momentum resulting from gravity and UAV control forces in the inverse kinematic control equation. This approach is simulated for a 2 and 3 degree-of-freedom aerial manipulator tracking trajectories with the end-effector. Although the end-effector position error is approximately zero throughout the simulated task, we see significant undesired UAV base motions of several centimeters in magnitude. To ameliorate this by exploiting the kinematic redundancy, we modify the generalized Jacobian by adding an additional task constraint which minimizes the reaction torques from the manipulator, to form the extended generalized Jacobian. While the second approach results in improved precision and reduced base motion by an order of magnitude as compared to the generalized Jacobian, a drawback is the reduction in the available workspace as the solution seeks to minimize the manipulator center of gravity translation. We also demonstrate and compare both approaches in a load picking task. All the algorithms are completed computationally faster than real time in the MATLAB simulations, illustrating their potential for application in real-world experiments.

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

“…x e,des . The method can be seen as the closed-loop version of the Generalized Jacobian method, originally developed for space robotic manipulators mounted on a floating base and modified in [9] for aerial manipulator control. It has to be noticed that in the case of aerial manipulators, it is necessary that the algorithm also takes into account the effect of external forces (effect that is instead negligible for space manipulators, for which the conservation of momentum assumption can be exploited).…”

“…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.…”

“…In this field, inverse kinematic control algorithms based on the Generalized Jacobian enable the precise positioning of the end-effector. An adaptation of the Generalized Jacobian for aerial manipulation is detailed in [9], where gravity and UAV control forces are also considered.…”

“…The first algorithm operates at the velocity level and is based on the Generalized Jacobian method adapted to aerial manipulators [9]. As for CLIK algorithms, they include a feedback term on the joint velocities to compensate for the position error of the end-effector due to unknown disturbances and modeling errors.…”

“…It has to be noticed that, since multicopters are underactuated systems, the horizontal position of the UAV cannot be controlled independently but only by applying a combination of thrust force and roll torque. The coefficients of the PID controller used in the simulations are summarized in Table 1 [9]. The UAV base, in addition to the reaction torque and force due to the movement of the manipulator, is subject to the action of the following external forces:…”