A Nullspace-Based Predictive Control Allocation for the Control of a Quadcopter Manipulating an Object Attached to the Ground

In this paper, we propose a novel optimal predictive control allocation for the control of a quadcopter manipulating an object attached to the ground. This controller sprucely takes advantage of the nullspace of the quadcopter attitude mapped to the effective force to compute the optimal sequence of controls and attitude references. In particular, at each time instant, the controller solves a nonlinear minimization problem, where a specialized term is added to the cost function to penalize the deviation of the desired attitude from its nullspace, which is the attitude subspace for which any thrust generates zero effective force on the system. The weight associated to this specialized term uses a Gaussian bell-curve function to make the tuning of the attitude-reference generation more flexible and enhance the performance of the controller. To demonstrate the effectiveness of the proposed controller, numerical simulations of two different cases are provided.