We introduce a differentiable moving particle representation based on the multi-level partition of unity (MPU) to represent dynamic implicit geometries. At the core of our representation are two groups of particles, named feature particles and sample particles, which can move in space and produce dynamic surfaces according to external velocity fields or optimization gradients. These two particle groups iteratively guide and correct each other by alternating their roles as inputs and outputs. Each feature particle carries a set of coefficients for a local quadratic patch. These particle patches are assembled with partition-of-unity weights to derive a continuous implicit global shape. Each sampling particle carries its position and orientation, serving as dense surface samples for optimization tasks. Based on these moving particles, we develop a fully differentiable framework to infer and evolve highly detailed implicit geometries, enhanced by a multi-level background grid for particle adaptivity, across different inverse tasks. We demonstrated the efficacy of our representation through various benchmark comparisons with state-of-the-art neural representations, achieving lower memory consumption, fewer training iterations, and orders of magnitude higher accuracy in handling topologically complex objects and dynamic tracking tasks.

Elucidation of the mechanism by which the shape of bones is formed is essential for understanding vertebrate development. Bones support the body of vertebrates by withstanding external loads, such as those imposed by gravity and muscle tension. Many studies have reported that bone formation varies in response to external loads. An increased external load induces bone synthesis, whereas a decreased external load induces bone resorption. This relationship led to the hypothesis that bone shape adapts to external load. In fact, by simulating this relationship through topology optimization, the internal trabecular structure of bones can be successfully reproduced, thereby facilitating the study of bone diseases. In contrast, there have been few attempts to simulate the external structure of bones, which determines vertebrate morphology. However, the external shape of bones may be reproduced through topology optimization because cells of the same type form both the internal and external structures of bones. Here, we constructed a three-dimensional topology optimization model to attempt the reproduction of the external shape of teleost vertebrae. In teleosts, the internal structure of the vertebral bodies is invariable, exhibiting an hourglass shape, whereas the lateral structure supporting the internal structure differs among species. Based on the anatomical observations, we applied different external loads to the hourglass-shaped part. The simulations produced a variety of three-dimensional structures, some of which exhibited several structural features similar to those of actual teleost vertebrae. In addition, by adjusting the geometric parameters, such as the width of the hourglass shape, we reproduced the variation in the teleost vertebrae shapes. These results suggest that a simulation using topology optimization can successfully reproduce the external shapes of teleost vertebrae. By applying our topology optimization model to various bones of vertebrates, we can understand how the external shape of bones adapts to external loads.

This paper deals with a micro mobile robot in water utilizing a PZT(Pb(Zr,Ti)O/sub 3/) as an actuator. A robot driven by a PZT requires a magnification mechanism and the effects of the resonance to enlarge the displacement of the PZT. In this paper, the authors propose a prototype micro mobile robot which has a new steering mechanism. The robot possesses a pair of legs and each leg has a pair of fins with some angle, which is essential to the improvement of the robot performance. A leg generates force both forward and backward according to frequency because the offset angle between a pair of fins works properly. Therefore, the robot can steer efficiently by combination of both modes. The size of the robot is 32 mm in length and 19 mm in width. This robot has many possible applications, such as small pipelines inspection and use in biomedical fields.

This paper deals with a micro-mobile robot in water utilizing PZT(Pb(Zr, Ti)O/sub 3/) as an actuator. A robot driven by PZT requires a magnification mechanism and the effects of the resonance condition to enlarge the displacement of the PZT to some extent. In this paper, we show a prototype micro-mobile robot in water (double-fin-fish robot), which possesses a pair of fins and moves them symmetrically. Therefore, the momentum of this robot is canceled and the tendency to move straight ahead is improved. The size of the robot is 50 mm in length. We propose a structure for the magnification mechanism, which is made by the wire cut method. The magnification ratio is 326 geometrically. This robot has many possible applications, such as small pipeline inspections and biomedical fields.>