A dynamic path-planning algorithm based on a general constrained optimization problem (GCOP) model and a sequential quadratic programming (SQP) method with sensor input is proposed in this paper. In an unknown underwater space, the turtle-inspired amphibious spherical robot (ASR) can realise the path-planning control movement and achieve collision avoidance. Due to the special underwater environments, thrusters and diamond parallel legs (DPLs) are installed in the lower hemisphere to realise accurate motion control. A propulsion model for a novel water-jet thruster based on experimental analysis and a modified Denavit–Hartenberg (MDH) algorithm are developed for multiple degrees of freedom (MDOF) to realize high-precision and high-speed motion control. Simulations and experiments verify that the effectiveness of the GCOP and SQP algorithms can realize reasonable path planning and make it possible to improve the flexibility of underwater movement with a small estimation error.

In an integral imaging (II) display system, the self-adjustment ability of the human eye can result in blurry observations when viewing 3D targets outside the focal plane within a specific range. This can impact the overall imaging quality of the II system. This research examines the visual characteristics of the human eye and analyzes the path of light from a point source to the eye in the process of capturing and reconstructing the light field. Then, an overall depth of field (DOF) model of II is derived based on the human visual system (HVS). On this basis, an II system based on the human visual distance (HVD) perception model is proposed, and an interactive II display system is constructed. The experimental results confirm the effectiveness of the proposed method. The display system improves the viewing distance range, enhances spatial resolution and provides better stereoscopic display effects. When comparing our method with three other methods, it is clear that our approach produces better results in optical experiments and objective evaluations: the cumulative probability of blur detection (CPBD) value is 38.73%, the structural similarity index (SSIM) value is 86.56%, and the peak signal-to-noise ratio (PSNR) value is 31.12. These values align with subjective evaluations based on the characteristics of the human visual system.

Trajectory prediction constitutes a key technology for intelligent systems to forecast future movements of dynamic agents, yet it faces significant challenges due to the uncertainty of motion behavior. We propose iDMa, a stochastic trajectory prediction framework that pioneers the integration of diffusion model with Mamba architecture to achieve high-precision and high-efficiency trajectory generation. Our approach introduces two key innovations: (1) a dual-parameter learning mechanism that optimizes noise estimation of mean and variance space, unlike conventional diffusion methods that employ fixed variance during the denoising process, so as to constrain the feasible domain more accurately; (2) a hybrid denoising backbone network that incorporates Transformer encoders and Mamba blocks. Compared to existing state-of-the-art methods, iDMa reduces the average displacement error (ADE) by 4.76% (0.20 vs. 0.21) on the ETH-UCY dataset and 1.85% (7.95 vs. 8.10) on the SDD dataset.