We present Shape Non-rigid Kinematics (SNK), a novel zero-shot method for non-rigid shape matching that eliminates the need for extensive training or ground truth data. SNK operates on a single pair of shapes, and employs a reconstructionbased strategy using an encoder-decoder architecture, which deforms the source shape to closely match the target shape. During the process, an unsupervised functional map is predicted and converted into a point-to-point map, serving as a supervisory mechanism for the reconstruction. To aid in training, we have designed a new decoder architecture that generates smooth, realistic deformations. SNK demonstrates competitive results on traditional benchmarks, simplifying the shapematching process without compromising accuracy. Our code can be found online: https://github.com/pvnieo/SNK.

Multilayer-perceptrons (MLP) are known to struggle with learning functions of high-frequencies, and in particular cases with wide frequency bands. We present a spatially adaptive progressive encoding (SAPE) scheme for input signals of MLP networks, which enables them to better fit a wide range of frequencies without sacrificing training stability or requiring any domain specific preprocessing. SAPE gradually unmasks signal components with increasing frequencies as a function of time and space. The progressive exposure of frequencies is monitored by a feedback loop throughout the neural optimization process, allowing changes to propagate at different rates among local spatial portions of the signal space. We demonstrate the advantage of SAPE on a variety of domains and applications, including regression of low dimensional signals and images, representation learning of occupancy networks, and a geometric task of mesh transfer between 3D shapes.

To better distill pose information from the object's geometry, we propose the implicit pose applier to output an intrinsic mesh property, the face Jacobian. Once the extracted pose information is transferred to the target object, the pose applier is fine-tuned in a self-supervised manner to better describe the target object's shapes with pose

Coordination of movement and configuration in robotic swarms is a challenging endeavor. Deciding when and where each individual robot must move is a computationally complex problem. The challenge is further exacerbated by difficulties inherent to physical systems, such as measurement error and control dynamics. Thus, how to best determine the optimal path for each robot, when moving from one configuration to another, and how to best perform such determination and effect corresponding motion remains an open problem. In this paper, we show an algorithm for such coordination of robotic swarms. Our methods allow seamless transition from one configuration to another, leveraging geometric formulations that are mapped to the physical domain through appropriate control, localization, and mapping techniques. This paves the way for novel applications of robotic swarms by enabling more sophisticated distributed behaviors.

Mean-shift-based approaches have recently emerged as the most effective methods for robot swarm shape assembly tasks. These methods rely on image-based representations of target shapes to compute local density gradients and perform mean-shift exploration, which constitute their core mechanism. However, such image representations incur substantial memory overhead, which can become prohibitive for high-resolution or 3D shapes. To overcome this limitation, we propose a memory-efficient tree map representation that hierarchically encodes user-specified shapes and is applicable to both 2D and 3D scenarios. Building on this representation, we design a behavior-based distributed controller that enables assignment-free shape assembly. Comparative 2D and 3D simulations against a state-of-the-art mean-shift algorithm demonstrate one to two orders of magnitude lower memory usage and two to three times faster shape entry while maintaining comparable uniformity. Finally, we validate the framework through physical experiments with 6 to 7 UAVs, confirming its real-world practicality.

We present a decentralized model for autonomous reconfiguration of homogeneous pivoting cube modular robots in two dimensions. Each cube in the ensemble is controlled by a neural network that only gains information from other cubes in its local neighborhood, trained using reinforcement learning. Furthermore, using geometric deep learning, we include the grid symmetries of the cube ensemble in the neural network architecture. We find that even the most localized versions succeed in reconfiguring to the target shape, although reconfiguration happens faster the more information about the whole ensemble is available to individual cubes. Near-optimal reconfiguration is achieved with only nearest neighbor interactions by using multiple information passing between cubes, allowing them to accumulate more global information about the ensemble. Compared to standard neural network architectures, using geometric deep learning approaches provided only minor benefits. Overall, we successfully demonstrate mostly local control of a modular self-assembling system, which is transferable to other space-relevant systems with different action spaces, such as sliding cube modular robots and CubeSat swarms.

Different from most of the formation strategies where robots require unique labels to identify topological neighbors to satisfy the predefined shape constraints, we here study the problem of identity-less distributed shape formation in homogeneous swarms, which is rarely studied in the literature. The absence of identities creates a unique challenge: how to design appropriate target formations and local behaviors that are suitable for identity-less formation shape control. To address this challenge, we propose the following novel results. First, to avoid using unique identities, we propose a dynamic formation description method and solve the formation consensus of robots in a locally distributed manner. Second, to handle identity-less distributed formations, we propose a fully distributed control law for homogeneous swarms based on locally sensed information. While the existing methods are applicable to simple cases where the target formation is stationary, ours can tackle more general maneuvering formations such as translation, rotation, or even shape deformation. Both numerical simulation and flight experiment are presented to verify the effectiveness and robustness of our proposed formation strategy.