Parafoil airdrop is an important way to deliver goods and materials to area where road vehicles are not easy to reach. However, it is difficult to deliver large quantities of goods and materials to a given location with only one parafoil. Airdropping multiple parafoils is an effective choice for transporting large quantities of goods and materials. To realize the cooperative airdrop of multiple parafoils, a cooperative guidance framework is proposed. First, a trajectory planning algorithm is designed to plan the multiphase trajectory for the parafoil group. Then, a trajectory tracking algorithm is developed for the pilot parafoil in the parafoil group to reliably follow the planned trajectory. Finally, a cooperative formation guidance strategy is designed based on the leader-follower consensus theory. Under this strategy, the position and speed of the follower parafoil can be consensus with those of the leader parafoil. Lyapunov's theorem proves the stability of this strategy. We evaluate the effectiveness of this framework through simulations. The results demonstrate that our algorithms can realize the precise airdrop of massive goods and materials with upwind landing using multiple parafoils. In addition, the parafoils could be gradually gathered to a desired formation, and safe distances could be maintained between parafoils during the airdrop process.

The airdropping of multi-parafoil systems is of great significance to earthquake relief and military material transportation. In order to achieve the coordinated motion of multiple parafoils, a formation guidance strategy based on a virtual structure is proposed, which enables the formation of multiple parafoils to follow the planned trajectory and land at the target precisely. Firstly, since the main movement mode of a parafoil is turning and gliding, a multiphase homing trajectory for the reference point is planned, which mainly consists of a turning and gliding phase. Then, the trajectories of all the points on the virtual structure are generated by superimposing the relative positions of the virtual structure on the planned trajectory. Based on Lyapunov stability theory, a guidance strategy is designed to guide all parafoils to track the corresponding points on the virtual structure and complete the desired formation task. The simulation results show that the guidance strategy based on a virtual structure can effectively guide multiple parafoils to achieve coordinated formation movement. Parafoils dropped from different positions and heading angles can gradually gather together and form a formation, track the planned trajectories, land at the target point precisely and align up against the wind.

The powered parafoil system is obtained by adding the propeller thrust to the unpowered parafoil system, and has coupling and nonlinear characteristics, which make its precise control more difficult than that of the unpowered parafoil system. To achieve the trajectory tracking control of the powered parafoil system in the field of precision airdrop, a mathematical model of the 6-DOF of the powered parafoil system is established first. Then, a new trajectory tracking strategy is proposed, which can overcome the limitations of the traditional guidance-based trajectory tracking strategy. We design lateral, longitudinal, and velocity controllers on the basis of the motion characteristics of the powered parafoil system. Then, we adopt the widely used PID control strategy in engineering. In response to the difficult of the PID controller parameter tuning of the powered parafoil system, we achieve the PID controller parameter tuning with the ecosystem particle swarm optimization (ESPSO) of the swarm intelligence optimization algorithm. The effectiveness of the algorithm is verified by simulation experiments. Results show that the proposed algorithm can obtain high trajectory tracking accuracy even when a deviation in the initial state and a random gust wind disturbance in the outside world occur regardless of the method of the multiphase homing or the optimal control homing adopted. The proposed trajectory tracking strategy also has strong robustness and adaptability.

This paper presents a new three-dimensional (3D) imaging method for detecting the spatial structure of a complex inner cavity based on positron annihilation and γ-photon detection. This method first marks carrier solution by a certain radionuclide and injects it into the inner cavity where positrons are generated. Subsequently, γ-photons are released from positron annihilation, and the γ-photon detector ring is used for recording the γ-photons. Finally, the two-dimensional (2D) image slices of the inner cavity are constructed by the ordered-subset expectation maximization scheme and the 2D image slices are merged to the 3D image of the inner cavity. To eliminate the artifact in the reconstructed image due to the scattered γ-photons, a novel angle-traversal model is proposed for γ-photon single-scattering correction, in which the path of the single scattered γ-photon is analyzed from a spatial geometry perspective. Two experiments are conducted to verify the effectiveness of the proposed correction model and the advantage of the proposed testing method in detecting the spatial structure of the inner cavity, including the distribution of gas–liquid multi-phase mixture inside the inner cavity. The above two experiments indicate the potential of the proposed method as a new tool for accurately delineating the inner structures of industrial complex parts.

A pair of 511KeV γ-photons is generated during a positron annihilation. Their directions differ by 180°. The moving path and energy information can be utilized to form the 3D imaging test method in industrial domain. However, the scattered γ-photons are the major factors influencing the imaging precision of the test method. This study proposes a γ-photon single scattering correction method from the perspective of spatial geometry. The method first determines possible scattering points when the scattered γ-photon pair hits the detector pair. The range of scattering angle can then be calculated according to the energy window. Finally, the number of scattered γ-photons denotes the attenuation of the total scattered γ-photons along its moving path. The corrected γ-photons are obtained by deducting the scattered γ-photons from the original ones. Two experiments are conducted to verify the effectiveness of the proposed scattering correction method. The results concluded that the proposed scattering correction method can efficiently correct scattered γ-photons and improve the test accuracy.