The closed kinematic structure of Gough–Stewart platforms causes the kinematic control problem, particularly forward kinematics. In the traditional hybrid algorithm (backpropagation neural network and Newton–Raphson), it is difficult for the neural network part to train different datasets, causing training errors. Moreover, the Newton–Raphson method is unable to operate on a singular Jacobian matrix. In this study, in order to solve the forward kinematics problem of Gough–Stewart platforms, a new hybrid algorithm is proposed based on the combination of an artificial bee colony (ABC)–optimized BP neural network (ABC–BPNN) and a numerical algorithm. ABC greatly improves the prediction ability of neural networks and can provide a superb initial value to numerical algorithms. In the design of numerical algorithms, a modification of Newton’s method (QMn-M) is introduced to solve the problem that the traditional algorithm model cannot be solved when it is trapped in singular matrix. Results show that the maximal improvement in ABC–BPNN error optimization was 46.3%, while the RMSE index decreased by 42.1%. Experiments showed the feasibility of QMn-M in solving singular matrix data, while the percentage improvement in performance for the average number of iterations and required time was 14.4% and 13.9%, respectively.

Quadrotors play a crucial role in the national economy. The control technology for quadrotor-slung load transportation systems has become a research hotspot. However, the underactuated load’s swing poses significant challenges to the stability of the system. In this paper, we propose a Lyapunov-based control strategy, to ensure the stability of the quadrotor-slung load transportation system while satisfying the constraints of the load’s swing angles. Firstly, a position controller without swing angle constraints is proposed, to ensure the stability of the system. Then, a barrier Lyapunov function based on the load’s swing angle constraints is constructed, and an anti-swing controller is designed to guarantee the states’ asymptotic stability. Finally, a PD controller is designed, to drive the actual angles to the virtual ones, which are extracted from the position controller. The effectiveness of the control method is verified by comparing it to the results of the LQR algorithm. The proposed control method not only guarantees the payload’s swing angle constraints but also reduces energy consumption.