The combination of Hamiltonian formalism and neural networks is playing an important role in dealing with chaotic systems. Aiming at the problem of motion control under the condition of unknown physical quantity and incomplete observation set, a trajectory prediction model based on conditional Hamiltonian generating network (CHGN) for incomplete observation image sequences is proposed. CHGN is composed of Conditional AutoEncoder (CVAE), Hamiltonian neural network (HNN) and Velocity–Verlet integrator. CVAE encoder converts the short-term continuous observation image sequence into target motion state features represented by generalized coordinates and generalized momentum, and generates the trajectory prediction image at the specified time. HNN is used to learn potential Hamiltonian physical quantities, so as to understand more chaotic system dynamics information to realize state cognition. Velocity–Verlet integrator predicts the motion state at any moment according to the Hamiltonian learned by HNN at the current moment. The motion state and the specified time are used as the input of CVAE decoder to generate the target prediction image from the potential motion space. Experimental results show that CHGN can accurately predict target trajectories over a long period of time based on incomplete short-term image sequences, and has better performance with minimum mean square error(MSE) on three physical system datasets than existing deep learning methods.

An accurate map is needed for the autonomous navigation of mobile robots in unknown environments. The application of laser radars has the advantages of high ranging accuracy and long ranging distances. Due to the small amount of data on laser radars and the influence of noise on the sensor itself, these amount to causing problems such as low accuracies of map construction and large positioning errors. Currently, the feature extraction of environmental line segments based on radar scanning data generally adopts the idea of recursion. However, the amount of calculations for applying recursion is large, and the threshold of extracted feature points needs to be set manually. Moreover, the fixed segmentation threshold will cause under-segmentation or over-segmentation. In this paper, an adaptive threshold-based feature extraction method for environmental line segments is proposed. The method denoises the original data first, and then an adaptive threshold of the nearest neighbor algorithm is provided to improve the accuracy of breakpoint judgment; next, the slope difference between adjacent line segments is evaluated according to the line segment fitting error in order to obtain the optimal corner feature. Finally, the point set is segmented to fit line-segment features. Based on actual environment tests, the environmental similarity of the line segment features extracted by the new algorithm in this paper increases by 8.3% compared with the IEPF (Iterative End Point Fit) algorithm. The algorithm avoids recursive operations, improves the efficiency by four times, and meets the real-time requirements of line segment fitting.