In triangular-lattice magnets, the coexistence of third-neighbor antiferromagnetic and nearest-neighbor ferromagnetic exchange interactions can induce rich magnetic phases including noncoplanar skyrmion crystals. Based on Monte Carlo simulation, we studied the dependence of magnetic phase transition on exchange interaction strength. Under the consideration of uniaxial anisotropy and magnetic field both perpendicular to the film plane, a large antiferromagnetic exchange interaction induces a high frustration. When the value of antiferromagnetic exchange interaction is one and a half times larger than the ferromagnetic one, a magnetic phase composed of canting spin stripes, never observed in the chiral magnets, forms. Interestingly, different canting spin stripes along three 120 degree propagation directions may coexist randomly in a magnetic phase, attesting that the canting spin stripes are three-fold degenerate states akin to helices and the multiple state of canting spin stripes is a circular configuration with zero skyrmion charge number. Moreover, skyrmions and antiskyrmions can be observed simultaneously in the configuration at the low temperature nearly close to 0 K, and their configuration and diameter properties are discussed. Finally, the mechanisms of skyrmion creation and annihilation are properly interpreted by comparing exchange and Zeeman energy terms.
The objective of the autonomous navigation aims to achieve the self-motion control for a robot with the environmental feedbacks and becomes popular recently. Problems of complex modeling, large amount of calculation, and lacking of environmental information always exist in autonomous navigation methods. This article proposes a self-navigation method with a fuzzy three-dimensional grid depicted by dual two-dimensional grid maps. Meanwhile, a synthetic preprocess is presented to perform localization through switching among the weighted three-point localization method, the two-point localization method, and the weighted average localization method. For reducing the amount of calculation, an improved fuzzy three-dimensional grid mapping method where the three-dimensional map is described by dual two-dimensional grid maps, the identifier map, and the height map is designed. Especially, the static and dynamic information within the map are divided and updated fuzzily. The global path planning is performed with the static information, and the real-time obstacle avoidance is conducted with the dynamic information. The results of simulations and experiments demonstrate that the proposed method has better properties in efficiency of navigation and lower amount of calculation than the competing methods.
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