| Abstract: |
| The problem of achieving an arbitrary orientation and tracking of suitable trajectory for a quadrotor is well studied
in literature. In this article, we propose a strategy to balance an inverted pendulum mounted on a quadrotor through a universal joint. This mechanical system, called flying inverted pendulum, was first introduced in [1] in which a linearization approach was used to stabilize the pendulum on the quadrotor. This is fairly restrictive if the initial position of the pendulum is not close to the inverted equilibrium position, and does not permit any statement on the domain of attraction of the controller. In this article, the quadrotor and pendulum are modeled as Lagrangian systems and the control law proposed admits convergence to the desired state from a large domain of initial conditions thus allowing aggressive maneuvers. The flying pendulum is the simplest model for a payload mounted on a quadrotor. Therefore the stability of such a mechanical system is a potentially important problem that has not been addressed in the literature. The problem of a payload suspended through cables from multiple quadrotors has been a topic of recent interest. In such a payload mounting, there can be issues of damage to the payload during landing of the quad. In the proposed model, a more practical method of transporting the payload is achieved by mounting it on top of the quad. In [1], the orientation of the quad is modeled using Euler angles which, once again, suffers from singularity issues and hence does not allow the control action to achieve aggressive maneuvers. Here, we employ a purely geometric model: the orientation of the quad is modeled as a rotation matrix and the pendulum is modeled as a spherical pendulum on the 2-sphere, thereby accounting for all possible configurations which the system may assume.
The contributions of this presentation are: 1. Geometric modeling of the system that allows a coordinate-free description
of the control law and a framework for making global statements for the stability, 2. a strict feedback form of
the part of the dynamics which has to be controlled is shown to exist which allows backstepping control to be
applied, and finally, 3. a backstepping control is used in a purely geometric setting by choosing appropriate Lyapunov functions.
[1] M. Hehn and R. D`Andrea. A flying inverted pendulum. In 2011 IEEE International Conference on Robotics and Automation, pages 763-770. IEEE, 2011. |
|